TWI813693B - Multi-band color vision filters and method by lp-optimization - Google Patents

Abstract

The invention generally relates to optical filters that provide regulation and/or enhancement of chromatic and luminous aspects of the color appearance of light to human vision, generally to applications of such optical filters, to therapeutic applications of such optical filters, to industrial and safety applications of such optical filters when incorporated, for example, in radiation-protective eyewear, to methods of designing such optical filters, to methods of manufacturing such optical filters, and to designs and methods of incorporating such optical filters into apparatus including, for example, eyewear and illuminants.

Description

Multi-band color filters and optimization methods using linear programming

The present invention generally relates to: optical filters that provide modulation and/or enhancement of the chromatic and luminescent aspects of color appearance of light to human vision; the use of such optical filters; such optical filters Applications of optical devices in ophthalmic lenses; therapeutic applications of such optical filters; industrial and safety applications of such optical filters for incorporation into radiation-protective glasses; methods of designing such optical filters ; Methods of making such optical filters; and designs and methods of incorporating these optical filters into devices including, for example, eyeglasses and illuminators.

Optical filters with wavelength-selective transmission acting on a light source or light receiver can change the appearance of color. Optical filters that improve color vision may provide therapeutic benefits for people with color vision deficiencies. Optical filters protect the eyes from high-energy radiation in the ultraviolet, visible and/or infrared spectrum. Devices incorporating optical filters include eyeglasses, windows, and illuminators.

Disclosed herein is a filter production method for designing optical filters that, for example, provide enhancement and/or modulation of color appearance relative to human color perception. Optical filter designs produced by this method may serve as the basis for fabrication specifications for fabricating such optical filters as, for example, interference filters by, for example, physical vapor deposition of multiple layers of dielectric materials onto an optical substrate. The interference filter may further include an absorptive metallic material layer. For example, these metal attenuating coatings can be produced by physical vapor deposition. The optical substrate may be transparent or may incorporate absorptive, photochromic or polarizing filtering materials by doping the substrate with these materials, laminating these materials between multiple substrates, or by Such materials are coated on one or both sides of the substrate to achieve the incorporation. The refractive index of the boundary surfaces both inside and outside the assembly can be matched to reduce transmission losses and generally improve the optical quality of the assembled filter, for example by incorporating appropriate anti-reflective filters. Such filters may, for example, be incorporated into eyewear, such as eyepieces, sunglasses, eyecups, monocles, safety glasses, contact lenses or any other suitable ophthalmic lens, or may be incorporated into a lighting body, such as a lamp assembly )middle. An eye lens is a lens for eyes. An ophthalmic lens may provide optical (focus) correction to the eye, or it may have zero diopter and provide no such correction. Eyepieces (such as sunglasses) and contact lenses are examples of ophthalmic lenses. In one aspect, a computer-implemented method for designing an optical filter that affects color vision in a desired manner includes using a computer to solve a linear equation given by: minimizing c ^T x , subject to the constraint of Ax ≤ b, and subject to the constraint of 1 ≥ x ≥ 0; where, in this method, the linear equation of the vector x is solved and the transmittance of the filter as a function of wavelength Calculated by the following expression: Assume , and assuming p, then ,and ; Among them, in this method, f is the designed optical filter, is the transmittance of f as a function of wavelength λ, E is a matrix of basic filters such that the behavior of matrix e _i is the transmittance of light as a function of the wavelength of each basic filter, and the number of basic filters is N. definition The expression of is a weighted summation of one of the basic filters, where the weighting coefficient is the corresponding element xi. The weighted sum is equal to the matrix-vector product expression q=Ex between the basic filter matrix E and the linear program solution vector x. also, The combined series of two optical filters is represented by the multiplication of the first filter q and the second filter p as a function of wavelength, where is the transmittance of p as a function of wavelength λ, and p is generally referred to as a "pre-filter" in the present invention, but component filters can generally be composed in any order. The linear program constraint 1≥x≥0 is equivalent to the constraint 1≥x _i≥0 , where i ranges from 1 to N. Furthermore, c in the above expression is a cost vector that guides the linear program solver toward a solution that provides a filter f that affects color vision in a desired manner. Calculate the total cost associated with the solution by ^{c T} x, which represents the vector inner product between the transpose of c and x. Providing a lower total cost solution is generally better relative to the filter's desired function (eg, color discrimination enhancement), but other measures of quality can also be used to determine the appropriateness of a particular solution. A in the above expression is a matrix and b in the above expression is a vector. Ax is the matrix product between matrix A and vector x. At least some of the elements of matrix A and at least some of the elements of vector b are related to: the minimum or maximum transmission level of filter f at one or more wavelengths of light; to one of the white points of the filter Constraints; or constraints on the color appearance of one or more reference lights (as viewed or illuminated through the filter); and/or constraints on the transmission of the filter f at one or more angles of incidence. The above expression as a function of wavelength λ can be tabulated by sampling uniformly on one wavelength scale (e.g., using steps of 1 nanometer) or another substantially equivalent scale (e.g., frequency or log wavenumber). Specifications of the transmittance of the filter ( _ei , p, f). Sampling can also be defined at any scale with uneven spacing between sample points. The optical filter f designed by the method (which can essentially be described as a multi-band filter) has a spectral transmittance, where a multi-band filter is a plurality of passbands interleaved with the stopband. Specifically, a filter used to affect color vision has three or more passbands separated by two or more stopbands, each stopband and each passband having a center and a width, wherein the The center is located between about 400 nanometers and about 700 nanometers in the visible spectrum, and the width can range between about 10 nanometers and about 110 nanometers. A lower band boundary is defined as the center minus half the width, and a band upper boundary is defined as the center plus half the width. The average transmittance of a frequency band is the average spectral transmittance of light within the boundaries of those frequency bands. The staggered stopbands share upper and lower boundaries and the complementary boundaries of adjacent passbands. A multiband filter is characterized by a minimum contrast ratio relative to the average transmission of the stopband and its adjacent passbands. For example, a multiband filter may comply with a lower limit on the contrast ratio such that each staggered stopband has an average transmission less than or equal to, for example, half the average transmission of an adjacent passband. A further feature of a multi-band filter is compliance with an upper limit on the contrast ratio such that some embodiments of the multi-band filter may be expected to be used with color vision. Filters incorporated into devices such as ophthalmic lenses are further characterized by a light transmittance defined as the average spectral transmittance of light transmitted through the filter weighted by the CIE 1924 photoluminescence function. Filters used in ophthalmic lenses, such as sunglasses, typically have a light transmission of at least 8%. In addition, the filter white point is defined as the chromaticity coordinate of average daylight (i.e., illuminant D65) in a suitable color space, where a (u', v') chromaticity coordinate means one in the CIELUV color space Position and an (x,y) chromaticity coordinate refer to a position in the CIE xyY color space. The white point of a filter subjectively corresponds to the apparent tint that the filter exerts on the field of view, with a white point described as neutral applying a small amount of this tint. In some variations, the filter passband is essentially rectangular, that is, the change in transmittance as a function of wavelength within the band boundaries is instantaneous or nearly instantaneous. The width of a rectangular passband is characterized by the distance between the short wavelength boundary and the long wavelength boundary. Rectangular bandwidth can be measured equivalently on a frequency scale. In some variations, the filter passband is Gaussian in nature, that is, the transmission as a function of wavelength changes gradually or essentially smoothly within the band boundaries. The width of a Gaussian band is characterized by the distance between the half-peak transmittance at the short-wavelength boundary and the half-peak transmittance at the long-wavelength boundary (also known as the full width at half maximum (FWHM)). The half-peak bandwidth can be measured equivalently on a frequency scale. In some variations, one or more of the passbands may have an irregular shape (ie, non-rectangular and non-Gaussian). For example, the passband may have a bimodal distribution, or may have a shoulder on one or more sides of the passband, or may be described as a skewed distribution, where in transmittance as a function of wavelength, The slope ratio between the two sides of the passband is between about 4:1 and about 1:4. In a variation on non-Gaussian bands, such passbands can be smoothed using, for example, a Gaussian kernel of just enough width to essentially eliminate irregularities and/or sharp transitions, in which case the passbands can be described as Essentially, it has a band center and half-peak width corresponding to a smooth passband. The basic filter may be, for example, a single passband filter with a passband width of about 1 nanometer, and each basic filter has a different passband center wavelength. These filters may also be called monochromatic filters and are defined as having the following spectral transmittance: ; in is the Dirac-delta function and is the wavelength transmitted by the filter, which typically ranges from about 400 nanometers to about 700 nanometers for a complete set of basic filters, and the number of such basic filters in the set is about 300. Alternatively, the base filters may be single passband filters each having a width greater than about 1 nanometer, with each base filter having a different passband center wavelength. In some of these variations, the passband can be rectangular (also called a square pulse function) and the spectral transmittance of a basic filter is defined as follows: ; in is the central wavelength, is the rectangular bandwidth, and H is the Heaviside step function. In such variations, the passband may have a width of, for example, about 10 nanometers and the band position may vary, for example, in steps of about 5 nanometers, between about 400 nanometers and about 700 nanometers, such that these basic filters The number of vessels is, for example, approximately 60. In some variations, the passband may have a Gaussian or a spectral transmittance that is Gaussian in nature, such as having a spectral transmittance defined as follows: ; in is the center wavelength, and the half-peak bandwidth is: , in is an exponential function, is the square root function, and is the natural logarithm. In other variations, the basic filter can be a multi-band filter with two or more passbands, and each basic filter has the center position and/or bandwidth of two or more passbands. a different combination. Any suitable set of basic filters can be used in the filter design method. For example, the cost vector c may be selected to direct the linear program solver toward a filter that improves color discrimination. In some variations, the cost vector is selected to enhance discrimination between red and green by increasing their apparent color purity. These red-green enhancement filters can also increase the apparent purity of blue and thus can generally be described as enhancing color discrimination. Alternatively, the cost vector may be selected to enhance discrimination between blue and yellow by increasing their apparent color purity. These blue-yellow enhancing filters may also tend to reduce the apparent purity of red and green colors. Additionally or alternatively, the cost vector may be selected to reduce transmission of short wavelength blue light between about 380 nanometers and about 450 nanometers. Additionally or alternatively, the cost vector may be selected to increase transmission of short wavelength cyan light between about 450 nanometers and about 500 nanometers. Any suitable cost vector can be used in the filter design method. In some variations, the elements of the cost vector c and/or A and b may be selected such that the discrimination of color provided by the filter is normal (i.e., the color appearance is substantially the same as that provided by a neutral density filter color appearance). In some variations, the filter design method includes solving a linear program to generate a test filter f and then evaluating the test filter according to performance criteria, manufacturing criteria, or both performance and manufacturing criteria. Some of these changes may also include adjusting matrix A, vector b, cost vector c, basic filter matrix E, pre-filter p, or any combination of the above and then solving the linear program expression again to provide another Experiment with filters. The cost vector c can be adjusted, for example, to further improve color discrimination (ie, color discrimination of a test filter compared to a current test filter). Evaluating the performance of a filter may include assessing the effect of the filter on color discrimination by determining a first contour by calculating the area enclosed by a first contour in a chromaticity plane in a color space. The area of a color gamut in which the first contour corresponds to the appearance of a set of reference colors viewed or illuminated by an observer through a test filter; by calculating the area bounded by a second contour in a chromaticity plane in a color space determine a second color gamut area by enclosing the area, wherein the second contour corresponds to the appearance of the set of reference colors viewed by or illuminated by the observer through a reference filter; and comparing the first color gamut area with the The second color gamut area. Alternatively or additionally, assessing the performance of a filter may include assessing the effect of the filter on color discrimination by determining one of the first distributions projected onto an axis in a chromaticity plane in a color space A first standard deviation, wherein the first distribution corresponds to the appearance of a set of reference colors viewed or illuminated by an observer through a test filter; determining one of the axes projected onto the chromaticity plane in the color space a second standard deviation of a second distribution, wherein the second distribution corresponds to the appearance of the set of reference colors to an observer as viewed through or illuminated by a reference filter; and comparing the first standard deviation to the second standard deviation. The axes useful for analysis include those defined by the protanopia confusion line, the deuteranopia confusion line, and the type III color blindness confusion line. In some variations, evaluating filter performance may include taking an average or a weighted average of the filter's performance over a range of angles of incidence away from normal incidence. The angular range may be, for example, between about 0 degrees and at least about 20 degrees or, for example, between about 0 degrees and at least about 30 degrees. In some variations, the color to be adjusted and/or enhanced by the filter is specified by the spectral reflectance of the color sample from the Munsell Color Encyclopedia. In some variations, as an alternative to or in addition to samples from the Munsell Color Encyclopedia, the spectral reflectance of color masks from Farnsworth D-15 is specified to be adjusted and/or enhanced by filters. color. In some variations, as an alternative to or in addition to samples from the Munsell Color Encyclopedia, the spectral reflectance of natural objects including, for example, leaves and flowers is specified to be adjusted and/or enhanced by filters. color. In some variations, at least some of the elements of matrix A and vector b in the above linear programming expression are related to: constraints on the appearance of a blue, red, green, or yellow traffic signal, as viewed through a light filter . These constraints may be based on, for example, industry or regulatory standards, and may, for example, require that traffic light colors fall within certain chromaticity and luminescence boundaries when viewed through a filter. Methods can provide a filter that satisfies these constraints and improves color discrimination or otherwise enhances color appearance. In some variations, at least some of the elements of matrix A and vector b in the above linear expression are related to constraints that provide stability of color appearance relative to changes in the angle of incidence of light on the filter. , as viewed through a filter or illuminated. The stability is provided by the configuration of the constraints such that the white point of the designed filter is constant or substantially constant at two or more angles of incidence. In addition, in these variations, the filter f may include a composition of an absorption pre-filter p and an interference filter q, where the change in transmittance of p as a function of the incident angle is According to Beer-Lambert's law and the change of transmittance of Ex as a function of incident angle is based on Snell's law, so that the transmittance of f at an incident angle of θ radians deviating from the surface normal vector can be expressed as And it is approximately represented by the following expression: ; where the effective reflectivity of _ei has a value of n with a value of about 1.85, and for θ between about 0 degrees and about 45 degrees, this approximation is sufficient. In some variations, at least some of the elements of matrix A and vector b in the above linear expression are related to constraints on the filter's transmission of blue light between about 380 nanometers and about 450 nanometers, such as Minimize this transmission. In some variations, at least some of the elements of matrix A and vector b in the above expressions relate to constraints on a minimum transmission specified by the filter between about 450 nanometers and about 650 nanometers. In some variations, at least some of the elements of matrix A and vector b in the above expressions relate to constraints on a minimum transmission specified by the filter between about 580 nanometers and about 620 nanometers. In some variations, at least some of the elements of matrix A and vector b in the above expressions relate to: for an electronic visual display, such as a liquid crystal display (LCD) with a light emitting diode (LED) backlight. ) constraint on the light transmission of emitted primary color light. In some variations, at least some of the elements of matrix A and vector b in the above expressions are related to normal colors over a range of incident angles on a filter combined with, for example, between about 0 degrees and about 30 degrees. Distinguish and stabilize color appearance to protect the eye from radiation constraints from a visible laser, such as a frequency-double Nd:YAG laser (which has laser output power at 532 nanometers and 1064 nanometers). In some variations, at least some of the elements of matrix A and vector b in the above expressions relate to: stable colors over a range of incident angles on a filter combining, for example, between about 0 degrees and about 30 degrees Appearance to protect the eye from radiation from a sodium illuminator (with concentrated power at approximately 589 nanometers). In some variations, at least some of the elements of matrix A and vector b in the above expressions relate to: constraints on providing a selected illuminant, the color of that illuminant as viewed after transmission through the filter The appearance matches the color appearance of the illuminant as viewed after reflection by the filter, and wherein the filtered illuminant transmitted by the filter provides enhanced discrimination of the selected reference color, and wherein the filtered illuminant is not transmitted by the filter Part of the light is reflected by the filter. In another aspect, the linear formula in the method summarized above is replaced by an equivalent numerical optimization procedure. In such variations, the equivalent procedure may include tabulating all combinations of band positions and bandwidths within a range of possible values; then evaluating each multi-band filter against constraint criteria and performance criteria; and then selecting through a filter subset of the constraint criteria; and then selecting the best performing filter in the subset as the test filter. Such changes may further include evaluating test filters against performance criteria, manufacturing criteria, or both performance and manufacturing criteria. Some of these changes may also include: adjusting the constraint criteria, the performance criteria, or any combination of the above; and then performing the numerical optimization procedure again to provide another test filter. The constraint criteria or performance criteria can be adjusted, for example, to further improve color discrimination (ie, color discrimination of a test filter compared to a current test filter). In another aspect, a computer-implemented method for evaluating the effect on color vision of a test filter includes using a computer; by computing a first profile in a chromaticity plane in a color space A first color gamut area is determined by enclosing an area corresponding to the appearance of a set of reference colors viewed or illuminated by an observer through the test filter; by calculating A second color gamut area is determined by the area enclosed by a second contour in a chromaticity plane, where the second contour corresponds to the appearance of the set of reference colors as viewed by or illuminated by the observer through a reference filter; and comparing the first color gamut area and the second color gamut area. In some variations, evaluating filter performance may include using an average or a weighted average of the color gamut area provided by the filter over a range of incidence angles away from normal incidence. The angular range may be, for example, from 0 degrees to at least about 20 degrees. In some of these variations, the importance weighting function is derived by estimating the likelihood that the filter is viewed at a specific angle based on a geometric model of the human eye and that the filter is located on the surface of a typical eyeglass frame. . In some variations, comparing the first color gamut area to the second color gamut area includes using a ratio of the first color gamut area to the second color gamut area. In some variations, at least some of the reference colors are selected from Munsell colors. Alternatively or additionally, at least some of the reference colors are selected from Farnsworth D-15. Alternatively or additionally, at least some of the reference colors are selected from colors present in the environment in which the test filter will be used to affect color vision. In the latter case, in some variations, at least some of the reference colors are selected from colors that naturally occur in an outdoor environment. In some variations, the reference color is selected to form a contour of medium saturation around the white point in the chromaticity plane. Additionally or alternatively, the reference color is selected to form a highly saturated contour around the white point in the chromaticity plane. For example, the reference filter may be selected to have a broadband transmission. In some variations, the reference filter is selected to have the same white point as the test filter relative to a selected illuminant (eg, relative to daylight). In some variations, the Munsell color, one of the best-fit test filters, is used to define the reference filter, where the measured spectral reflectance of the Munsell color sample is defined as the spectral transmittance of the reference filter. In another aspect, a computer-implemented method for evaluating the effect on color vision of a test filter includes using a computer; determining a first projection onto an axis of a chromaticity plane in a color space. a first standard deviation of a distribution corresponding to the appearance of a set of reference colors viewed by or illuminated by an observer through the test filter; determining the chromaticity plane along the chromaticity plane in the color space a second standard deviation of a second distribution of an axial projection, wherein the second distribution corresponds to the appearance of the set of reference colors to an observer viewing or illuminating through a reference filter; comparing the first standard deviation with the Second standard deviation. In some variations, the axes are defined as red blind confusion lines. In some variations, the axis is defined as the deuteranopia confusion line. In some variations, the axis is defined as the line of confusion for type 3 color blindness. In some variations, evaluating filter performance may include taking an average or a weighted average of the standard deviations of the distribution provided by the filter over a range of incidence angles away from normal incidence. The angular range may be, for example, from about 0 degrees to at least about 20 degrees. In some of these variations, the importance weighting function is derived by estimating the likelihood that the filter is viewed at a specific angle based on a geometric model of the human eye and that the filter is located on the surface of a typical eyeglass frame. . In some variations, comparing the first standard deviation to the second standard deviation includes taking a ratio of the first standard deviation to the second standard deviation. In some variations, at least some of the reference colors are selected from Munsell colors. Alternatively or additionally, at least some of the reference colors are selected from Farnsworth D-15. Alternatively or additionally, at least some of the reference colors are selected from colors present in the environment in which the test filter will be used to affect color vision. In the latter case, in some variations, at least some of the reference colors are selected from colors that naturally occur in an outdoor environment. In some variations, the reference color is selected to form a contour of medium saturation around the white point in the chromaticity plane. Additionally or alternatively, the reference color is selected to form a highly saturated contour around the white point in the chromaticity plane. For example, the reference filter may be selected to have a broadband transmission. In some variations, the reference filter is selected to have the same white point as the test filter relative to a selected illuminant (eg, daylight). In some variations, one of the Munsell colors that best fits the test filter is used to define the reference filter, where the measured spectral reflectance of the Munsell color sample is defined as the spectral transmittance of the reference filter. In another aspect, a multi-band filter for affecting color vision includes a first, second and third passband separated by two stopbands. The passbands and the stopbands are configured to enable enhanced color discrimination by a normal observer (e.g., evaluation of the filter's functional performance may consider the filter's color response to an observer relative to the CIE 1931 2-degree standard sleep effect). The first passband has a center between about 435 nanometers and about 465 nanometers, the second passband has a center between about 525 nanometers and about 555 nanometers, and the third passband Having a center located between about 610 nanometers and about 660 nanometers. The width of each of the passbands is between about 20 nanometers and about 80 nanometers, and the width of each of the stopbands is at least about 40 nanometers. In some variations, the passband is configured (e.g., appropriately positioned and/or shaped) such that the filter provides stable color for incident angles between about 0 degrees and at least about 30 degrees that deviate from the surface normal vector Appearance such that, for all or nearly all such angles of incidence, the white point of average sunlight is contained in the CIELUV(u',v') color space and has a radius of approximately 0.02 units for an observer based on the CIE 1931 2-degree standard in one area. In some such variations, this area has a radius of approximately 0.01 units. In a further variation, the CIE 1964 10-degree standard observer may be used to calculate chromaticity coordinates in addition to or as an alternative to the CIE 1931 2-degree standard observer. In some variations, the passband is configured such that the filter provides a stable color appearance for angles of incidence between about 0 degrees and at least about 30 degrees that deviate from the surface normal vector, such that for all or nearly all such incidences angle, the white point of average sunlight is contained in an area with a radius of approximately 0.02 units on the CIELUV(u',v')1964 2-degree standard observer chromaticity scale. In some such variations, this area has a radius of approximately 0.01 units. In some variations, multi-band filters are configured to enhance blue-yellow discrimination. In such variations, the first passband has a center located between about 450 nanometers and about 475 nanometers, the second passband has a center located between about 545 nanometers and about 580 nanometers, and the The tee strip has a center located between about 650 nanometers and about 690 nanometers. In each of these variations, the passband width ranges from about 20 nanometers to about 60 nanometers. In some such variations, the filter is configured to provide a green traffic signal as defined by industry standard ANSI Z80.3-2010 that is desaturated or nearly desaturated (as permitted by that standard). A chromaticity coordinate. In some variations, the multi-band filter has a light transmission of between about 8% and about 40%, and the bands are configured such that the filter is considered "non-extruding" according to industry standard ANSI Z80.3-2010 color". In some variations, the multiband filter is configured so that the white point of the filter is neutral or nearly neutral, allowing the filter to provide the same performance as per industry standard ANSI Z80.3-2010, Section 4.6.3.1. Any point on the boundary of the defined average daylight color restriction area is at least approximately 0.05 units apart from one (x, y) chromaticity coordinate. In a further variation, the filter is configured so that the white point is at or nearly located on the average daylight color limit area. In some variations, the stopband has a minimum transmission of about one-fifth of the optical transmission. The minimum transmittance is the lowest value of the spectral transmittance within the boundaries of the stop band. In some variations, the optical filter is configured to enhance color discrimination and suppress short wavelength light below at least about 440 nanometers. In such variations, the first passband has a center located between about 450 nanometers and about 470 nanometers and has a width between about 10 nanometers and about 40 nanometers, and the second passband has a center located between about 545 nanometers and about 545 nanometers. The third passband has a center between about 630 nanometers and about 675 nanometers and a width between about 30 nanometers and about 60 nanometers. One width between nanometers and about 90 nanometers. In some such variations, the filter has a light transmission between about 20% and about 35%. In some of these variations, the percentage increase in gamut area relative to the Farnsworth D-15 color is greater than zero for angles between 0 degrees and at least about 25 degrees. In some such variations where the white point is neutral, the importance weighted percentage increase in gamut area relative to the Farnsworth D-15 color may be at least 20%. In some variations, the multi-band filter has a light transmission between about 8% and about 40%, and the bands are configured such that the white point of the filter is at or nearly located as defined in accordance with industry standard ANSI Z80.3 -2010 is considered to be at the limit of a filter that does not produce strong colors. In some variations, the filter is made by incorporating a neutral density absorption filter and an interference filter. In some variations, the spectral transmittance of the interference filter is significantly smoothed and the interference filter includes less than about 50 layers of dielectric material and/or has a total thickness of less than about 3 microns. In a further variation, the filter is fabricated by incorporating a neodymium-containing substrate and the interference filter. The optical filter may further include a neutral density filter. In some variations, the neutral density absorbing filter includes a metallic attenuating coating that can be incorporated into a layer of the interference filter. Because neutral density filters have a generally flat spectral transmittance, a filter configured for use with a neutral density filter can be composed of a number of essentially equivalent options. For example, a circularly polarizing filter can be replaced with a metallic attenuating coating to achieve a filter with the same or nearly the same spectral transmittance. If appropriate, any of the above modified filters may be incorporated into the glasses. Such eyewear may include, for example, eyepieces (eg, sunglasses), goggles, contact lenses, or any other suitable ophthalmic lens. In another aspect, a multi-band filter for affecting color vision includes a first, second and third passband separated by two stopbands. The passbands and the configurations are configured to provide normal color discrimination and suppress short wavelengths below approximately 450 nanometers. In some variations, the filter has three passbands, a first passband having a center wavelength of about 465 nanometers and a half-maximum width of about 20 nanometers, and a first stopband having a minimum transmittance of about 14%, The second passband has a center wavelength of about 550 nanometers and a half-maximum width of about 40 nanometers, the second stopband has a minimum transmittance of about 50% between about 580 nanometers and about 610 nanometers, and The third passband has a center wavelength of approximately 660 nanometers and a half-maximum width of approximately 80 nanometers. In some variations, the filter has four passbands, a first passband having a center wavelength of about 465 nanometers and a half-maximum width of about 20 nanometers, and a first stopband having a minimum transmission of about 17% , the second passband has a center wavelength of about 550 nanometers and a half-maximum width of about 35 nanometers, the second stopband is located at about 560 nanometers and has a minimum transmittance of about 40%, and the third passband is located at is at about 595 nanometers and has a half-maximum width of about 35 nanometers, and the fourth passband is located at about 660 nanometers and has a half-maximum width of about 80 nanometers. In some variations, the passband is positioned and/or shaped such that the filter provides a stable color appearance for angles of incidence between about 0 degrees and about 40 degrees that deviate from the surface normal vector, such that for all or nearly all For these angles of incidence, the (u', v') chromaticity coordinates of average sunlight are contained in one of approximately 0.01 units of the observer's chromaticity (u', v') scale according to the CIELUV color space 1931 2-degree standard. within a radius area. In some variations, the percentage increase in gamut area relative to the Farnsworth D-15 color is greater than zero for angles between 0 degrees and at least about 25 degrees. In some variations, the white point was neutral and the importance-weighted percentage relative to the gamut area increase of the Farnsworth D-15 ranged from about 0% to about 10%. In some variations, the multi-band filter has a light transmission between about 8% and about 40%, and the bands are configured such that the white point of the filter is at or nearly located as defined in accordance with industry standard ANSI Z80.3 -2010 is considered to be at the limit of a filter that does not produce strong colors. In some variations, the filter is made by incorporating a neutral density absorption filter and an interference filter. In some such variations, the neutral density absorbing filter is a linear polarizer. In a further variation, the filter was made without an absorbing element. In some variations, the filter is fabricated by depositing an interference filter onto a photochromic substrate. If appropriate, any of the above modified filters may be incorporated into the glasses. Such eyewear may include, for example, eyepieces (eg, sunglasses), goggles, contact lenses, or any other suitable ophthalmic lens. In another aspect, a multi-band filter for affecting color vision includes a first, second and third passband separated by two stopbands. The passbands and the stopbands are configured to enhance red-green discrimination for an observer with red-green color vision deficiency. Accordingly, the evaluation of a filter's performance metric can take into account the physiological characteristics of the observer. The first passband has a center wavelength between about 440 nanometers and about 455 nanometers, the second passband has a center wavelength between about 530 nanometers and about 545 nanometers, and the third passband Having a center wavelength between about 610 nanometers and about 640 nanometers. The width of each of the passbands is between about 10 nanometers and about 60 nanometers, and the width of each of the stopbands is at least about 40 nanometers, which may vary depending on the desired light transmittance and whiteness of the filter. Click Hue to select the width of these bands. In some variations, the passband is positioned and/or shaped such that the filter provides a stable color appearance for angles of incidence between about 0 degrees and about 30 degrees that deviate from the surface normal vector, such that for all or nearly all At these angles of incidence, the white point of sunlight is contained in an area with a radius of approximately 0.02 units on the CIELUV 1931 2-degree standard observer chromaticity (u', v') scale. In some variations, the passband is positioned and/or shaped such that the filter provides a stable color appearance for angles of incidence between about 0 degrees and about 35 degrees that deviate from the surface normal vector, such that for all or nearly all At these angles of incidence, the white point of sunlight is contained in an area with a radius of approximately 0.04 units on the CIELUV 1931 2-degree standard observer chromaticity (u', v') scale. In some variations, the passband is positioned and/or shaped such that the filter provides a stable color appearance such that the white point is displaced from its position at an angle of incidence of 0 degrees by an incident angle dependent distance of between about 20 degrees at an incident angle to about 40 degrees. There is a local minimum at an angle between degrees of incidence, where the white point displacement at the local minimum is less than 0.02 units of the CIELUV 1931 2-degree standard observer chromaticity (u', v') scale. In some variations, the passband is positioned and/or shaped such that the filter provides a stable color appearance such that the white point is displaced from its 0 degree incident angle position by an incident angle dependence distance of between about 20 degrees and about 40 degrees. There is a local minimum at an angle between them, where the white point displacement at the local minimum is less than 0.01 units of the observer chromaticity (u', v') scale according to the CIELUV 1931 2-degree standard. In some variations, the multi-band filter has a light transmission between about 8% and about 40%, and the bands are configured such that the filter is considered non-transmissive according to industry standard ANSI Z80.3-2010. Powerful color. In some variations, the multi-band filter has a light transmission between about 8% and about 40%, and the bands are configured such that the white point of the filter is neutral or nearly neutral, such that the white point The (x, y) chromaticity coordinates fall within approximately 0.05 units of (0.31, 0.33) relative to the illuminant D65 and in accordance with the CIE xyY 1931 2-degree standard observer color space. In some variations, the stop band has a minimum transmission of about one-fifth of the light transmission between about 450 nanometers and about 650 nanometers. In some variations, the stop band has a minimum transmission of about one-fifth of the light transmission between about 580 nanometers and about 650 nanometers. In some variations, one or more of the passbands has a skewed distribution in which the slope ratio between two sides of the passband in transmittance as a function of wavelength is between 4:1 and 1:4 . In some variations, one or more of the passbands have an irregular distribution, where the passbands can be described as having essentially a shoulder on one or both sides of the passbands. In some variations, one or more of the passbands has a bimodal distribution, in which the center wavelengths of two modes are within +/- 10% and the distributions around the modes partially overlap. This configuration can also be described as dividing the passband into adjacent partially overlapping sub-bands. In some variations, the first passband has a bimodal distribution with a first mode at about 435 nanometers and a second mode at about 455 nanometers. In such variations, the peak transmittance of the first mode may be equal to or greater than the peak transmittance of the second mode. In some variations, the filter is configured relative to an angle of incidence in which the second passband center wavelength is between about 525 nanometers and about 535 nanometers, as defined by industry standard ANSI Z80.3-2010 A yellow traffic signal that is reddish or almost reddish (as permitted by the standard) provides a chromaticity coordinate. In some variations, the optical filter is configured to enhance red-green discrimination for an observer with a greenish color. In a preferred variation, the third passband has a center wavelength between about 620 nanometers and about 640 nanometers. In some such variations, the first passband has a center at about 445 nanometers, the second passband has a center wavelength at about 535 nanometers, and the third passband has a center wavelength at about 635 nanometers. . In some variations, the filter is configured to enhance red-green discrimination for an observer with mild green tint. In some of these variations, the white point is neutral and the importance-weighted percentage increase relative to the gamut area of the Farnsworth D-15 color is at least about 30%. In further such changes, the percentage increase in gamut area relative to the Farnsworth D-15 color is greater than zero for angles between 0 degrees and at least about 25 degrees. In some variations, the filter is configured to enhance red-green discrimination for an observer with moderate green tint. In some of these variations, the white point is neutral and the importance-weighted percentage increase relative to the gamut area of the Farnsworth D-15 color is at least about 35%. In further such changes, the percentage increase in gamut area relative to the Farnsworth D-15 color is greater than zero for angles between 0 degrees and at least about 25 degrees. In some variations, the filter is configured to enhance red-green discrimination for one observer with severe deuteranomaly. In such variations, the stop band may have a minimum transmission that is one-fifth of the light transmission between about 580 nanometers and about 650 nanometers and less than that between about 475 nanometers and about 580 nanometers. The light transmittance is about one-fifth (for example, about one-tenth). In some of these variations, the white point is neutral and the importance-weighted percentage increase relative to the gamut area of the Farnsworth D-15 color is at least about 40%. In further such changes, the percentage increase in gamut area relative to the Farnsworth D-15 color is greater than zero for angles between 0 degrees and at least about 25 degrees. In some variations, the filter is configured to enhance red-green discrimination for an observer with redness. In some such variations, the third passband has a center wavelength between about 605 nanometers and about 620 nanometers. In some such variations, the first passband has a center wavelength of about 440 nanometers, the second passband has a center wavelength of about 530 nanometers, and the third passband has a center wavelength of about 615 nanometers. In some such variations, the white point is neutral and the percentage increase in gamut area relative to the Farnsworth D-15 color provided by the filter at normal incidence is at least about 40%. In further such changes, the percentage increase in gamut area relative to the Farnsworth D-15 color is greater than zero for angles between 0 degrees and at least about 25 degrees. In some variations, the filter is made by incorporating a neutral density absorption filter and an interference filter. In a further variation, the filter is fabricated by incorporating a neodymium-containing substrate along with the neutral density absorption filter and an interference filter. If appropriate, any of the above modified filters may be incorporated into the glasses. Such eyewear may include, for example, eyepieces (eg, sunglasses), goggles, contact lenses, or any other suitable ophthalmic lens. In another aspect, a multi-band filter includes three or more passbands separated by two or more stopbands. The passbands and the stopbands are configured to transmit the blue primary color light, the red primary color light and the green primary color light of an electronic visual display such that the lights appear to have approximately the same luminosity and the light transmittance of the primary color light The light transmittance is at least about 15% greater than that of sunlight. In some of these variations, the white point is neutral and the percentage increase in gamut area relative to the Farnsworth D-15 color is greater than zero for angles between 0 degrees and at least about 25 degrees. In some of these changes, the weighted percentage importance relative to the increase in gamut area of the Farnsworth D-15 color is at least about 20%. In some variations, the multi-band filter has a light transmission between about 8% and about 40%, and the bands are configured such that the white point of the filter is neutral or nearly neutral, such that the white point The (x, y) chromaticity coordinates fall within approximately 0.05 units of (0.31, 0.33) relative to the illuminant D65 on the CIE xyY 1931 2-degree standard observer color space. In some variations, the filter has three passbands, and a first passband has a center wavelength of about 450 nanometers and a width of about 20 nanometers, and a second passband has a center wavelength of about 535 nanometers and A width of approximately 25 nanometers, and the third passband has a center wavelength of approximately 615 nanometers and a width of approximately 30 nanometers. In some variations, the filter has four passbands, a first passband having a center wavelength of about 455 nanometers and a width of about 20 nanometers, a second passband having a center wavelength of about 540 nanometers and a width of about 25 nanometers, the third passband having a center wavelength of about 615 nanometers and a half-maximum width of about 25 nanometers, and the fourth passband having a center wavelength of about 680 nanometers and about 25 nanometers 1 half peak width. In some variations, the passband is positioned and/or shaped such that the filter provides a stable color appearance for angles of incidence between about 0 degrees and about 40 degrees that deviate from the surface normal vector, such that for all or nearly all At these angles of incidence, the white point of average sunlight is contained in an area with a radius of approximately 0.01 units on the CIELUV 1931 2-degree standard observer chromaticity (u', v') scale. In some variations, the computer monitor with the filter disposed thereon is a liquid crystal display (LCD) with a light emitting diode (LED) backlight. In some variations, the white point is neutral and the importance-weighted percentage increase relative to the gamut area of the Farnsworth D-15 color provided by the filter is at least about 20%. In some variations, the filter is made by incorporating a neutral density absorption filter and an interference filter. If appropriate, any of the above modified filters may be incorporated into the glasses. Such eyewear may include, for example, eyepieces (eg, sunglasses), goggles, contact lenses, or any other suitable ophthalmic lens. In another aspect, a multi-band filter that provides enhanced eye safety is configured to: provide normal color appearance and also provide a blocking band, wherein the blocking band protects the eye from about 450 nanometers to about 650 nanometers Visible radiation at one or more wavelengths between 10 and 100 meters; and providing blocking over a range of angles of incidence between about 0 degrees and about 30 degrees that deviate from the surface normal vector of the filter. In some variations, the multi-band filter has a light transmission between about 8% and about 40%, and the bands are configured such that the white point of the filter is neutral or nearly neutral, such that the white point The (x, y) chromaticity coordinates fall within approximately 0.05 units of (0.31, 0.33) relative to the illuminant D65 on the CIE xyY 1931 2-degree standard observer color space. In some variations, the protective blocking band has a short wavelength boundary at about 530 nanometers and a long wavelength boundary at about 560 nanometers from visible radiation at about 532 nanometers. In such variations, the filter may include four passbands separated by three stopbands, with the middle stopband being the guard band. The first passband has a center wavelength of about 440 nanometers and a width of about 20 nanometers, the second passband has a center wavelength of about 515 nanometers and a width of about 25 nanometers, and the third passband has a center wavelength of about 515 nanometers and a width of about 25 nanometers. A center wavelength of 570 nanometers and a width of about 25 nanometers, and the fourth passband has a center wavelength of about 635 nanometers and a width of about 25 nanometers. In these changes, the importance-weighted percentage relative to the increase in gamut area of the Farnsworth D-15 color is approximately zero. In some variations, the percentage increase in gamut area relative to the Farnsworth D-15 color is approximately zero for angles between 0 degrees and at least about 25 degrees. In some variations, the blocking band has a short wavelength boundary at about 585 nanometers and a long wavelength boundary at about 620 nanometers, and is therefore protected from visible radiation at about 589 nanometers. In such variations, the filter may include four passbands separated by two stopbands, with the long wavelength stopband providing protection. In some variations, the first passband has a center wavelength of about 455 nanometers and a width of about 20 nanometers, the second passband has a center wavelength of about 540 nanometers and a width of about 20 nanometers, and the The three-pass band has a center wavelength of approximately 570 nanometers and a width of approximately 20 nanometers, and the fourth pass-band has a center wavelength of approximately 635 nanometers and a width of approximately 30 nanometers. In some of these variations, the white point is neutral and the importance-weighted percentage increase relative to the gamut area of the Farnsworth D-15 color ranges from about 0% to about 15%. In some of these variations, the percentage increase in gamut area relative to the Farnsworth D-15 color is greater than zero for angles between 0 degrees and at least about 25 degrees. In some variations, the passband is positioned and/or shaped such that the filter provides a stable color appearance for angles of incidence between about 0 degrees and about 35 degrees that deviate from the surface normal vector, such that for all or nearly all At these angles of incidence, the white point of average sunlight is contained in an area with a radius of approximately 0.01 units on the CIELUV 1931 2-degree standard observer chromaticity (u', v') scale. In some variations, the filter is made by incorporating a neutral density absorption filter and an interference filter. If appropriate, any of the above modified filters may be incorporated into the glasses. Such eyewear may include, for example, eyepieces (eg, sunglasses), goggles, contact lenses, or any other suitable ophthalmic lens. In another aspect, a multi-band filter for affecting color vision includes three or more passbands separated by two or more stopbands. The passbands and the stopbands are configured to maximize reception of blue light by retinal ganglion cells and maximize normal color discrimination. In some variations, the multiband filter has three passbands separated by two stopbands, where a first passband has a center located at approximately 485 nanometers and a half-maximum width of approximately 90 nanometers, and a second passband The passband has a center wavelength of about 580 nanometers and a half-maximum width of about 25 nanometers, and the third passband has a center wavelength of about 630 nanometers and a half-maximum width of about 25 nanometers. In some variations, the multiband filter has four passbands separated by three stopbands, with a first passband having a center wavelength of about 430 nanometers and a half-peak width of about 30 nanometers, and a second passband having a center wavelength of about 430 nanometers and a half-maximum width of about 30 nanometers. The band has a center wavelength of about 495 nanometers and a half-maximum width of about 50 nanometers, the third passband has a center wavelength of about 565 nanometers and a half-maximum width of about 20 nanometers, and the fourth passband has a center wavelength of about 565 nanometers and a half-maximum width of about 20 nanometers. A center wavelength of 630 nanometers and a half-maximum width of about 20 nanometers. In some variations, the passband is positioned and/or shaped such that the filter provides a stable color appearance for angles of incidence between about 0 degrees and about 30 degrees that deviate from the surface normal vector, allowing for use in all or almost all applications. For all such angles of incidence, the white point of average sunlight is contained in an area with a radius of approximately 0.01 units on the CIELUV 1931 2-degree standard observer chromaticity (u', v') scale. In some variations, the white point is neutral and the importance weighted percentage relative to the gamut area increase of the Farnsworth D-15 color ranges from about 0% to about -10%. In some variations, the multi-band filter has a light transmission between about 8% and about 40%, and the bands are configured such that the white point of the filter is at or nearly located as defined in accordance with industry standard ANSI Z80.3 -2010 is considered to be at the limit of a filter that does not produce strong colors. In some variations, the filter is made by incorporating a neutral density absorption filter and an interference filter. In a further variation, the filter is fabricated by incorporating a neodymium-containing substrate along with the neutral density absorption filter and an interference filter. In some variations, the filter specifications are significantly smoothed such that fewer than about 50 layers of material can be used to fabricate the interference filter. If appropriate, any of the above modified filters may be incorporated into the glasses. Such eyewear may include, for example, eyepieces (eg, sunglasses), goggles, contact lenses, or any other suitable ophthalmic lens. In another aspect, a multi-band filter includes three or more passbands and two or more stopbands configured to modulate and/or enhance light by human vision. Color appearance. Spectral transmittance of filter f as a function of wavelength λ It can be approximately expressed by the following expression: ; Among them, in the above expression, is the passband and is the weighting coefficient for adjusting the passband, and is the minimum transmittance of the filter. The above expression as a function of wavelength λ can be tabulated by sampling uniformly on one wavelength scale (e.g., using steps of 1 nanometer) or another substantially equivalent scale (e.g., frequency or log wavenumber). Specifications of filter transmittance (f, u). Sampling can also be defined at any scale with uneven spacing between sample points. In some variations, the filter includes three passbands and two stopbands (ie, in the above expression, N=3). In some variations, the filter includes four passbands and three stopbands (ie, in the above expression, N=4). In some variations, the filter passband is rectangular in nature, that is, the change in transmittance as a function of wavelength at the band boundaries is instantaneous or nearly instantaneous. The width of a rectangular passband is characterized by the distance between the short wavelength boundary and the long wavelength boundary. The rectangular bandwidth can be equivalently measured on a frequency scale. The spectral transmittance of a rectangular passband can be defined by the following expression: ; in is the central wavelength, is the rectangular bandwidth and H is the Heaviside step function. In some variations, the filter passband is Gaussian in nature, that is, the change in transmittance as a function of wavelength at the band boundaries is gradual or essentially smooth. The width of a Gaussian band is characterized by the distance between the half-peak transmittance on the short-wavelength side and the half-peak transmittance on the long-wavelength boundary (also known as the full width at half maximum (FWHM)). The half-peak bandwidth can be measured equivalently on a frequency scale. The spectral transmittance of a Gaussian band can be defined by the following expression: ; in is the center wavelength, and the half-peak bandwidth is: . In some variations, one or more of the passbands may have an irregular shape (ie, non-rectangular and non-Gaussian). For example, the passband may have a bimodal distribution, or may have a shoulder on one or more sides of the passband, or may be described as a skewed distribution, where in transmittance as a function of wavelength, the passband The slope ratio between the two sides of the belt is between about 4:1 and about 1:4. In a variation on non-Gaussian bands, such passbands may be smoothed with a Gaussian core that is wide enough to essentially eliminate irregularities and/or sharp transitions, in which case the passband may be described as having Corresponds to the band center and half-peak width of one of the smooth passbands. In some variations, the passband is positioned and/or shaped such that the filter provides a stable color appearance for angles of incidence between about 0 degrees and about 35 degrees that deviate from the surface normal vector, allowing for use in all or almost all applications. For all such angles of incidence, the white point of sunlight is contained in an area with a radius of approximately 0.01 units on the CIELUV 1931 2-degree standard observer chromaticity diagram. In some variations, the passband is positioned and/or shaped such that the filter provides a stable color appearance for angles of incidence between about 0 degrees and about 40 degrees that deviate from the surface normal vector, allowing for use in all or almost all applications. For all such angles of incidence, the white point of sunlight is contained in an area with a radius of approximately 0.01 units on the CIELUV 1931 2-degree standard observer chromaticity diagram. In some variations, the passband is positioned and/or shaped such that the filter provides a stable color appearance for angles of incidence between about 0 degrees and about 45 degrees that deviate from the surface normal vector, allowing for use in all or almost all applications. For all such angles of incidence, the white point of sunlight is contained in an area with a radius of approximately 0.01 units on the CIELUV 1931 2-degree standard observer chromaticity diagram. In some variations, the passband is positioned and/or shaped such that the filter provides a stable color appearance such that the white point is displaced from its position at an angle of incidence of 0 degrees by an incident angle dependent distance between about 20 degrees at an incident angle to about 45 There is a local minimum at an angle between degrees of incidence, where the white point displacement at the local minimum is less than 0.02 units of the CIELUV 1931 2-degree standard observer chromaticity (u', v') scale. In some variations, the passband is positioned and/or shaped such that the filter provides a stable color appearance such that the white point is displaced from its position at an angle of incidence of 0 degrees by an incident angle dependent distance between about 20 degrees at an incident angle to about 45 There is a local minimum at an angle between degrees of incidence, where the white point displacement at the local minimum is less than 0.01 units of the CIELUV 1931 2-degree standard observer chromaticity (u', v') scale. In some variations, the multiband filter is fabricated as an interference filter. In some variations, multiband filters are fabricated to include an interference filter and one or more neutral density absorption filters, with the interference filter providing a passband and a stopband. In some variations, multi-band filters are fabricated to include an interference filter and one or more broadband absorption filters, with the interference filter providing a passband and a stopband. In some variations, multi-band filters are fabricated to include an interference filter and one or more narrowband absorption filters, wherein the interference filter and absorption filter are jointly configured to provide a passband and stop band. In any of the above variations, the multiband filter f may include an absorption filter p and an interference filter q, where the change in transmittance of p as a function of incident angle is according to the Beer-Lambert law, And the change of the transmittance of q as a function of the incident angle is based on Snell's law, so that the transmittance of f at an incident angle of θ radians deviating from the surface normal vector can be expressed as And it is approximately represented by the following expression: , ; Among them, the effective refractive index of the interference filter q has n with a value of approximately 1.85, and the spectral transmittance of p at normal incidence is , the spectral transmittance of f at normal incidence , the spectral transmittance of q at normal incidence , and approximate values of θ between about 0 degrees and about 30 degrees are sufficient. In some of these changes, the spectral transmittance of q can be shifted toward longer wavelengths, as calculated by the following expression: ,and ; in is one of the coefficients for determining the displacement, and A criterion chosen to maximize the filter's performance over a range of angles of incidence. In some variations, the filter includes an interference filter, wherein the spectral transmittance of the interference filter is significantly smoothed, and the width of the smoothing core is selected not to unduly compromise the performance of the filter while also allowing The optical filter can be fabricated as a low-order stack of dielectric materials. If appropriate, any of the above modified filters may be incorporated into the glasses. Such eyewear may include, for example, eyepieces (eg, sunglasses), goggles, contact lenses, or any other suitable ophthalmic lens. In another aspect, a computer-implemented method for determining the distribution of physical thickness of an optical filter on a surface includes: using a computer; defining the spectral transmittance of the optical filter; defining the optical filter in Spectral transmittance over a range of angles of incidence; defining a geometric model of the surface; defining a geometric model of a human eye; configuring the geometric models to approximate the geometry of an eyeglass frame in which the surface is mounted and a lens located in front of the eye; calculating, for each location on the surface, the angle of incidence of light passing through the location to be imaged on the retina of the eye; and specifying a solid thickness for each location, where the solid thickness is configured such that The spectral transmittance is constant or substantially constant at all or nearly all locations on the surface relative to the calculated angle of incidence. In another aspect, a computer-implemented method for determining the distribution of physical thickness of an optical filter on a surface includes: using a computer; defining a spectral transmittance of an optical filter; defining the optical filter Spectral transmittance over a range of angles of incidence; a geometric model that defines the surface; a geometric model that defines the relative physical thickness of the filter deposited onto the surface (e.g., as the physical thickness achieved by a specific process distribution predictions and measurement results); defining geometric models of a human eye; configuring these geometric models to approximate the geometry of an eyeglass frame, where the surface is a lens mounted in the frame and in front of the eye; calculating A position on the surface that corresponds to the center of the field of view; calculates the angle of incidence of light passing through the center position; defines an importance distribution for each position relative to the center position; specifies a solid thickness at the center position, where the solid thickness is Select so that light passing through the central location and imaged onto the retina is filtered according to a defined spectral transmittance; calculates the weighted average effect on color vision at the surface of the lens as +/- 10 of the specified central solid thickness associated with a solid thickness variation range within %; and then selecting an offset center solid thickness within the range so that the importance weighted average effect on color vision is maximized. In another aspect, a lens for eyeglasses incorporating a multi-band filter includes an optical substrate, one or more reflective interference filters and positioned on one or both sides of the reflective filters One or more absorption filters configured to reduce the luminosity of reflected light on one or both sides of the lens. In some variations, the interference filter includes a low-level stack having from about 12 to about 50 layers of dielectric material, or from about 1 micron to about 3 microns thick, or having from about 12 to about 50 One of the dielectric material layers is a low-level stack and is between 1 micron and 3 microns thick. In some variations, the interference filter includes a high-order stack having from about 50 to at least about 200 layers of dielectric material, or from about 6 microns to at least about 12 microns thick, or from about 50 to at least about One of 200 layers of dielectric material is stacked in a high order and is between 6 microns and at least about 12 microns thick. The dielectric material layer included in the interference filter may include thin films of titanium dioxide and silicon dioxide, for example. The material layer can be produced, for example, by physical vapor deposition in, for example, a magnetron sputtering machine. Alternatively or additionally, the layer of dielectric material may be produced, for example by spin-on deposition. In some variations, a neutral density absorbing filter is provided by a metallic attenuating coating. The layer of metallic material may be produced, for example, by physical vapor deposition. In such variations, the metal layer may be interleaved or partially interleaved with the dielectric layer of the interference filter. In some variations, a photoactivated neutral density absorbing filter is provided by incorporating the photochromic material into a glass or polymer substrate. In these variations, interference filters can be deposited on the convex surface of the lens. In some variations, a linearly polarizing neutral density absorbing filter is provided by incorporating a polarizing filter into a laminated composite lens or by coating onto the surface of the lens. In such variations, the polarizer may be located between the interference filter and the side of the lens facing the eye. In some variations, an absorbing filter is provided by organic dyes in a polymer substrate. The polymeric material may be combined by any suitable method, such as, for example, by incorporation into an optical substrate medium, laminating a film between two optical substrates, or spin coating or dip dyeing the surface of an optical substrate. into the lens. In some variations, an absorbing filter is provided by incorporating inorganic materials into a glass or polymer substrate. In several of these variations, the inorganic materials may include rare earth ions of indium, phosphorus, neodymium, or any mixture of the above. In some variations, one or more absorptive filters are configured to affect the color appearance of sunlight reflected from the outer surface of the lens (the surface furthest from the eye), where the color appearance is configured for eye pleasure. In some variations, the absorbing filter includes: a first circular polarizer positioned on one side of the interference filter and configured to absorb light reflected by the interference filter; and a second circular polarizer a circular polarizer positioned on the side of the interference filter opposite the first circular polarizer and configured to absorb light reflected by the interference filter, and the first circular polarizer and the third Two circular polarizers are configured to transmit light through the interference filter. In some variations, one on the side of the lens closest to the eye is provided by a first circular polarizer affixed to one side of the interference filter and configured to absorb light reflected by the interference filter. Absorption filter. In a variation incorporating one or more circular polarizers, a circular polarizer including a linear polarizer and a quarter-wavelength retarder, the linear polarizer element may be configured to provide, for example, about 60% to about 90% partial polarization efficiency. In variations that include a linear polarizer, the linear polarizer can be configured to attenuate horizontally polarized light to reduce glare from sunlight reflected from horizontal surfaces due to the Brewster's angle phenomenon. In some variations, all functional layers of the filter are positioned on one side of the optical substrate, and the opposite side of the substrate has an anti-reflective coating that reduces scattering and resonance of reflected light within the optical substrate, and the anti-reflective coating The coating has a luminosity-weighted reflectance of less than about 0.5%. In some variations, the entire functional layer of the filter is sandwiched between two optical substrates, and the outer surfaces of the optical substrates are anti-reflective coated to reduce scattering and resonance of reflected light within the optical substrates. In some variations, the edges of the lens can be sealed with an index-matched absorptive polymer coating that reduces the transmission and scattering of stray light within the optical substrate and also protects the filter layers from contamination (e.g., Avoid water or solvent penetration into dielectric or metallic material layers). In some variations, all functional layers of the filter are metal or metal oxide coatings compatible with fabrication by physical vapor deposition. In some variations, the optical substrate is chemically tempered glass. In such variations, the glass may absorb ultraviolet light between about 280 nanometers and about 400 nanometers, for example. In some variations, the interference filter is deposited on a surface such that the physical thickness of the dielectric material layer is configured such that the optical thickness is constant or substantially constant at two or more locations on the surface, The effective incident angles of the light to the filter at the two or more positions differ by at least 20 degrees, and the effective incident angle of the light corresponds to a beam of light that passes through the lens and is imaged on the retina of the eye. In some variations, the optical substrate is curved with a radius of curvature between about 50 millimeters and about 200 millimeters. In such variations, interference filters and/or attenuating coatings may be positioned on the concave side of the surface. If appropriate, lenses of any of the above variations may be incorporated into eyeglasses including, for example, eyepieces (eg, sunglasses), goggles, or contact lenses. In another aspect, a light source includes an illuminator, a first beam shaping element, a multi-band interference filter, and a second beam shaping element. The light radiated from the illuminator is substantially collimated by the first beam shaping element. A collimated light beam is incident on the multi-band filter, where the light beam is divided into a transmission part and a reflection part. The transmitted portion and the reflected portion of the light have the same or substantially the same white point relative to the selected illuminant. The transmitted portion of the light provides illumination that enhances the apparent purity of red and green, and the reflective portion of the light provides illumination that enhances the apparent purity of blue and yellow. The second beam shaping element combines the transmitted portion and the reflected portion of the light into an output beam, wherein the transmitted light and the reflected light are at least partially spatially separated in the output beam. In some variations, the output beam has a central portion consisting primarily of light transmitted by the multi-band filter and an outer portion consisting primarily of light reflected by the multi-band filter. In some variations, the functions of the first beam shaping element and the second beam shaping element are combined in a single beam shaping element. In some variations, the beam collimation angle of light from the illuminant incident on the multi-band filter is approximately 20 degrees. In these variations, for all or nearly all positions within the collimated beam, the white point of the filter relative to the illuminant may, for example, be contained on the CIELUV 1931 2-degree standard observer chromaticity scale with approximately Within a radius of 0.01 units. In some variations, the multiband filter includes three passbands separated by two stopbands, where a first passband has a center wavelength of approximately 450 nanometers and a bandwidth of approximately 15 nanometers, and a second passband The band has a center wavelength of approximately 535 nanometers and a bandwidth of approximately 20 nanometers, and the third passband has a center wavelength of approximately 625 nanometers and a bandwidth of approximately 30 nanometers. In some variations, the stopband has a minimum transmission of about 10%. In a further variation, the stopband has a minimum transmission of about 1%. In some variations, the illuminator includes one or more phosphor-based white light-emitting diodes and one or more red light-emitting diodes. A broadband combination of light from the white light-emitting diode and the red light-emitting diode emitted by the illuminant has an equivalent color temperature between about 5000 K and about 7000 K and a CRI between about 80 and about 90 . In some variations, the illuminator includes a phosphor-based white LED, a cyan LED, and a red LED. The light emitted by the combined diode has a broadband spectral radiant flux with a correlated color temperature between about 5000 K and about 7000 K and a CRI between about 90 and about 100. In some of these variations, the spectral radiant flux configuration of the illuminant is a best approximation of average daylight (D65). In some variations, an ophthalmic lens having a multi-band spectral transmittance is provided, the ophthalmic lens including an optical substrate and an interference filter, wherein the interference filter has a spectral transmittance between about 30% and about 80%. a light reflectivity and a light transmittance between about 8% and about 70%. All methods and variations disclosed herein for designing, evaluating, or otherwise qualifying optical filters, eyeglasses, ophthalmic lenses, illuminators, and other optical components or devices may include steps for making such articles, making such articles another step or a step that provides one of the manufacturing specifications of the article to another article, whether or not this step is explicitly stated in the description of a particular method, article, or variation thereof. These and other aspects, embodiments, variations, features and advantages of the present invention will be further apparent to those skilled in the art with reference to the [Embodiments] of the present invention and the accompanying drawings which are first briefly described.

Cross-references to related applications This application is related to Provisional U.S. Patent Application No. 61/449,049, titled "MULTI-BAND OPTICAL FILTERS FOR GOOD COLOR APPEARANCE", filed on March 3, 2011, the entire text of which is incorporated herein by reference. [Embodiments] should be read with reference to the drawings, where the same reference numerals refer to the same elements throughout the different drawings. The drawings, which are not necessarily to scale, depict selected embodiments and are not intended to limit the scope of the invention. [Embodiment] illustrates the principles of the present invention by way of example rather than by way of limitation. [Embodiments] will enable those skilled in the art to clearly make and use the invention, and describe several embodiments, adaptations, variations, substitutions and uses of the invention, including what is currently considered the best mode of carrying out the invention. As used in this specification and the accompanying claims, the singular forms "a", "a" and "the" include plural referents unless the context clearly indicates otherwise. The teachings of the present invention may be beneficially read in conjunction with a general understanding of the science of optics, the science of human color vision, the science of colorimetry, and related topics. For a general reference on these topics, see, for example, Günter Wyszecki and W.S. Stiles, "Color Science: Concepts and Methods, Quantitative Data and Formulae" (Wiley, 1982, ISBN #0471021067). Without loss of generality, the present invention may assume a conventional configuration of the human visual system: specifically (if not otherwise stated), a human visual system with a 2-degree field of view and the photochromatic perception of a normal human observer. . Photochromatic vision occurs when the level of illumination is high enough that rod photoreceptor cells are inactive, for example when the average surface illumination is about 10 lux or greater. In this disclosure, unless otherwise stated, the CIE 1976 L*u'v' (LUV) color space (which uses a CIE 1931 standard observer with a 2-degree field of view) is used to calculate the color appearance model. Details of this calculation are given by CIE standard S014-5/E:2009. The CIE 1976 Uniform Color Chart System (UCS) is used to illustrate the chromaticity diagram, where the chromaticity coordinates are the (u', v') values, as calculated from this standard. For those of ordinary skill, these teachings are accomplished by introducing a variable in the spectral absorbance of the photopigment and/or the selection of pre-receptor eye components (which include eye media and macular pigment) and provide procedures (e.g. taking into account color vision deficiency, age and/or ocular pathology). In the present invention, illuminant D65 (D65) means light with a typical spectral radiant flux of sunlight and a correlated color temperature of 6500 Kelvin, and is determined by the joint ISO/CIE standard ISO 10526:1999/CIE S005 /E-1998 definition. In the present invention, references to "sunlight", "sunlight" or "average daylight" mean the illuminant D65. Illuminating body E is meant to be an ideal lamp defined as having equal power as a function of wavelength. Illuminating body A means a lamp, usually an incandescent light bulb, which is defined as having the spectral radiant flux of an ideal blackbody radiator according to Planck's law and a correlated color temperature of 2848 K. The lamp series including illuminants FL1 to FL12, which represent the spectral radiant flux of typical types of fluorescent lamps, is defined by CIE Publication No. 15:2004. Munsell colors are a set of color samples formulated with specific pigments to establish a defined color standard in a spectral domain. Munsell colors are available in printed form in the Munsell Color Encyclopedia (Glossy Edition, ISBN #9994678620, 1980). Published by Parkkinen J.P.S., Hallikainen J. and Jaaskelainen T. "Characteristic spectra of Munsell colors" (Journal of the Optical Society of America A, Vol. 6, No. 2, 1989, pp. 318 to 322) Munsell A measurement of the spectral reflectance of a color. The Farnsworth D-15 is a standardized color discrimination test that includes 15 Munsell color samples forming a profile with a chromaticity between 2 and 4 on the Munsell scale. Farnsworth D-15 is described in the publication "The Farnsworth dichotomous test for color blindness panel D15 manual" (News York: Psych Company; 1947, Farnsworth D). Figures included in this disclosure may be program flow diagrams that visually depict generalized objects and the flow of operations that process and produce such objects. Figure 58 depicts an example of a program flow diagram for facilitating visual language understanding. In this diagram, rounded boxes (eg, 5801 and 5803) depict objects that may be understood as physical entities, virtual entities (such as numerical data), or composite objects containing a heterogeneous collection of component objects. A composite object containing a heterogeneous collection of objects is depicted by a rounded box with a double line frame (such as shown at 5808 and 5811). A dotted arrow depicts a component object extracted from a composite object, such as shown by connecting entities 5801 and 5803. The flow of objects in the program is shown by a solid arrow, for example, shown by connecting entities 5801 and 5802. A square box (such as 5802 and 5805) represents an operation. Operations can create objects, transform objects, or analyze objects. The output of an operation is shown by an arrow pointing away from its box. The output of an operation depends on the input of the operation which can be traced by following all the arrows in the box that lead to the operation. An operation can be formed into a composite operation by encapsulating another program graph, such as shown at 5806. This construct enables program flow diagrams to be expanded across multiple pages, whereby a composite operation defined in one diagram can be called when referencing another diagram. Operations may be connected together in series or parallel, and the details of the order in which particular operations are performed are not necessarily defined by the program flow diagram syntax but must be inferred from the accompanying description. A double-line arrow (such as shown connecting 5808 and 5809) represents the iteration of the process of multiple homogeneous objects. Use a double-line square box to show repeated operations, such as 5809. An iterated operation changes its input relative to each iterated object, but can maintain a constant input relative to the unrepeated object, such as shown along the flow arrow connecting 5807 and 5809. The program flow diagrams used in the present invention are provided to facilitate understanding when interpreted together with the accompanying detailed description. Color perception may generally be understood as arising from the interaction of the spectral radiant flux of light incident on the retina and the spectral absorbance of the retinal photoreceptor cells. The procedure for sensing color perception and the application of an optical filter for affecting color perception are depicted in the process flow chart of Figure 1 . Here, an illuminant 101 (such as sunlight) radiates into an optical system 102. Light emitted by an illuminant can generally be considered white light. Within optical system 102, white light is reflected from a surface of reference color 104 (103). Then, the reflected light can be described as a colored light, assuming that the reference color is not neutral (ie, not grayish). Thereafter, wavelength selective transmission 105 can transform the colored light by passing through an optical filter 106 . Since the law of conservation of energy must be observed, the portion of the light that is not transmitted must be reflected or absorbed by the filter at this interface. The optical system 102 is invariant with respect to the reordering of its internal operations, ie, the filter can be applied equivalently before or after illuminating the reference color. An observer can then perceive the filtered light through the process of visual phototransduction 115 . In visual phototransduction under light-sensitive conditions, light is absorbed at 107, 109 and 111 by three types of retinal photoreceptor cells including short-wavelength cone cells 108, medium-wavelength cone cells 110 and long-wavelength cone cells 112. The total energy absorbed by each cell is converted into neural stimulation that is transmitted via the optic nerve into the visual cortex, ultimately resulting in color perception. To model color appearance, it is sufficiently assumed that the input-output response of cones is linearly proportional to the energy absorbed. This linear response can be called a trichromatic value, which can be viewed as a vector in three-dimensional space with non-negative components. As described, the space of trichromatic values is sometimes referred to as SML color space or frustum excitation space. The distances between points in three-color space do not necessarily correspond exactly to the perceived differences between pairs of color stimuli, so it is advantageous to employ a color appearance model 118 (as discussed further below with reference to Figure 3) that would The three-dimensional tricolor vector is transformed into a one-dimensional component of luminosity 117 (also called brightness or intensity) and a two-dimensional component of chrominance 116 (which represents the apparent color of the stimulus independent of luminosity). Chroma can be viewed as a vector value in one of two dimensions, in which case the vector value can be called a chroma coordinate. Chroma can be further divided into hue and saturation (also called purity, which is essentially the perceived difference between a color stimulus and a white stimulus). It should be noted that the spectral absorbance of retinal photoreceptor cells 108, 110, and 112 (Fig. 1) is observer dependent and varies between individuals. Furthermore, the formation of a color appearance model 118 may also depend on the observer 113, however, without loss of generality, a standard model may be used in the subsequent description. Figure 2A shows a graph of the spectral absorbance rate of photopigments of retinal cones (including short-wavelength cones 201, medium-wavelength cones 202 and long-wavelength cones 203) of a normal human eye. However, as mentioned previously, the spectral absorbance of retinal photoreceptor cells can vary from person to person. These differences are the root cause of color vision deficiency. For example, individuals with protanism have a medium-wavelength cone photopigment that has a spectral absorbance shifted toward longer wavelengths; and individuals with protanism have a long-wavelength cone photopigment that has a spectral absorbance that is shifted toward longer wavelengths. One of the short wavelength shifts is spectral absorbance. Individuals with deuteranomaly experience more difficulty than normal individuals in distinguishing red from green. Individuals with protanopia also experience more difficulty than normal individuals in distinguishing red from green, and also tend to view red as less bright. This can be achieved by shifting a photopigment template on a log wavenumber scale (e.g., by using Spectral sensitivities of the middle- and long-wavelength sensitive cones derived from measurements in observers of known by Stockman, A. and Sharpe, L.T. genotype." (Vision Research, Issue 40, 2000, pp. 1711 to 1737) published template) and approximately represents the spectral absorbance of abnormal retinal photopigments. The table in Figure 2B lists known genotype variants in the population and the associated wavelengths of maximum photopigment absorbance, with the leftmost row of the table containing an indication of genotype 204 (for details, see Asenjo, A.B., Rim, "Molecular determinants of human red/green color discrimination" by J. and Oprian, D.D., Neuron, 1994, Volume 12, Pages 1131 to 1138), the next line indicates normal, green-weak or red-weak Classification 205 and in which the abnormality type is further classified according to the severity which can be mild, moderate or severe, and the remaining rows indicate the wavelength (in nanometers) of the maximum absorbance of the short wavelength cone photopigment 206, medium The wavelength is the wavelength (in nanometers) at which the maximum absorbance of cone photopigments is 207 and the wavelength (in nanometers) at which the long-wavelength cone photopigments are maximum absorbance 208. This table contains the most common types of inherited color vision deficiencies: deuteranomaly, which has a global prevalence of approximately 4% (and approximately 8% in males and less than 1% in females); protanism, which has a prevalence of approximately 0.5% (approximately 0.5% in females). 1% are male and less than 0.1% are female). The higher prevalence of color vision deficiency in males has been attributed to the genetic abnormality of the X-recessive gene. Abnormalities in the short-wavelength cone photoreceptor pigments are called type III achromatopsia. Inherited achromatopsia type III is rare, however, acquired achromatopsia type III color vision deficiency occurs when the cones (specifically, short-wavelength cones) are damaged, for example, by exposure to certain toxins such as mercury . Individuals with type III color deficiency will experience more difficulty than normal individuals in distinguishing blue from yellow. Standard observer models of color vision may be constructed to best fit the normal population and do not necessarily provide a good model of color perception for any particular individual or subpopulation. However, if the physiological properties of any individual are sufficiently obtained, then a physiologically relevant observer model of any individual can be constructed. As shown in Figure 3, the perceived color appearance of light according to one of the three-color models can be represented graphically, where the axes of the graph correspond to the neural excitation of short wavelength cones 310, the neural excitation of medium wavelength cones 306, and The neural excitation of long wavelength cones 301, and the trichromatic value is a point 302 that corresponds to the color appearance of a particular light (eg, reflected by a reference color or emitted by an illuminant). Trichromatic values are three-dimensional points whose dimensions correspond to the fraction of light energy absorbed by the various cones. Light itself can be viewed as an essentially infinite-dimensional vector, and its spectrum can be measured using a spectrophotometer. However, trichromatic values are only three-dimensional. Therefore, many different lights can be mapped to the same point in the three-color space, and a set of lights mapped to the same point in the three-color space is called a color-changing pair. The projection from the spectral domain of light to the three color domains of color appearance is a linear mapping, therefore, light addition and scalar multiplication are retained. This property implies the geometric shape of the trichromatic values. For example, if a composite light is formed from a non-negative additive mixture of a collection of lights (i.e., a convex linear combination), then the trichromatic values of the composite light must be contained within a convex polyhedron whose angles are the three components of the light. Color value. Referring again to Figure 3, the origin of the axis 307 corresponds to the appearance of black (ie, the absence of light and zero neural excitation). A spectral locus is a set of trichromatic values that form a profile 309 corresponding to the color appearance of the set of monochromatic light (ie, ideal light having energy of only a single wavelength). Since any light can be considered as a convex linear combination of the set of monochromatic lights, the trichromatic values are always contained within a generalized cone whose vertex is the origin 307 and whose boundaries are defined by the spectral locus 309. For subsequent analysis of optical filters, and as briefly discussed above, the three-color representation can be usefully divided into a one-dimensional component of luminosity and a two-dimensional component of chromaticity. These transformations are also linear mappings. The luminosity response is a line in the three-color space consistent with the origin and the three-color values of the illuminant E. The perceived luminosity of a light can be calculated by projecting the tristimulus values onto the luminosity response line 303 and then measuring the vector norm of the projection 305 . The luminosity line (which is also outlined by spectral locus 309 in this diagram) is also orthogonal (perpendicular) to one of the planes of equivalent illuminant tristimulus values, and can be calculated by projecting the tristimulus values onto this plane 304 One light perceives chromaticity. The chromaticity projection can then be further transformed by an affine mapping to produce a chromaticity coordinate (which is a two-dimensional value in a space), where the distance between the chromaticity coordinates is the distance between the equivalent illuminant lights. The perceived differences are approximately proportional, which is known as one of the Unicolor Color Systems (UCS), such as the CIE 1974 UCS. In the first-order colorimetric system, it can be observed that the distance from white light (such as illuminant E) to the spectral locus changes with wavelength. Specifically, yellow monochromatic light (e.g., having a spectral radiant flux at a single wavelength (nominally 585 nanometers)) and cyan monochromatic light (e.g., having a characteristic wavelength of about 490 nanometers) Monochromatic light) appears to be subjectively more similar to white light and correspondingly closer to white light on the UCS diagram than blue monochromatic light, green monochromatic light, or red monochromatic light. Therefore, filters that substantially block yellow and/or cyan wavelengths can improve the apparent purity of color, and a typical form of such filters includes at least three passbands and at least two stopbands. Spectral transmittance of multi-band filter f as a function of wavelength λIt can be approximately expressed by the following expression:; Among them, in the above expression,for the passband andTo adjust the weighting coefficient of the passband,is the minimum transmittance of the filter, and n is the number of passbands equal to or greater than 3. The above expression can be tabulated by sampling uniformly on a wavelength scale (e.g. using steps of 1 nanometer) or another substantially equivalent scale (e.g. frequency or log wavenumber) where the wavelength λ is Specification of transmittance (f, d) of the filter as a function. Sampling can also be defined at any scale with uneven spacing between sample points. In some variations, the filter passband (d) is essentially rectangular, that is, the change in transmittance as a function of wavelength at the band boundaries is instantaneous or nearly instantaneous. The width of a rectangular passband is characterized by the distance between the short wavelength boundary and the long wavelength boundary. Rectangular bandwidth can be measured equivalently on a frequency scale. The spectral transmittance of a rectangular passband can be defined by the following expression:; inis the central wavelength,is the rectangular bandwidth, and H is the Heaviside step function. In some variations, the filter passband is Gaussian in nature, that is, the change in transmittance as a function of wavelength at the band boundaries is gradual or essentially smooth. The width of a Gaussian band is characterized by the distance between the half-peak transmittance on the short-wavelength side and the half-peak transmittance on the long-wavelength boundary (also known as the full width at half maximum (FWHM)). The half-peak bandwidth can be measured equivalently on a frequency scale. The spectral transmittance of a Gaussian band can be defined by the following expression:; inis the center wavelength, and the half-peak bandwidth is:. In some variations, one or more of the passbands may have an irregular shape (ie, non-rectangular and non-Gaussian). For example, the passband may have a bimodal distribution, or may have a shoulder on one or more sides of the passband, or may be described as a skewed distribution, where in transmittance as a function of wavelength, the passband The slope ratio between the two sides is between about 4:1 and about 1:4. In a variation on non-Gaussian bands, these passbands can be smoothed with a Gaussian kernel that is wide enough to essentially eliminate irregularities and/or sharp transitions, in which case the passband can be described as ( Essentially) has a band center and half-peak width corresponding to a smooth passband. A general method for evaluating filter performance is to determine which of the possible filter configurations is better for a particular application involving color vision. This classification method can be performed by measuring the relative gamut area between two filters relative to a set of reference colors. As used herein, a gamut area is the area within a contour defined by the coordinates of a set of reference colors in a chromaticity diagram. The positions of the reference colors in the chromaticity diagram are filter dependent, and therefore the color gamut area is also filter dependent. A flow chart of a procedure for calculating the relative gamut area is presented in Figure 4. In the method depicted in Figure 4, relative gamut areas are defined relative to a test filter 401, a reference filter 405, an illuminant 402, an observer 404 and a set of reference colors 403. The test filter and the reference filter preferably have the same white point, ie the tristimulus values of the filtered illuminant are the same for both filters. This restriction does not require the adoption of a colorimetric adaptation model (such as the von Kries model) that can bias the results. The method may benefit from an appropriate selection of one of the set of reference colors, as described later in this disclosure with reference to Figures 6A and 6B. Additionally, the reference filter is preferably selected to have a broadband spectral transmittance such that the reference filter provides minimal or no distortion of color appearance. For any given test filter, the test filters can be compared, for example, by spectral reflectance sets in terms of Munsell colors and then the Munsell color that best fits the reference filter (e.g., has a Select the color of the illuminant that most closely resembles the white point) to find a suitable reference filter, where the reflectance of the selected Munsell color is defined as the transmittance of the reference filter. The color gamut area of the test filter is calculated in operation 406, and the color gamut area of the reference filter is calculated in operation 407. For example, a ratio 410 is used to compare the resulting gamut areas 408 and 409 to obtain a relative gamut area 411. A relative gamut area of 1.0 implies that the test filter provides no distortion of color appearance, and the test filter Said to provide normal color discrimination. A relative gamut area greater than 1.0 implies that the test filter increases the perceived difference between the reference colors. Generally speaking, these differences increase more between red and green, so the test filter is said to provide enhanced red-green discrimination. A relative gamut area less than 1.0 implies that the test filter reduces the perceived difference between the reference colors. Generally speaking, this effect is associated with an increase in the difference between blue and yellow. Therefore, the test filter is said to provide enhanced blue-yellow discrimination. It should be understood that relative gamut area measurements based on analysis of chromaticity coordinates of reference colors are independent of the perceived luminosity of those reference colors, e.g., an increase in apparent difference between color stimuli is not based on a color presentation The fact that one color is a rare dark color and another color appears as a rare bright color. Alternatively, such increases or decreases can be expressed as a percentage of gamut area increase (PGAI), which is defined by the following expression:,and,and; inis calculated relative to the gamut area of the test filter f, reference color S, illuminant I and observer O (as described below in conjunction with Figure 5), andis relative to the reference filterand color gamut area under similar conditions. To evaluate filters in the context of this invention, one or the other of two methods for calculating the percent increase in gamut area is used. In one method, the illuminant I is defined as the illuminant D65, the observer O is defined as the CIE 1931 2-degree standard observer combined with the CIELUV (u', v') color difference system, and the reference color S is specified For any color of the Farnsworth D-15 panel, the percentage increase in color gamut area is given by the following expression:. In another approach, the reference color is given by a selected natural sample (as described in conjunction with Figure 6B), and the percentage increase in gamut area is given by the following expression:. In the above two expressions, the gamut area is calculated relative to the given conditions. The calculation of the color gamut area in operations 406 and 407 of FIG. 4 may be performed, for example, as detailed in the program flow chart of FIG. 5 . With respect to a specific illuminant 502, a filter 503 and a set of reference colors 501, an optical interaction 505 occurs for each reference color. As explained above with respect to operation 102 of FIG. 1 , the optical interaction may be, for example, that the reference color reflects filtered light from the illuminant; or that the filter filters light from the illuminant that has been reflected by the reference color. Light. These optical interactions result in a set of colored and filtered light received by an observer 507 (i.e., observer model) and converted by visual light transduction 506 into a set of trichromatic values, as described above, for example with respect to FIG. 1 operation 115 explained. The set of tristimulus values is further transformed by a color appearance model 508 and restored to a set of chromaticity coordinates 509 . For these coordinates, which are points on a two-dimensional chromaticity diagram, a grid can be formed using, for example, Delaunay triangulation algorithm 510 . The resulting grid can be converted into an area by summing the areas of each triangle in the grid, and the final result of the calculation is the color gamut area 512. The calculation of the color gamut area benefits from the fit specification of the reference color set, which in turn depends at least in part on the intended use of the filter. The reference color should contain at least three elements whose chromaticity coordinates form a triangle surrounding the white point (i.e., the chromaticity coordinates of the illuminant). Preferably, the reference color sets include a sufficient number (e.g., at least 5) and include a sufficient diversity of spectral reflectances such that the color gamut area calculation is stable with respect to changes in the transmittance of the filter, which decreases to a Risk of over-specialization in filter design. In some cases, it may be preferable to smooth the spectral transmittance of the reference color to achieve the desired stability. For example, a set of Munsell colors can be selected for gamut area calculations such that their equal chromaticity coordinates approximately form a circle of medium saturation around the white point. The spectral reflectance of these Munsell colors is broadband and varies with respect to hue in a controlled manner. This is evident in the graph of Figure 6A, which shows Munsell 5B 5/4 at 601, Munsell 5G 5/4 at 602, Munsell 5Y 5/4 at 603, Munsell 5R 5/4 at 604, and 605 Munsell 5P 5/4 is a selection of Munsell colors. In a further variation, it may be preferable to select a set of Munsell colors with high saturation. Alternatively or additionally, some or all of the reference colors may be taken from Farnsworth D-15 (which is also referred to herein as D-15). D-15 includes a set of 15 Munsell reference colors that form a medium-saturated outline around a white point. A filter that provides an increase in gamut area relative to those D-15 colors will also tend to provide an increased score based on the D-15 cover configuration test when an observer performs the test and views the sample through the filter. Alternatively or additionally, some or all of the reference colors may be sampled directly from the environment in which the filter will be used. In particular, several of the embodiments shown subsequently can be usefully incorporated into sunglasses, and since sunglasses are typically worn outdoors in sunlight, by measuring the spectral reflectance of naturally colored objects such as leaves and flowers. Find reference colors quickly and optimally. The graph in Figure 6B shows the spectral reflectance of these natural objects, which includes the spectral reflectance of blue flowers 606, the spectral reflectance of green leaves 607, the spectral reflectance of yellow flowers 608, the spectral reflectance of red flowers 609 and the spectral reflectance of purple flowers. Rate 610. These natural colors were taken from "Spectral representation of color images" by Parkkinen, J., Jaaskelainen, T. and Kuittinen, M. (IEEE 9th International Conference on Pattern Recognition, Rome, Italy, November 14-17, 1988 , Volume 2, pages 933 to 935), one of the database of 218 measured samples published. It can be easily observed from the graphs of Figure 6A and Figure 6B that colors in nature have a more diverse distribution than Munsell colors, and further contain certain distinctive features: for example, the green color 607 in nature depends on the wavelength of about 540 nanometers. The spectral reflectance of chlorophyll has a characteristic peak at about 525 nanometers, whereas colors described as green, relative to Munsell colors (which are artificial pigments), generally have a peak reflectance at about 525 nanometers. As shown in the diagrams of Figures 7A-7C and 8A-8C, the calculation of relative gamut area (as described above) and the chromaticity profile of multi-band filters on color appearance can be conveniently visualized effect. In Figure 7C, the spectral transmittance of a reference filter is shown at 711, which is also a Munsell color selected to best match the white point of the test filter shown at 712. The illuminant is designated illuminant D65 and its spectral radiant flux 710 is graphed in Figure 7B. In Figure 7A, a chromaticity diagram is used to plot the chromaticity coordinates of selected Munsell colors as viewed with a given illuminant and different filters. In the chromaticity diagram, the enclosed solid line 709 is the spectral locus corresponding to the chromaticity coordinates of the monochromatic spectral light, and the line segment 708 is called the purple light connecting line. The white point of the filter is essentially the same and is shown at point 706. The chromaticity coordinates of selected Munsell colors (as viewed through reference filter 711) are shown along the open circles of dashed outlines 701 and 705. The solid circles along solid outlines 702 and 703 show the chromaticity coordinates of selected Munsell colors (as viewed through test filter 712). The inner contour corresponds to a medium saturated selected Munsell color, and the outer contour corresponds to a highly saturated selected Munsell color. By examining the contours, it will be understood that the chromaticity coordinates of the colors (as viewed through the test filter) cover a large area of the chromaticity diagram, and in particular, the chromaticity coordinates appear along There is a clear increase in the separation of the chromaticity coordinates on the red to green axis (green appears primarily near the "front" of the upper left corner of the trajectory (roughly at (0, 0.5)) and red appears essentially at the upper right corner of the trajectory (0.5, 0.5)). Therefore, a test filter (which has a relative gamut area greater than 1.0 compared to the reference filter) can be described as enhancing red-green discrimination. In the example of Figure 7A, the reference colors for the inner contour starting at point 704 and traveling clockwise are: Munsell 10B 5/4, Munsell 10BG 5/4, Munsell 10G 5/4, Munsell 10GY 5/4, Munsell 10Y 5/4, Munsell 10YR 5/4, Munsell 10R 5/4, Munsell 10RP 5/4, Munsell 10P 5/4, Munsell 10P 5/4 and Munsell 10PB 5/4. The reference colors for the outline starting at point 707 and traveling clockwise are: Munsell 7.5B 5/10, Munsell 10BG 5/8, Munsell 2.5BG 6/10, Munsell 2.5G 6/10, Munsell 7.5GP 7/10 , Munsell 7.5GY 7/10, Munsell 2.5GY 8/10, Munsell 5Y 8.5/12, Munsell 10YR 7/12, Munsell 5YR 6/12, Munsell 10R 6/12, Munsell 2.5R 4/10, Munsell 7.5RP 4 /12, Munsell 2.5RP 4/10, Munsell 7.5P 4/10, Munsell 10PB 4/10 and Munsell 5PB 4/10. Continuing with the visualization of color gamut area, the graphs in Figures 8A through 8C show the effects of the same test filter and reference filter relative to natural colors. In Figure 8C, the spectral transmittance of the reference filter is shown at 810, and the spectral transmittance of the test filter is shown at 811. The spectral radiant flux 809 of the illuminant is shown in Figure 8B. In Figure 8A, the white point of the filter is shown at 804. The dashed outlines 807 and 808 correspond to the chromaticity coordinates of the selected natural color (as viewed through the reference filter), and the solid outlines 802 and 803 correspond to the chromaticity coordinates of the same natural color (as viewed through the test filter). viewed). The inner contour corresponds to the appearance of five natural colors, and the spectral reflectances of the five natural colors are also presented in counterclockwise order starting from point 807 at 606, 607, 608, 609 and 610 in the graph of Figure 6B. The outer contour corresponds to the appearance of the most saturated example of natural color available in the previously referenced database. While natural color may be a better choice for analyzing the effectiveness of a filter in an outdoor context (for example, for incorporation into sunglasses), Munsell color provides a visualization that is easier to interpret, so , the remaining figures in this invention use Munsell color for this purpose. To date, examples of multi-band filters for enhancing color appearance, such as those in Figures 7C and 8C, have structures with three rectangular passbands and two stopbands. This filter can be uniquely specified by enumerating the start and end wavelengths of each band giving 6 degrees of freedom. Thus, a computer can be used to: fully enumerate the entire set of possible filters; then rank the performance of each such filter using the associated gamut area metric as described above; and then select the best filter for a desired effect. Optimal filters (such as for enhancing red-green discrimination, or enhancing blue-yellow discrimination, or maintaining normal color discrimination). Increasing the number of degrees of freedom that characterizes a filter can expand the search to a larger set, for example by allowing the transmittance to vary within a frequency band or increasing the number of possible frequency bands. Along these lines, a computer-implemented method for designing optical filters that affect color vision in a desired manner is listed below. Assume that the desired filter includes a pre-filter and a multi-band interference filter in the optical assembly. First, specify the following: the transmittance of the prefilter over the entire visible spectrum; the desired white point of one of the optical filters; the desired minimum total light transmission of one of the optical filters; an illuminant; plural a reference color; and an initial test multi-band interference filter including a plurality of contiguous stop wavelength bands and pass wavelength bands covering the visible spectrum. Then, one or more new experimental multi-band interference filters are generated by changing the stop wavelength band stops and the boundaries of the pass wavelength bands, the transmittance, or the boundaries and transmittance of the initial test multi-band interference filter. device. Next, the white point and total light transmission of the optical filter were determined for each combination of the prefilter and one of the new experimental multi-band interference filters. Next, the effect of the optical filter on color vision was evaluated for each combination of the pre-filter and one of the new experimental multi-band filters using specified illuminants and reference colors. Next, one of the new experimental multi-band interference filters (for the new experimental multi-band interference filter, the optical filter meets the specified white point and the specified minimum total light transmission and affects color vision in the desired manner) Selected to be the multi-band interference filter in the optical filter. In this approach, the prefilter can have a transmission of approximately 100% across the entire visible spectrum. That is, a pre-filter is selected. The initial test interference filter may include, for example, five or more stopbands and passbands in total. Generating a new test interference filter may include, for example, changing the number of passbands, the number of stopbands, or the number of passbands and the number of stopbands in the initial test interference filter. Additionally or alternatively, generating new experimental interference filters may include varying the shape of one or more of the stopband or passband. Assessing the effect on color vision may include any of the assessment methods disclosed in this specification. Methods also include: specifying a color constraint that constrains the appearance of a reference color, such as viewed or illuminated through an optical filter; and evaluating each combination of a pre-filter and one of the new experimental multi-band filters against that reference The effect of color appearance on color; and the selection of one of the new experimental multi-band interference filters for which the optical filter satisfies specified color constraints for use in optical filters as Multiband interference filters. Any of the color constraints disclosed in this specification can be used with this method. As one possible drawback of the above approach, the optimal filter for achieving the desired effect may in some cases not be a member of the filter set under investigation. Furthermore, the above strategy becomes unwieldy due to the doubling of the number of possible filters to be evaluated and the additional free variables. Another related approach is to use a quasi-Newton adaptation method to search among a subset of possible filters and move incrementally toward the desired filter in an evaluated optimal direction. However, in some cases the solution found by this type of method may only be a local optimum. One further difficulty with these methods involving direct enumeration and local search is that it is difficult or impossible to impose constraints on the filter, such as, for example, specifications of the filter white point relative to a selected illuminant. Instead, each test filter typically must be evaluated to determine whether it meets these constraints. To constrain the white point, a filter can be represented as a linear combination of color change pairs of the white point, for example as a weighted combination within a trichromatic color change pair set (i.e., essentially including three different wavelengths of light) , however, this requires a representation with one of thousands of degrees of freedom because the number of such color change pairs is large and quasi-Newton search methods are generally too slow when the search space has so many dimensions. Furthermore, this approach cannot easily implement specifications beyond the additional constraints of the filter's white point. One approach to computationally efficient filter design that implements the specifications of multiple constraint criteria (described in detail below) is to employ a linear programming approach. This approach can have various advantages: a linear program solver uses a sequence of incremental steps to quickly locate the optimal solution, whereas the solution of a linear program is unique and globally optimal (relative to the input). Additionally, the solution can be constrained to meet useful criteria related to the chromaticity and luminescence aspects of color appearance. Commercially available linear program solvers can quickly determine whether a given set of constraints has no solution (i.e., is infeasible), and these solvers can also quickly determine linear programs with thousands of free variables and hundreds of constraints. the best solution. Linear stylization can be used when a problem that can be expressed as a linear system is subject to linear constraints and a linear cost function. Next, details related to how to conceive the design criteria of a filter that affects color vision and how to convert the design criteria into a linear program are elaborated. The filter generation method disclosed below incorporates a linear program solver (abbreviated as LP), which can generally be described as being used to determine the optimal solution for a resource allocation problem subject to linear constraints with respect to a linear cost function. One of the solutions. When applied to the problem of designing filters for color vision, the resources to be allocated can be understood as the transmittance of the filter as a function of wavelength, the linear constraints are derived from the usage requirements of the filter, and the linear cost function Essentially a mechanism that guides a linear program solver toward one of the better solutions within a range of feasible solutions. The method of filter generation by linear programming can be practiced by using a computer to solve a linear program given by the following expression: Minimize c^T x, is subject to the constraint Ax≤b, and Subject to the constraint of 1≥x≥0; Among them, in this method, the linear equation of the vector x is solved, and the transmittance of the filter as a function of wavelengthCalculated by the following expression: like,and If p, then,and; Among them, in this method, f is the designed optical filter,is the transmittance of f as a function of wavelength λ. E is one of the basic optical filter matrices, such that the matrix e_i The behavior is the transmittance of light as a function of the wavelength of each basic filter, and the number of basic filters is N. definitionThe expression is a weighted summation of one of the basic filters, where the weighting coefficient is the corresponding element x_i . The weighted sum is equal to the matrix-vector product q=Ex between the basic filter matrix E and the linear program solution vector q. also,The combined series of two optical filters is represented by the multiplication of the first filter q and the second filter p as a function of wavelength, whereis the transmittance of p as a function of wavelength λ, and p is generally referred to as a "pre-filter" in the present invention, but the filters can be composed in any order. The linear program constraint 1≥x≥0 is equivalent to the constraint 1≥x_i ≥0, where i ranges from 1 to N. Furthermore, c in the above expression is a cost vector that guides the linear program solver towards a solution that provides a filter f that affects color vision in the desired manner. by c^T x calculates the total cost associated with the solution, c^T x represents the vector inner product between the transpose of c and x. A solution that provides a lower total cost x is generally better relative to the required functionality, but other measures of quality can also be used to determine the appropriateness of a particular solution. A in the above expression is a matrix, and b in the above expression is a vector. Ax is the matrix product between matrix A and vector x. At least some of the elements of matrix A and at least some of the elements of vector b are related to: the minimum or maximum transmission level of filter f at one or more wavelengths of light; to one of the white points of the filter Constraints; or constraints on the color appearance of one or more reference lights, as viewed or illuminated through a filter; and/or such transmission constraints of the filter f at one or more angles of incidence. The above expression as a function of wavelength λ can be tabulated by sampling uniformly on one wavelength scale (e.g., using steps of 1 nanometer) or another substantially equivalent scale (e.g., frequency or log wavenumber). The transmittance of the filter (e_i , p, f) specifications. Sampling can also be defined at any scale with uneven spacing between sample points. The basic filter may be, for example, a single passband filter with a passband width of about 1 nanometer, and each filter has a different passband center wavelength. These filters may also be called monochromatic filters and are defined as having the following spectral transmittance:; inis the Dirac Δ function, andIs the wavelength transmitted by the filter, which typically varies between 400 nanometers and 700 nanometers for the entire basic filter set. In this case, the basic filter matrix E is essentially a 301×301 unit matrix. Alternatively, the base filters may be single passband filters each having a width greater than about 1 nanometer, with each base filter having a different passband center wavelength. In some of these variations, the passband can be rectangular (also called a square pulse function) and the spectral transmittance of a basic filter is defined as follows:; inis the central wavelength,is the rectangular bandwidth, and H is the Heaviside step function. A typical choice for a rectangular bandwidth is about 10 nm, in which case the number of basic filters can also be reduced so that there is a 5 nm spacing between adjacent filters. In some variations, the passband may have a Gaussian or one that is Gaussian in nature spectral transmittance, such as defined by:; inis the center wavelength, and the half-peak bandwidth is:. In other variations, the basic filter may be a multi-band filter having two or more passbands, and each basic filter has a center wavelength and/or frequency of the two or more passbands. A wide range of different combinations, in which case the number of basic filters can be larger (eg thousands of combinations). A multi-passband basic filter may be configured, for example, by adjusting the bandwidth and/or band transmittance levels into color-changing pairs relative to illuminant 904 and reference filter 912 (FIG. 9). Any suitable set of basic filters may be used in the filter design method, where a suitable basic filter must have at least one physically achievable transmittance spectrum (e.g., have a transmittance value between 0 and 1), A calculation of the costs associated with the filter must further be implemented, which is described below in connection with the discussion of Figures 12A and 12B. Preferably, the basic filter has compact support (i.e., transmittance is 0 outside a finite interval), so that numerical calculation methods of sparse linear algebra can be applied, including interior point methods for solving a linear equation . It should be observed that f as defined in the above expression includes a weighted summation of basic filters, where the basic filters are generally single passband or multi-passband filters (for example, including as previously described one or more rectangular or Gaussian bands), it can be inferred that the designed filter f can be understood as a multi-band filter, however, the number of passbands is very large in nature (e.g., at least 60) and constitutes The passbands can partially overlap. Therefore, the range of possible filters f that can be designed by the method includes multi-band filters with three or four frequency bands as well as multi-band filters with more complex transmittance curves. However, in practice, as will be shown in the figure, the most useful filter designs usually have three or four characteristics that can be essentially described as frequency bands, but the essential shape of these frequency bands can in some cases be irregular, i.e. Non-rectangular and non-Gaussian. For example, one or more passbands may be described as having a bimodal distribution, or may have a shoulder on one or more sides of the passband, or may be described as a skewed distribution, where the wavelength is In the transmittance function, the slope ratio between the two sides of the passband is between about 4:1 and about 1:4. In a variation on non-Gaussian bands, such passbands may be smoothed with, for example, a Gaussian kernel that is only wide enough to essentially eliminate irregularities and/or sharp transitions, in which case the passbands may be described It is essentially a frequency band center and half-peak width corresponding to a smooth passband. Figure 9 contains a process flow diagram describing a procedure for generating an optical filter (according to a specification of a design criterion). Computer-implemented filter generator operations described in greater detail below are presented in block 903. Design criteria input into the operation of the filter generator (also described in more detail below) may include, for example, cost vector 901 (vector c in the linear program expression provided above), spectral transmittance constraints 902, color appearance constraints 915. Filter white point constraint 908, illuminant 904, reference filter 912, observer 918, basic filter 913 (matrix E in the expression provided above), select pre-filter (above) p in the expression provided in the article, it can be set to be effectively skipped) 919 , the smoothing kernel 920 is selected, and the bias coefficient 923 is selected. Still referring to Figure 9, the basic filter and various other design criteria are input to a three-color constraint calculation operation 910 (described in further detail below with respect to Figure 11), which produces a constraint projection bound 906 (linear program expression The vector b) in and the constrained projection norm 909 (matrix A in the linear program expression). Next, a linear program 907 is formulated from the constrained projection bound 906, the constrained projection norm 909, and the cost vector 901 (as described by the linear program expression provided above). Next, the linear program is solved by a linear program solver 905 , which provides a solution to the linear program as a solution vector 911 . Solution vector 911 is the optimal vector x in the linear program expression provided above. The elements of solution vector 911 are coefficients x_i , which gives the corresponding basic filter e_i (These are the rows of matrix E representing the basic filter set 913) provide the weighting factors. Next, operation 914 performs a summation of the basic filters weighted by corresponding elements of solution vector 911 to provide a first filter, the first filterThen smoothed at 916 (optionally), then biased at 922 (optionally) and combined with a second filter (pre-filter)919 combination to produce designed filter specifications921. This can be achieved, for example, by combining an absorptive prefilterwith an interference filterAnd manufacturing composite designed filters921 , wherein the interference filter component is specified by the output of operation 914 and/or operation 916 . The pre-filter may be transparent in nature (i.e.,uniform or nearly uniform), or may have a neutral density (i.e.,is constant or nearly constant), or may have a broadband transmittance (i.e.,varies smoothly and slowly with wavelength), or may have narrow-band or multi-band transmittance. Methodological considerationsThese properties of p in the specification enable the resulting filter f to meet the input design criteria. Preferred pre-filters are described in detail in conjunction with Figures 24A, 24B, 28A and 28Bchoice. In particular, the use of pre-filters with narrow-band absorbance may be preferable for some applications and is demonstrated and described in detail in connection with Figures 20A and 20B. Simultaneous methods for designing and fabricating interference filters (such as using non-quarter-wavelength optical monitoring) can produce filters with virtually any spectral transmittance curve. However, the number of layers of dielectric material required to implement a particular filter specification varies. Any desired limit on the total number of layers of dielectric material requires, for example, that the spectral transmittance curve has a finite complexity. For example, the slope of transmittance as a function of wavelength must be continuous and bounded. To improve manufacturability, a smoothing operation 916 may be performed on the filter specifications provided by the weighted sum operation 914 . For example, a smoothing kernel 920 may be applied by frequency domain convolution in 916 to the optimal filter provided at operation 914 . The smoothing core may, for example, be a Gaussian core with half the peak width, which is 2% of the central wavelength. In a further example, the smooth core can be a Gaussian core with half the peak width, which is about 10% of the center wavelength, such that the filter can be implemented with a low order dielectric stack (eg, less than about 50 material layers) Specifications. Alternatively or additionally, the basic filter can be smoothed (eg by being sized as a Gaussian filter rather than a rectangular filter). The smoothed filter type output from smoothing operation 916 may then be used as a specification for fabricating a (eg, interference) filter. In general, the amount of smoothing can be adjusted to improve manufacturability subject to the requirement that the desired function of the filter (eg, its effect on color vision) is not significantly degraded by smoothing. For example, the width of the smoothing core can be chosen to be the widest core such that the peak transmission within the passband of the filter is not significantly reduced. Although smoothing is optional, all filter embodiments described herein (as designed by the linear programming approach described above) employ a smooth core having a half-maximum width between about 10 nanometers and about 25 nanometers. Specifically, to improve filter performance, a bias factor 923 can be used to bias the filter specifications toward longer wavelengths ( 922). The selection of bias coefficients is described in further detail in conjunction with FIGS. 29A-29B and 30A-30B. Returning now to the various inputs to filter generator operation 903 (Fig. 9), a cost vector 901 (c in the linear stylized expression above) must be specified so that a cost can be associated with each basic filter. For example, if the basic filters are each single-passband filters, then a functionSpecify a cost as a function of wavelength and the cost of each basic filter is calculated by the following expression:. Alternatively, if the basic filter is a three-passband filter (where each basic filter has three or more passbands), the cost function 901 may be, for example, one of the relative gamut areas of the basic filter. A function, such as the cost associated with a basic filter, can be defined as follows:; inis the color gamut area provided by the basic filter, andIs the color gamut area provided by a best-fit reference filter. The cost vector 901 may be specified at the beginning of the filter design process and not further changed during the design of the filter. Alternatively, the cost vector 901 may be varied during a design process in an iterative design process, such as, for example, the process described in greater detail below with respect to FIG. 12 . The specification of a cost vector provides a way for the filter generation method to guide the linear program solver toward a better filter design because the linear program solver will avoid basic filters that have a relatively high cost. Incorporation (i.e., positive weighting) of optical devices (if none must satisfy one or more constraints). The optimal filter design can vary depending on the intended application of the filter, and therefore, the specification of the cost function should also vary appropriately. For example, Figure 12A shows two functions of cost as a function of wavelength (eg, for use with a set of single-passband basic filters as previously described), where the cost functions are chosen to maximize filtering. The relative color gamut area of the optical device design leads to the method of designing a filter that enhances red and green discrimination. To design a filter that enhances blue-yellow discrimination, these cost functions can be inverted, for example, by multiplying by negative 1. Cost function 1201 is configured to maximize the relative gamut area relative to the selected Munsell color, as shown at 601, 602, 603, 604, and 605 in Figure 6A. Cost function 1202 is configured to maximize relative gamut area relative to selected natural colors, as shown at 606, 607, 608, 609, and 610 in Figure 6B. Other than the same design criteria, the cost function for Munsell colors leads to filter 1204 (Figure 12B) and the cost function for natural colors leads to filter 1203 (see also Figure 12B). It should be noted that the passband in the natural filter 1203 is red-shifted by about 10 nanometers compared to the Munsell color filter 1204, and a similar preference for longer wavelengths is also found in the short wavelength passband. These details are not insignificant. For example, natural filters 1203 result in less green hue distortion. The spectral reflectance of green mainly depends on the chlorophyll content in the plant, and leaf green has a significantly longer lifespan than artificial green pigments. The reflectance peak wavelength is consistent with the analysis of the two different sets of reference colors as previously discussed in connection with Figures 6A and 6B. Referring again to Figure 9, observer 918 is typically a standard observer with normal vision. If the filter design is intended to correct for one of the most extreme defects, a specific defect observer may be selected. Illumination 904 is selected based on the intended use of the filter and the environment, and may be, for example, any suitable illuminant disclosed herein. Reference filter 912 is selected to set the intended white point of the designed filter, where the white point is the chromaticity coordinate of the selected illuminant as viewed through the reference filter, and the designed filter will be Characterized by the same white spot. Reference filters have also been used in a relative gamut area calculation (as described above) to compare the designed filter to a reference filter, such as described below with respect to FIG. 13 . The remaining design criteria inputs shown in Figure 9 are spectral transmittance constraints 902, filter white point constraints 908, and color appearance constraints 915. Each color appearance constraint includes: a reference light (defined by its spectral radiant flux); a luminosity constraint that requires the resulting filter to specify the luminosity of the reference light as viewed through the filter at a bounded interval within; and a selection of chromaticity constraints such that the resulting filter must specify that the chromaticity coordinates of the reference light as viewed through the filter are contained within the convex hull of the bounding chromaticity coordinates. The previously mentioned viewing conditions are also specified with respect to the observer 918 and the pre-filter 919. Additionally, the spectral transmittance constraint 902 and the filter white point constraint 908 are special cases of the color appearance constraint 915 as indicated by the dashed flow arrow. A spectral transmittance constraint can be expressed as a color appearance constraint, where the reference light is a monochromatic light with a specific wavelength, and the luminosity of the monochromatic light is bounded within a certain luminosity interval (it should be noted that a The chromaticity of monochromatic light cannot be changed by any filter). Some spectral transmittance constraints are required; for example, the transmittance must be bounded between 0.0% and 100.0% at each visible wavelength to create a passive optical filter. The filter's white point constraint includes a reference light (which is the selected illuminant) and further provides a luminance equation constraint and a chromaticity boundary. In general, the chromaticity boundary can be of essentially infinitesimal size, allowing the white point to be precisely set. Alternatively, the chromaticity boundary may have a wider boundary, which for example contains an approximately circular area centered on the white point of the reference filter. For color vision needs, the filter white point is typically set or otherwise constrained to be within a central region of the chromaticity diagram corresponding to colors that are not considered to be strong colors. For the design of filters to be used in sunglasses, the illuminant preferably represents daylight (eg, illuminant D65) and has a luminosity bounded by the illuminant between about 8% and about 40%. As mentioned above, a color appearance constraint is specified as a boundary based on chromaticity coordinates and a bounding interval based on the luminosity of a reference light's color appearance. These data can be geometrically understood as a constrained polyhedron in a three-color model, as shown in the diagrams of Figures 10A and 10B. More specifically, a filter that provides a color appearance that satisfies the constraint is configured such that the tristimulus values of the reference light as viewed through the filter are contained in an essentially conical convex polyhedron ( 1001, 1002), wherein the chromaticity boundary forms a closed outline of a wall-like surface (eg, 1005), and the luminosity limit interval defines two cap-like surfaces including a lower luminosity limit 1007 and an upper luminosity limit 1006. The cap-like surfaces are parallel to the isoluminous plane 1004 and are each contained in a plane shifted from the origin by a corresponding upper luminosity limit and a lower luminosity limit, respectively. Each of these wall-like surfaces is contained in a plane intersecting the origin. The chromaticity boundary is specified by the convex hull of a set of chromaticity coordinates that define the walls of the cone 1005 when converted into trichromatic values. Example tristimulus 1003 satisfies this chromaticity boundary if and only if the vector norm of the projection of the trichromatic value onto the inwardly pointing surface normal vector (not shown) of all walls is non-negative. In addition, if and only if the vector norms of the projections of the trichromatic values onto the inward-pointing surface normal vectors (not shown in the figure) of the upper cover and the lower cover are respectively greater/less than the lower luminosity limit and the upper luminosity limit, Then the example tristimulus value 1003 satisfies the luminosity limit. These surface normal vectors are vectors in three-color space that, by definition, are perpendicular to the plane containing a surface. If the lower limit of luminosity is zero, then the cone reaches one of its vertices at the origin. If the luminosity has no upper limit, then the cone extends infinitely in the same direction as the luminosity response line. The geometry of this generalized cone allows a color appearance constraint to be transformed into a system of linear constraints, as described in additional detail below. Referring again to Figure 9, the color appearance constraint 915 is converted into a set of linear constraints through the calculation at 910. The operation at 910 is iterated with respect to each color appearance constraint 915 and each basic filter 913 to result in a linear constraint projection bound 906. Vector and matrix constraining projection norm 909. The process flow chart of FIG. 11 further details the conversion of a color appearance constraint into a linear constraint of a system, where the three-color constraint calculation 1102 corresponds to operation 910 in FIG. 9 . Herein, a color appearance constraint 1101 may be specified as a reference light 1105, a chromaticity boundary 1106, and a luminance bounding interval 1104. These bounds can be converted into a generalized polyhedral pyramid in the three-color space of the observer 1103 (operation 1109), as explained in conjunction with the description of Figures 10A and 10B. From the resulting geometry, operation 1109 provides: a matrix 1112 of vectors normal (perpendicular) to the surface of the polyhedron and pointing inward from the surface of the polyhedron; and offsets from the origin of planes containing a surface 1113 Shift a vector that is zero for wall surfaces and equal to the upper and lower luminosity limits for cap surfaces as described previously. Next, the interaction between the bounding geometry of the color constraint and each elementary filter 1107 is determined as follows. Calculate the transmittance 1108 of the reference light 1105 through the basic filter 1107, then calculate the transmittance 1111 through the pre-filter 1210, then calculate the retinal photopigment absorbance 1115 of the filtered light received by the observer 1114 ( that is, visual light transduction), resulting in trichromatic values 1117 corresponding to the reference light as viewed through the base filter and the pre-filter. Next, a matrix-vector product 1116 is used to project the trichromatic values 1117 onto the surface normal vectors (in matrix 1112) of the constrained polyhedron, resulting in a set of vector lengths (range) of trichromatic values for each surface of the constrained polyhedron. ) 1119 and corresponding bounds 1118 that will ensure suppression relative to color appearance constraints. These constrained projection norms are linear properties of the base filter with respect to the constraints. For example, if the trichromatic value projected onto a surface normal vector has length zero, then the base filter is effectively orthogonal to the constraint and any number of filters can be incorporated without violating this particular bound. in the solution. If the constraint projection norm is nonzero, then the magnitude of the norm gives the ratio that causes the designed filter to move toward or away from the constraint boundary as a function of the linear weighting of the basic filter. Referring again to Figure 9, these results are accumulated in the constrained projection norm matrix (A in the above linear program expression) 909 and the constrained projection bound vector (b in the above linear program expression) 906, where the results are now Presents a suitable format that is compatible when incorporated into linear program 907. In some embodiments, a color appearance constraint 1101 (FIG. 11) may also include the angle of incidence of the reference light 1105 relative to the base filter 1107, in which case an appropriate transformation may be applied to correctly calculate 1108 and 1111 The resulting transmission of light in such that the trichromatic values of the reference light as viewed through the basic filter and the pre-filter also take into account that angle of incidence of the reference light. For example, if the filter is to be fabricated as an interference filter, the angle of incidence can be used to displace the basic filter (based on a percentage of wavelength) according to Snell's law. (See, for example, curve 1601 in Figure 16A). Additionally, if the prefilter is of an absorbing type, the calculation can take into account path length differences according to Beer-Lambert's law. Then, the composite filter f can be expressed by the total composition of components q = Ex and p, such that the transmittance of f at an angle of incidence θ radians away from the surface normal vector can be expressed asAnd it is approximately represented by the following expression:; where e_i The effective refractive index has a value of n of about 1.85, and for θ between about 0 degrees and about 45 degrees, this approximation is sufficient. Incorporating color appearance constraints at non-zero angles of incidence is particularly useful for providing filter designs with improved color stability under non-ideal viewing conditions. To evaluate the optical filter of the present invention, the white point displacement of an optical filter f relative to the incident angle θ is defined by the following expression:, Among them, in the above expression, (u₀ ,v₀ ) and (u₀ ,v₀ ) are the CIELUV (u', v') chromaticity coordinates (relative to the CIE 1931 2-degree standard observer) of an illuminant D65 viewed through a filter at normal incidence and θ degrees deviated from incidence. Instead, the white point displacement is calculated relative to the CIE 1964 10-degree standard observer. Referring now to the process flow diagram of Figure 13, in some embodiments, a filter design process is iterative. This iterative process may begin with an initial specification of filter design criteria 1301 input into the filter generator 1303 of the design program 1302 . Design criteria 1301 may include, for example, some or all of the design inputs shown in FIG. 9 . Additional process-related information 1309 may also be input into the selected manufacturing analysis program 1308 (described further below) also within the design program 1302. This manufacturing information may include, for example: time constraints on the use of manufacturing equipment; manufacturing costs or budgets; and physical constraints on filter structure, such as, for example, on thickness, thickness uniformity, composition, or use in manufacturing a Limitations on the uniformity of the composition of the material layers of the filter. Filter generator 1303 may, for example, be the same or substantially the same as filter generator 903 described above with reference to FIG. 9 . Filter generator 1303 generates a test filter 1305, which may be, for example: an optimal filter type related to transmission as a function of wavelength or frequency (e.g., output by operation 914 in Figure 9); A smooth optimal filter type that relates to transmission as a function of wavelength or frequency (such as output by operation 916 in Figure 9); or a composite filter design that incorporates an optional pre-filter (For example, output by operation 917 in Figure 9). The optical performance of test filter 1305 (FIG. 13) may optionally be analyzed at operation 1307. This performance analysis may include, for example, calculating the relative gamut area 1314 relative to a reference filter 1304, an illuminant 1306, and a set of reference colors 1301 (all of which are optional additional inputs to the design program 1302). The relative gamut area may be calculated, for example, using the procedure described above with reference to FIG. 4 . If the relative gamut area is undesirable (ie, too high or too low), the cost function may be adjusted at operation 1315 and the filter design criteria 1301 updated accordingly before another iteration through the design process 1302 . In embodiments in which the cost function is adjusted as just described, the first iteration of the design process 1302 may utilize, for example, two Gaussian functions, each characterized by a center wavelength, a width, and an amplitude. Sum form of an initial cost function as a function of wavelength. The cost function may further include a monotonic bias incorporated by adding or multiplying with any monotonic function. For example, a monotonic function can be linear. When the design program is iterated and the relative gamut area is calculated in each iteration, the cost function can be adjusted using any suitable conventional maximization method that adjusts the cost function to increase (or, alternatively, decrease) the gamut area. Adjusting the cost function may include, for example: changing parameters characterized by a Gaussian; changing parameters characterized by any monotonic bias present; or changing parameters characterized by a Gaussian and changing parameters characterized by a bias. Any other suitable form of the cost function or parameterization of the cost function may also be used, or any other suitable method for adjusting the cost function may be used. As an alternative to using relative gamut area to assess the performance of a test filter with respect to color discrimination, in some embodiments, the distribution of a reference color in chromaticity space is characterized by calculating one or more standard deviations of the distribution . These standard deviations may be calculated at projection distributions along the red-green and blue-yellow axes of the chromaticity space or along any other suitable choice of directions or axes. Projections onto the deuteranopia confusion line may be better used to evaluate filters to be used by deuteran-weak observers. Projections onto the protanopia confusion line may be better used to evaluate filters to be used by protanopic observers. Projection onto the confusion line for type III color blindness may be better used to evaluate filters to be used by observers with type III color blindness, or may be used to evaluate filters that ensure: along a vertical or nearly vertical axis of red-green discrimination Complementary increases in standard deviation do not negatively affect blue-yellow discrimination. A test filter that increases one or more of these standard deviations compared to a reference filter may be considered to enhance color discrimination along one or more corresponding directions in chromaticity space. A test filter that reduces one or more of these standard deviations compared to a reference filter may be considered to impair color discrimination along one or more corresponding directions in chromaticity space. Similar to what was described above with respect to relative gamut area, in some embodiments, the cost function used in the design process 1302 can be iteratively adjusted to maximize or minimize the chromaticity space as viewed through the test filter. One or more standard deviations from the reference color distribution. Now return to the performance analysis operation 1307 (Fig. 13) in the design process 1302. Operation 1307 may also assess compliance with industry or government regulatory standards (for example, such as the American National Standards Institute (ANSI) Z80.3-2010 (2010 (Approved on June 7) or ANSI Z87.1-2010 (Approved on April 13, 2010), the full texts of these two standards are incorporated herein by reference). This analysis can be performed, for example, to ensure that the test filter is safe for use by a human observer in the intended application (eg, when operating a motor vehicle). Based on the results of this standards compliance analysis 1313, operation 1316 may conceive of additional or modified color appearance constraints for the filter design criteria 1301 to guide the filter design process 1302 to comply with the standards. In addition to or as an alternative to performance analysis 1307 , test function 1305 may be analyzed for manufacturability at operation 1308 . This operation may produce, for example, an estimated manufacturing cost 1312 and a manufacturing specification 1311 that provides tolerances and/or processing procedures. The estimated manufacturing cost 1312 may be expressed, for example, as a total manufacturing time, a total financial cost, or both. Based on the estimated manufacturing cost 1312 , operation 1317 optionally adjusts color constraints, smoothing (eg, operation 916 in FIG. 9 ) or color constraints and smoothing to direct the filter design process 1302 toward one with a lower estimated manufacturing cost. filter. For example, the width of smooth core 920 (FIG. 9) may be increased, or the constraints on spectral transmittance in certain regions may be appropriately relaxed or tightened. If the constraints added or modified at operations 1316 or 1317 result in infeasible design criteria (i.e., design criteria that cannot solve the linearly formulated problem), a linear program solver (eg, 905 in Figure 9) can detect this situation . Constraints can then be relaxed or revised until feasibility is restored. The entire filter design and analysis process 1302 can be repeated until a satisfactory (eg, optimal) filter design is achieved, at which time the manufacturing specifications 1311 can be adopted and used to fabricate the optical filter. Filters as described herein may filter light based on, for example, absorption, reflection, or absorption and reflection of light. Filters may include, for example, any suitable combination of interference filters, absorption filters, and polarizing filters (polarizing filters typically include a pair of linear polarizers surrounding a wavelength-selective polarization rotator). Interference filters and interference filter portions of composite filters (as disclosed herein) may, for example, be fabricated using about 12 to 200 layers with a total thickness of about 6 microns per 100 layers and having about Dielectric coatings with a typical effective refractive index between 1.8 and about 1.9. Such multilayer interference coatings may be applied, for example, to glass or optical polymer substrates having a base curve between 0 and about 10 diopters, where diopter is defined as a refractive index calibrated to 1.523 by a lens meter. The measured value of the spherical curvature. The interference filter designs disclosed herein and intended for use in eyeglasses may also be specified for use in combination with a circular polarizer, details of which are given in Figures 24A and 24B and the accompanying description. Further designs of the interference filters disclosed herein and intended for use in eyeglasses may also be specified for use in combination with a neutral density absorber or a broadband absorber or a narrowband absorber, details of which are shown in Figure 28A and 28B and the accompanying description and are disclosed in conjunction with the discussion of FIGS. 20A and 20B. In general, in what follows, it is assumed that the process involves (at least) physical vapor deposition of dielectric material in a sequence of coatings having different thicknesses and refractive indexes to form an interference filter. Industrial machines and processes are readily available and enable high-throughput, high-precision fabrication of such filters, which include filters with irregular configurations of regions and/or passbands of partial transmission. Any other suitable process may be used instead or in combination with this physical vapor deposition process. If not otherwise constrained, filters designed to enhance red-green discrimination may tend to reduce the transmission of yellow light, which may cause a yellow traffic signal to appear darker and more like red (eg, orange or reddish). Similarly, a filter that enhances blue-yellow discrimination may tend to cause green light to appear more similar to blue or white (eg, unsaturated). To avoid this and similar potential problems, filters incorporated into general-purpose eyeglasses (such as sunglasses), for example, can be configured so that the resulting eyeglasses provide one of certain colors (specifically, the colors of average daylight and traffic light). Adjust appearance. For certain glasses, this may require, for example, meeting industry or government regulatory standards. Configurations that meet the requirements can be designed using the methods described above, such as by applying suitable constraints to the filter design. A luminosity constraint ensures that light (eg, daylight, traffic light) appears appropriately brighter when viewed through filtered glasses. A chromaticity constraint, which is specified as a convex boundary in chromaticity coordinates, ensures that such light falls within the constrained boundary and is therefore perceived by the observer as having a hue with the correct standard color name, that is, ensuring that daylight is essentially white; and traffic signals are correctly identified as, for example, traffic signal green lights, traffic signal yellow lights, and traffic signal red lights. Figure 14A shows an example of this "general use" constraint for general purpose glasses. Example chromaticity boundary 1401 states: Yellow traffic lights do not appear orange or red. Point 1402 shows the chromaticity of a yellow traffic light as viewed through an unconstrained red-green discrimination enhancement filter, and point 1401 shows the chroma of a yellow traffic light under a compliant red-green discrimination enhancement filter. Example chromaticity boundaries 1406 specify that green traffic lights do not appear yellow, blue, or overly desaturated. Point 1404 shows the chromaticity of the green traffic light, which is essentially the same under both filters. Example Chroma Boundary 1405 states: Daylight does not exhibit strong colors. Point 1403 shows essentially the same chromaticity of sunlight under the two filters. Figure 14B shows a graph 1408 of the spectral radiant flux of daylight, a graph 1407 of the spectral radiant flux of a green traffic signal, and a graph 1409 of the spectral radiant flux of a yellow traffic signal. Figure 14C shows the transmittance 1411 of the unconstrained filter and the transmittance 1410 of the constrained filter. In filter 1410, the effect of the constraint is evident in that the long passband has essentially been split into two passbands to form a four-passband filter. As shown in this example, the limiting constraint is on the reddest side of the yellow chroma boundary. However, as shown in the further description in conjunction with Figures 15A and 15B, it may be better to force the split passband to have an irregular shape (such as having a shoulder on the short wavelength side for the replacement split sub-band) a single passband, or smoothing a split passband with a core that is wide enough to essentially merge the subbands into a single passband. A further concern related to the incorporation of multi-band filters into eyeglasses is that the stopband can significantly suppress the luminosity of some narrowband light, such as from light-emitting diodes, lasers and sodium vapor lamps. In some embodiments, it may be preferable to set a lower limit of the minimum transmittance of a filter to ensure a minimum brightness of all monochromatic light. For example, in Figure 15A, graph 1501 shows a lower spectral transmittance limit of about 7% transmission between about 450 nanometers and about 650 nanometers. A filter incorporating constraints is illustrated by its spectral transmittance plot 1504 in Figure 15B. Filter 1504 is a four-passband filter to which a fourth passband has been added to satisfy a yellow traffic light constraint (as described in connection with Figures 14A-14C). In some embodiments, this additional passband may preferably be converted into a band shoulder on the short wavelength side of the long wavelength passband. This change may be preferable because the resulting filter may provide one of the more stable appearances of yellow light (specifically, narrow-band yellow light) with respect to changes in angle of incidence, assuming that a multi-band filter is incorporated with An interference filter is characterized by a blue shift in the spectral transmittance at an angle of incidence other than normal incidence, as described further below. Replacing the fourth passband with a shoulder may be accomplished, for example, by adding a minimum spectral transmittance constraint in the desired region (eg, as shown by graph 1502 in Figure 15A). In graph 1502, the minimum transmission has been set to about 18% between about 580 nanometers and about 635 nanometers. The resulting modified filter transmittance is shown by plot 1503 (Fig. 15B), which shows the depicted shoulder on the short wavelength side of the long wavelength passband. A passband with a shoulder as just described may also be used at other locations within the three-passband filter. For example, in some embodiments, it may have the effect of adding a minimum transmittance constraint to cause a shoulder on the long wavelength side of the mid-wavelength passband to reduce narrowband fluorescent lamps ( Color distortion such as FL10 to FL12). In a further example, some embodiments have a shoulder on either the short wavelength side or the long wavelength side of the short wavelength passband, which is described in more detail in connection with Figures 16A and 16B. In further examples, the passband may have an irregular shape (i.e., non-rectangular and non-Gaussian) with one configuration that is essentially a bimodal distribution, where the two modes at least partially overlap; or the passband may There is a shoulder on one or more sides of the passband; or the passband may be described as a skewed distribution in which the slope ratio between the two sides of the passband in transmittance as a function of wavelength is between about 4 :1 to approximately 1:4. One further constraint applicable to these filters is on the white point, ie, the chromaticity coordinate of a typical illuminant (such as daylight). If the white point is within a moderate radius of the neutral point (i.e., the chromaticity coordinate corresponding to unfiltered daylight), the filter can be considered non-color-promoting. Thus, the visual mechanism of chromaticity adaptation will enable the observer to adjust to a new color balance after wearing the glasses for several minutes. In some embodiments, it may be preferable to minimize this adjustment, such as by configuring the white point to be neutral (i.e., such that the chromaticity coordinate of daylight is at or nearly at the center of region 1405 (FIG. 14)) Waiting time. In those cases where a neutral white point is expected, a constrained region can be given for the appearance of daylight, for example, the (x,y) chromaticity coordinates of illuminant D65 are approximately (0.31, 0.33), and The best filters provide a white point within about 0.05 units of this point. In some cases, in particular, such as when the cost function is configured to maximize or minimize the transmission of blue light, it may be preferable to allow the white point to be within a larger area (eg, area 1405 (FIG. 14) any position). In further cases, a specific hue of the white point may be specified for other reasons including pleasing to the eye. As mentioned above, the transmission spectrum of a multi-band interference filter is sensitive to the angle of incidence deviation of the incident light. Specifically, the effective optical thickness of an interference filter (i.e., the wavelength at the refractive index boundary at which destructive interference occurs within the filter) decreases as the angle of incident light away from normal incidence increases. At small wavelengths, the spectral transmittance suffers a shift toward one of shorter wavelengths (a blue shift). Normal incidence is defined by a vector normal to the surface on which the interference filter is deposited. In this document, normal incidence may be referred to as zero degree angle incidence, ie, the angle means the deflection from the normal vector. Additionally, a multi-band filter incorporating an absorbing filter can change the transmittance according to the Beer-Lambert law, where absorption tends to be attributed to transmission as the angle of incident light away from normal incidence increases. The greater the effective path length of the absorbing medium increases. In any of the above variations, the multiband filter f may include an absorption filter p and an interference filter q, where the change in transmittance of p as a function of angle is according to the Beer-Lambert law, and The change of the transmittance of q as a function of angle is based on Snell's law, so that the transmittance of f at an incident angle of θ radians deviating from the surface normal vector can be expressed asAnd it is approximately represented by the following expression:,; Among them, in the above expression, the effective refractive index of q is n with a typical value of about 1.85, and the spectral transmittance of p at normal incidence is, the spectral transmittance of f at normal incidence, the spectral transmittance of q at normal incidence, and this approximation is sufficient for θ between about 0 degrees and about 45 degrees. The incidence angle sensitivity of a filter has implications related to the incorporation of the filter into a device such as eyeglasses, where the effective angle of incidence of light has significant variation as a function of position on the surface of the lens (along with Figure 29A 29B and 30A-30B), and also has implications associated with incorporating such filters into devices such as lamp assemblies, where a perfect beam of an illuminator cannot be achieved collimation. The change in the spectral transmittance of a filter as a function of incident angle is one of the physical properties of the filter. However, the main concern is the perceptual implications of these changes, which can be quantified by measuring the changes in chromaticity and luminosity of a reference light as viewed through the filter as a function of angle of incidence. In particular, it is useful to consider changes in the chromaticity coordinate (i.e., the filter white point) with respect to the illuminant because the change in the white point as a function of incidence angle is generally the same as that under the illuminant. These changes are related to the entire set of reference colors being viewed. Additionally, additional color appearance constraints can be constrained at two or more angles of incidence (e.g., 0 degrees and 25 degrees off the normal axis or 0 degrees) by employing additional color appearance constraints in the filter generation method as previously described. degree, 25 degrees and 35 degrees), so that the chromaticity coordinates of the illuminant remain essentially unchanged at the specified angle and intermediate angles. In Figure 17C, graph 1707 (similar to graph 811 of Figure 8C) shows the spectral transmission of an example filter that provides enhanced red-green discrimination. Graph 1707 shows the spectral transmission of the filter at normal incidence, and graphs 1706 and 1705 show the (blue) filter at approximately 20 and 30 degrees off-normal incidence, respectively. shift) spectral transmission. Figure 17A also shows the effect on the appearance of selected outlines of Munsell colors as viewed through three filters. Profile 1703 corresponds to the normal filter (0 degrees incident angle), profile 1702 corresponds to the first shifted filter (approximately 20 degrees incident angle), and profile 1701 corresponds to the second displaced filter (approximately 30 degrees incident angle) ). It should be understood from these profiles that the color appearance under this filter is not stable with respect to these changes in the angle of incidence. Furthermore, we observed that filters with the greatest red-green discrimination enhancement tend to locate the passband in which the change in absorbance as a function of wavelength of one or more retinal photopigments is greatest. Therefore, the best filter for enhancing color discrimination (specifically, for enhancing red-green discrimination) is also the worst filter for providing a stable color appearance. In Figure 16B, graph 1603 (similar to graph 1503 of Figure 15B) shows the spectral transmission of an example filter that provides enhanced red-green discrimination. Graph 1604 shows an example of a spectral transmission similar to 1603 that provides enhanced color appearance and also provides stable color appearance by constraining the white point to be substantially the same at normal incidence and approximately 30 degrees off normal incidence. Spectral transmission of the optical filter. Multi-band filters that provide stable color appearance may, for example, achieve stability by having frequency bands positioned and/or shaped such that the stimulation of each of the three cones changes when viewing a stable reference light Approximately linear in the angular range and the variation between the three cells essentially describes a system with at most one degree of freedom, where this degree of freedom only acts in the direction of the luminescence. For example, in some embodiments, these frequency bands may be preferably located near the wavelength of peak sensitivity of one or more of the retinal photopigment absorbances, or may have a double peak as a function of incidence angle within a desired range formula distribution or other irregular shapes (which are used to make stimulus changes constant or almost constant). In a further embodiment, the shape of a passband (eg, a long wavelength passband) can be configured such that the change in stimulation of long wavelength cones is inversely proportional to the change in stimulation of medium wavelength cones as a function of incident angle, thus ensuring The required restrictions on degrees of freedom to maintain constant chromaticity. However, we have found that these band positions and/or shapes are generally suboptimal for enhancing color discrimination, and therefore one utility of the linear programming approach may be based on the fact that it provides a solution that satisfies a color stability constraint, This solution maximizes color discrimination enhancement. Specifically, these changes in filter band position preferably occur in the outermost frequency bands. For example, the rate of change of stimulation of short-wavelength cones can be made substantially constant by positioning the short-wavelength band at approximately 450 nanometers. Alternatively, in some cases, it may be preferable to split the short wavelength passband near the peak of the short wavelength cone absorbance (such as shown in graph 1605), whereby the passband may be described as having a pair of Peaked distribution (having a first mode at about 435 nanometers and a second mode at about 455 nanometers). In a further example, the long wavelength passband is characterized by a bimodal distribution with a first mode at approximately 620 nanometers and a second mode at approximately 650 nanometers, or may have a skewed distribution, a convex shoulder (usually on the short wavelength side) or other irregular (i.e., non-Gaussian) distribution. The behavior of a filter with a stable white point relative to a range of incidence angles is shown in the graphs of Figures 18A-18C. Figure 18C shows the transmittance of the filter at normal incidence in graph 1807 and the transmittance of the filter at approximately 20 degrees of incidence in graph 1806. It can be observed in these plots that the split sub-band structure in the short wavelength region identified by reference numeral 1805 essentially acts as a comb filter tuned to be stable upon wavelength shift. The illuminant whose color appearance has been stabilized is a daylight illuminant, as shown in graph 1804 in Figure 18B. In the chromaticity diagram of Figure 18A, the chromaticity coordinates 1803 of the illuminant are the same at the two incident angles. Figure 18A also shows the effect on the appearance of selected profiles of Munsell colors. Profile 1801 corresponds to a normal filter (0 degrees incidence angle), and profile 1802 corresponds to a displaced filter (approximately 30 degrees incidence angle). As can be understood from the position of these contours, the filter provides a moderately stable appearance of these reference colors, with most of the loss of saturation occurring primarily with the highest saturated colors (e.g., as described previously in connection with the Munsell contours of Figure 8A) associated. The chromatic stability demonstrated by this filter can significantly reduce the appearance of a "hot spot" in the center of the lens (caused by incident angle-induced blue shift) and generally contribute to improved visual comfort. For example, as shown in Figure 18C, a filter that provides color stability may provide weaker red-green discrimination enhancement due to the effect of the constraints imposed. In some embodiments, it may be preferable to incorporate a pre-filter with a narrow band absorbance, where the absorption band(s) are located near where the stopband in the filter design is intended. Therefore, a composite filter including a narrow-band absorption filter and an interference filter can achieve the desired color stability without degrading the desired color enhancement. Two examples of such filters are shown in Figures 20A and 20B. In Figure 20A, the solid curve at 2001 shows the spectral transmittance of an absorbing filter including neodymium in a glass substrate. Neodymium is a rare earth material characterized by a strong absorption band at approximately 590 nanometers and a secondary absorption band at approximately 520 nanometers. In Figure 20B, the solid curve at 2002 shows the transmittance of an interference filter that when combined with the neodymium absorbing filter provides enhanced red-green discrimination and within 0 to 30 degrees of incidence angle for stable color appearance. Referring again to Figure 20A, the dashed curve at 2001 illustrates the spectral transmittance of an absorbing filter including narrow band organic pigments Exciton P491 and Exciton ABS584 in a polymer substrate. Exciton P491 is characterized by a strong absorption band at approximately 491 nanometers, and Exciton ABS584 is characterized by a strong absorption band at approximately 584 nanometers. In Figure 20B, the dashed curve at 2002 shows the transmittance of an interference filter that when combined with the organic pigment filter provides enhanced red-green discrimination and incident angles from 0 degrees to 30 degrees. Stable color appearance. These examples can be designed by incorporating the absorption filter as a pre-filter by linear programming methods as previously described. To provide color stability to a normal observer, it is generally desirable to constrain the chromaticity coordinates such that the white point shift is less than about 0.01 units relative to the CIELUV (u',v') chromaticity space and constrain it relative to about 0 degrees to about Angle between 35 degrees CIE 1931 2 degree observer. In some cases, the angular range may be increased to about 0 degrees to about 45 degrees. The displacement tolerance can be increased to approximately 0.02 units for observers with deuteranomaly, and can be further increased to approximately 0.04 units for observers with protanism or severe deuteranomania because of this Both observers are insensitive to color shift and their color perception is not necessarily fully characterized by a standard observer model. In addition, for such anomalous observers (whose color matching function is significantly different from that of the CIE 1931 2-degree standard observer), an observer-specific color matching function can be used to calculate the constraints to achieve color stability. In such cases, the resulting filter may have the following properties when analyzed for white point displacement stability according to the CIE 1931 2 degree observer: the white point displacement function is at an angle between about 20 degrees and about 40 degrees incident angle There is a local minimum at; and the distance from the local minimum to the normal white point is less than about 0.02 units. A geometric model of a lens and eye (e.g., where the lens incorporated into the glasses and located in front of the eye) can be used to calculate the effective angle of incidence as a function of lens position and the relative importance of the effective angle of incidence as a function of lens position. The effective angle of incidence is thus defined as the angle between the normal vector of a lens at a lens position and the normal vector of a beam of light passing through that lens position to be imaged onto the retina of the eye. The geometric model as mentioned previously is shown in Figure 29A (top view) and Figure 29B (perspective view). Here, the geometric shapes of the left eye and the right eye are represented by hemispheres 2904 and 2905 respectively. The human eye (usually the eye of an adult) has a radius of curvature of approximately 12.5 mm and an interpupillary distance of approximately 60 mm. Color perception is primarily derived from vision in the central 10 degrees. However, the eye can also rotate in its socket, so the angular range required for color perception is greater than 10 degrees. The geometric shapes of the left and right lenses (having a typical shape of eyeglasses) are represented by spherical segments 2901 and 2902. Dashed arrow 2906 illustrates a beam of light passing through a central location on the lens, and dashed arrow 2909 illustrates a beam of light passing through a distal location on the lens. These light beams also generally image the center and distal positions of the retina. Shown at 2907 and 2908 are the surface normal vectors of the lens at the location where it passes through these beams. The lenses in the glasses may have a radius of curvature between about 50 mm and about 150 mm (in this example, the radius of curvature is 87 mm). Since this radius is significantly larger than the radius of the eye, the angle between the incident beam and the surface normal vector at the corresponding lens position tends to increase with increasing distance from the center, as shown in Figure 29A and Figure 29B from 2908 to 2909 (compared to the angle between 2907 and 2906). For any frame pattern (e.g., the edge profile of a lens and the positioning of the lens relative to the eye) and any lens curvature, the lens position can be calculated (e.g., using a computer) from the geometric model just described by The effective angle of incidence of the function: iterates over points located on the lens; constructs the surface normal vector and the retinal image beam; and then calculates the angle between the two vectors at the surface location. The results of this calculation are shown in the profile diagram of Figure 30A, where the boundary 3004 indicates the edge of a lens, and the interior profile shows the effective angle of incidence as previously described. For example, the effective angle of incidence is about 10 degrees along profile 3001, At contour 3002 it is about 20 degrees, and at contour 3003 it is about 30 degrees. Next, it is useful to calculate the relative importance as a function of the effective angle of incidence. Referring now to Figure 30B, one of the functions of relative importance as a function of effective angle of incidence consists of the product of two components: first, an estimate of the proportion of the lens surface area viewed at a particular angle; and second, an estimate along an axis. An estimate of the likelihood that the eye will be able to see through the lens at a particular angle. In this article, a Gaussian statistical model is used to estimate the directional distribution, as illustrated by curve 3007 with a standard deviation of about 10 degrees. Thus, the eye is most likely looking along the normal angle of incidence. However, it should be noted that there is only a single point on the lens where the angle of incidence is normal (eg, point 3005 in FIG. 30A ) and the surface area of the lens is, for example, between 10 degrees and 15 degrees (eg, between 10 and 15 degrees in FIG. 30A ). (between contours 3001 and 3006 in 30A). On the surface of a typical lens, the angle of incidence is up to about 35 degrees from the normal, and within this range, the area ratio of the lens surface as a function of degree increases approximately linearly, as shown by curve 3009 in Figure 30B represented. The product of the area weighting curve and the directional distribution curve gives an importance weighting function, such as that shown at curve 3008. Therefore, the importance-weighted PGAI can be defined by the following expression:,and, inis an exponential function, θ is the effective incident angle ranging from 0 degrees to 30 degrees,are the test filter f and the reference filter as viewed or illuminated at an angle of incidence θPGAI,is the standard deviation of the eye orientation distribution, which typically has a value of about 10 degrees, and k is a weight normalization factor. To evaluate the filters of the present invention, two specific series of equations are given for the importance weighted percentage increase in color gamut area, where the standard deviation of the eye orientation angle is set to approximately=10 degrees and the reference color is designated as D15 or natural sample. These series of equations are given by the following expressions:,,and which have been previously provided in this invention for calculation ofandconditions. Specifically, the above expression isThe defined performance measure can be used to classify the properties of a filter f, and can be used in filters if the white point of the filter is neutral and the white point remains neutral over a moderate range of angles of incidence. The percentage increase or decrease in absolute effectiveness between groups. in the text,Use of the calculation is limited to filters that have a white point that is neutral and stable relative to these angular changes. For values between approximately -10% and approximately 10%value, the filter can be described as providing essentially normal color discrimination. For values between about 10% and about 40%, the filter can be described as enhancing red-green discrimination, with larger values corresponding to better performance. For values less than about -10%, the filter can be described as enhancing blue-yellow discrimination. The values mentioned previously assume that the filter provides an essentially neutral white point, i.e. (x,y) of the illuminant D65 for all or nearly all angles of incidence between 0 degrees and about 30 degrees. The chromaticity coordinates are approximately (0.31, 0.33). As mentioned previously, estimates of color gamut area can vary with white point, so filters that are not stabilized by white point shift cannot be meaningfully evaluated using an importance-weighted PGAI metric. Additionally, some hues of the white point (specifically, green) can provide larger values for PGAI, however, such increases do not necessarily correspond to enhanced color discrimination. In further embodiments, the calculation may also take into account changes in physical thickness caused by a manufacturing process. For example, in physical vapor deposition onto a curved substrate, coating thickness tends to decrease with distance from the sputter source and/or the effective angle of incidence between the sprayed particles and the surface normal to the curved substrate. In a further embodiment, the calculation of the effective angle of incidence as just described can be used as the basis for a manufacturing specification such that the filter is fabricated on a curved substrate such that the filter has a physical thickness profile such as The effective angle of incidence is compensated by having a profile that increases thickness toward the edge of the lens (eg, increases linearly from the normal solid thickness at the center to approximately +10% solid thickness at the edge of the lens). An interference filter can be fabricated to achieve an optical thickness that is constant or substantially constant relative to the effective angle of incidence at all or nearly all locations on the lens. In some embodiments, performance analysis of a filter may include using relevant importance data to determine the importance-weighted average performance of a filter when incorporated into eyeglasses. The importance-weighted average performance can be improved by adjusting the spectral transmittance specification of the filter (specifically, by red-shifting the specification). For example,The spectral transmittance of can be shifted toward longer wavelengths, as calculated by the following expression:,and; inis one of the coefficients for determining the displacement, andSelected to maximize the importance weighted average relative gamut area increase and/or decrease and/or standard deviation along one axis of the color space. alternatively,Some other performance metrics may be selected to improve, such as reducing the importance weighted average solar blue light transmittance. Because the typical amount of bias required is usually about 1% to about 4% (=1.01 to 1.04), so the optimal offset coefficient can be determined effectively by expressing the value between about 1.0 and about 1.1 in a table.. For example, a red-green enhancement filter with a mid-wavelength passband at about 530 nanometers may preferably be red-shifted to about 535 nanometers (=1.01) with improved importance weighted average relative gamut area. Another aspect related to the incorporation of multi-band filters into eyeglasses (in particular, such filters include an interference filter) is the management of reflectivity on one or both sides of the lens. Has transmittanceThe reflectivity of an ideal interference filter is the transmittancecomplement, defined by the following expression:. For example, a filter incorporated into a pair of sunglasses may have a light transmission of about 20%, so if the filter was only made to be an interference filter, the filter would have a light transmission of about 80%. 1. Light reflectivity. This high reflectivity can cause significant visual discomfort because the user can see the image of the object behind the object or the image of his or her own eyes reflected in the lens. For general use, the light reflectance on the inner surface of the lens should be at most about one-fifth the light transmittance of the lens, although in some cases light reflectance up to about one-half the light transmittance is acceptable. High reflectivity can be partially mitigated by improved shielding around the frame (e.g., utilizing side shielding on the temple arms). An absorption filter (such as the one described previously) can significantly improve the reflectivity on one or both sides of the lens, e.g.In particular, the reflectivity on this side is significantly reduced because the reflected light must pass through the absorption filter twice, as is used to calculate by the interference filterThe reflectivity of a filter f composed of an absorption filter p is shown by the following expression:,and; Among them, in the above expression,is the spectral reflectance of the filter. Relative to such composite filters for enhanced color discrimination, the ratio between the peak transmittance and the average transmittance of the composite filter f should preferably be as high as possible. In a further example, theBreaking down into two component absorbing filters, the two absorbing filters are then placed on opposite sides of the lens, e.g.,and,and; Among them, in the above expression,gives the spectral reflectance on one side of the lens (e.g., the outer surface), andGives the spectral reflectance on the other side of the lens (e.g., the inner surface). In some instances,Can be a neutral density filter, such as gray glass with about 40% transmittance. For example, this combination can achieve a light transmission of approximately 20%, a peak transmission of approximately 40%, and a light reflectance of approximately 8% on one side of the lens (i.e.,Has a light transmittance of approximately 50%). In a further example,Can be a neutral density filter consisting of two absorbing filters that are both colored (for example, a brown glass and a blue glass, the combination of which produces a neutral transmission of about 40%) . These colors can be selected to affect the color of reflected light on the outer surface of the lens (eg, for eye pleasure). Neutral density and colored absorbers can also be formed from organic dyes and incorporated into a polymer substrate, and/or applied as a coating (eg, by spin coating or dip coating) to one or more surfaces of the lens . Preferably, you can useThe spectral transmittance is complementary to the narrow band selective absorber to form, thus achieving a higher ratio of peak transmittance to average transmittance of the composite filter (e.g., higher than possible using neutral density absorption). For example, the narrow-band organic dyes Exciton P491 and Exciton ABS584, which absorb at about 491 nanometers and about 584 nanometers, respectively, can be used to form such complementary absorption suitable for use with red-green discrimination enhancement filters as disclosed herein body. Alternatively, certain rare earth elements (such as neodymium, phosphorus, and phenyl) have narrow-band absorptivity in the visible spectrum and may be similarly employed. For example, a modified neodymium-containing glass lens ACE manufactured by Barberini GmbH can be used as an optical substrate for depositing an interference filter. Additionally, the incorporation of a narrowband absorber (and an interference filter) can improve the quality of the filter design incorporating color stability constraints on the white point, as previously described in connection with Figures 20A and 20B, in particular In summary, the narrowband absorber improves the color discrimination provided by the filter at angles of incidence greater than 20 degrees from the normal axis. Alternatively or additionally,Reflected light can be absorbed by incorporating one or more circular polarizers. In some embodiments, a circular polarizer is located on the inner surface of the lens to attenuate reflections that would otherwise be visible to the user's eyes. A circular polarizer can also be located on the outer surface of the lens to attenuate front side reflections. A lens incorporating a circular polarizer can achieve a peak transmission of approximately 40%, a light transmission of approximately 20%, and a light reflectance of approximately 2% on one or both sides of the lens. Circular polarizers with a spherical curve of 6 diopters or greater can be manufactured, for example, by thermoforming and incorporated into a lens, for example, by lamination. Additionally, these circular polarizers can be formed using linear polarizers that achieve only partial polarization (eg, about 70% polarization efficiency), thereby increasing light reflectivity without compromising one or both sides of the lens. Achieve a higher peak transmittance. An example configuration of a lens incorporating a circular polarizer is depicted in Figures 24A and 24B, where the layers (from front to back) are a vertically oriented linear polarizer 2401, a quarter-wave retarder 2402, An optically transparent substrate 2403, a multilayer interference coating 2404 deposited on the surface of the substrate, a quarter-wavelength retarder 2405, and a (eg, vertically oriented) polarizer 2406. In Figure 24B, light incident on the outer side of the compound lens is shown along arrow 2413. The incident light passes through a polarizing filter, then through a quarter-wavelength retarder (thus becoming circularly polarized), and then separated by an interference filter into a transmitted component that is ultimately received by the eye 2409 and absorbed by the retina 2412 and a reflected component 2414 that travels in the opposite direction toward the light source but is absorbed before it can emerge from the composite lens. Reflected component 2414 is circularly polarized, however, reflection at interference filter 2404 causes its handedness to flip, for example, from right to left, so that as it travels in reverse through circular polarizer 2402, it appears as Horizontally polarized and absorbed by linear polarizer 2401. Still referring to Figure 24B, a similar process of reflection-absorption can occur for stray light entering the rear side of the lens (as shown along beam 2408) to cause reflected light 2411 to be absorbed before it reaches the eye. In another embodiment,It may be a neutral density filter fabricated from a metallic attenuating coating using physical vapor deposition. Preferably, these absorption filters and an interference filter can be fabricated by physical vapor deposition (i.e., in the same process), so that the attenuation layer can surround the dielectric layer and/or be associated with the dielectric layer. Some of them are staggered or partially staggered. Due to the properties of the metal layer when incorporated into the interference filter, these attenuating coatings can provide better reflection attenuation than an equivalent bulk dielectric neutral density absorber. For example, these designs can achieve a peak transmission of approximately 35%, a light transmission of approximately 20%, and a light reflectivity of approximately 2% on one side of the lens. Alternatively, these designs can achieve a peak transmission of approximately 35%, a light transmission of approximately 20%, and a light reflectivity of approximately 4% on both sides of the lens. Alternatively, such designs may achieve a peak transmission of approximately 50%, a light transmission of approximately 20%, and a light reflectivity of approximately 4% on one side of the lens. Alternatively, these designs can achieve a peak transmission of approximately 60%, a light transmission of approximately 20%, and a light reflectivity of approximately 8% on one side of the lens. An additional feature of these designs is having all functional layers of the filter positioned on one side of an optical substrate (such as interference coatings and (several) attenuating coatings). In these designs, the opposite sides of the substrate can be anti-reflective coated to reduce scattering and resonance of light within the optical substrate (eg, multiple internal reflections). In these designs, the anti-reflective coating preferably provides a light reflectivity of no greater than 0.5% because lower quality anti-reflective coatings (e.g., having a light reflectivity of about 1% or greater ) can reduce, but not completely eliminate, the visibility of internal reflection artifacts under general-purpose outdoor conditions (specifically, when viewing unusual bright spots (such as reflections of sunlight) reflected from metal surfaces in a typical outdoor scene) . An example configuration of a lens incorporating an attenuating coating is depicted in Figures 28A and 28B, where the layers (from front to back) are anti-reflective coating 2801, optical substrate (eg, glass) 2802, first attenuating coating Layer 2803, multi-layer interference coating 2804 and second attenuating coating 2805. In Figure 28B, light incident on the outer side of the lens is shown along arrow 2811. The incident light passes through the anti-reflective coating and optical substrate, then passes through the first attenuation coating, and is then split by an interference filter into a lens component that is ultimately received by the eye 2807 and absorbed by the retina 2809 and travels in the opposite direction toward the light source However, one of the reflection components 2812 is substantially absorbed during the second pass through the first attenuating coating. Still referring to Figure 28B, a similar process of reflection-absorption can occur for stray light entering the rear side of the lens (as shown along beam 2806) to cause reflected light 2810 to be absorbed before it reaches the eye. In some examples, the attenuating coating is staggered or partially staggered with the dielectric layer of the interference coating. In some examples, the attenuating coating is on the backside only, ie, the first attenuating coating 2815 is not included. Next, several implementations including exemplary multi-band filters for incorporation into eyeglasses are disclosed along with the detailed description of FIGS. 31A-42E, 45A-45E, 48A-53E, and 55A-57E. example. The figures all conform to a general format that is easily understood from their common layout. First, the details of the format are generally described using, for example, FIGS. 31A to 31E and 59A to 59B. Next, details related to the design of each corresponding embodiment are described in further discussion with reference to each specific figure and the elements within the figure. In the graph of Figure 31A, the curve shows transmittance constraints, which include the minimum transmittance as a function of wavelength at solid curve 3101 and the maximum transmittance as a function of wavelength at dotted curve 3102, and a further curve display The dotted curve 3103 on the same graph shows a cost function as a function of wavelength (which is a unitless dimension). The transmittance constraints, as well as additional color appearance constraints (not shown by the graph) and the cost function form inputs to a linear program solver, where the inputs are processed as previously described in this disclosure, which involves converting these constraints into And the method of transforming the cost function into a standard linear program. In the graph of Figure 31B, the curve shows the spectral transmittance of a component of a filter f designed to affect color vision in a desired manner according to the constraints and guidance cost function as described in conjunction with Figure 31A filter. As explained above, by Specifies an "ideal" filter as generated by linear programming methods. The solid curve 3104 defines a weighted combination of basic filters q as selected by the linear stylization method as previously disclosed, and the dashed curve 3106 defines the transmittance of a selected pre-filter p, which in this example is a neutral density filter. Dashed curve 3105 shows the (optionally) smoothed and (optionally) biased linear program solution q'. The spectral transmittance of the filter assembly is listed in rows 5 to 8 of Figure 59B (q', q, p, and f, respectively). Rows 2, 3, and 4 listed in Figure 59B are used to generate filter objects (respectively,,) is a manufacturing specification of the minimum transmittance, target transmittance and maximum transmittance as a function of wavelength. Lines 9, 10 and 11 (respectively,and c) give the minimum spectral transmittance, maximum spectral transmittance and cost function used in filter design. The wavelengths corresponding to each column of the table are listed in row 1 in steps of 5 nanometers, which provide appropriate spectral resolution to reproduce any of the embodiments disclosed herein. The graph of Figure 31C includes three curves, of which the solid curve 3107 is the design target for manufacturing the filter.(Solved using a linear equation that is optionally biased and optionally smoothedreplace), the dotted curve 3108 is a minimum transmittance limit, and the dotted curve 3109 is a maximum transmittance limit. The minimum transmittance limit and the maximum transmittance limit will be used in the specification of the manufacturing tolerances of the target filter. The target transmittance, minimum transmittance, and maximum transmittance can be calculated by the following expressions:,,and; where, in the above expression, the symbolRepresents the core function k and filterfrequency domain convolution between, andis the bias coefficient as described previously. The core function k is typically characterized by having a half-maximum width between about 10 nanometers and about 25 nanometers. For this embodiment, the width is about 25 nanometers, but in further embodiments the width can be at given changes within a certain range. Furthermore, in the definitionandWhenandProvides a wavelength shift tolerance of approximately +/- 2 nanometers (equivalent to approximately +/- 0.5% at 400 nanometers). These tolerances are empirically selected to produce modest results for use with a high-precision physical vapor deposition process, however, the specific choice of tolerances is not intended to limit the scope of the invention. Any values suitable for these parameters and the resulting tolerances may be used. In FIG. 31D , along the solid curve 3110 and the dashed curve 3111 , the comparison with a best-fit broadband reference filter as a function of the incident angle θ is shown.Percent Relative Gamut Area Increase (PGAI) of the filter, where the solid curve shows the calculated relative gamut area increase relative to the Farnsworth D-15 sample, and the dashed curve shows the calculated relative to natural samples (NWS). The importance weighted percentage of relative gamut area increase can be calculated from any of these data by calculating the weighted average PGAI based on the eye model previously described in conjunction with Figures 29A-30B and assuming a standard deviation of eye orientation of 10 degrees. (For example). Figure 31E shows a solid line graph 3112 of the white point displacement of a filter as a function of incident angle, where the white point corresponds to the illuminant as viewed through the filter relative to the CIE 1931 2 degree standard observer. The CIELUV (u', v') chromaticity coordinates of D65 and the white point displacement as a function of the incident angle are defined as the white point chromaticity coordinates at 0 degrees incident angle (ie, normal incidence) and the deviation from the normal direction The distance between the chromaticity coordinates of the white point at the angle of incidence. To perform this calculation, assume that filter component q' is an interference filter with an effective refractive index of approximately 1.85 and component p is an absorption filter. In addition, the table in Figure 59A lists the relative filterVarious additional performance criteria were evaluated, including those previously defined in the detailed description of the invention and selected metrics defined by industry standard ANSI Z80.3-2010. Specifically, for some embodiments, marked "” column can be used to provide a robust estimate of the general quality of color enhancement provided by the filter. This increase in quantity correlates with improved scores based on the Farnsworth D-15 cap configuration test and is generally associated with a visual experience that can be described as color enhancement. In the following, the linear stylizations described herein are described with reference to FIGS. 31A-42E, 45A-45E, 48A-53E, and 55A-57E and the corresponding tables presented in FIGS. 59A-80B. Some additional embodiments of method designed optical filters. In these figures, detailed descriptions of elements indicated by reference numerals xx01 to xx12 (where xx is the figure number, e.g., 31 in Figures 31A to 31E) correspond to that given above with respect to Figures 31A to 31E A detailed description of the components, with further details provided as appropriate for each individual case. In one embodiment, the design criteria of the three-pass red-green color discrimination enhanced multi-band filter, the spectral transmittance of the components, and the components are shown in the graphs of FIGS. 31A to 31E and listed in FIGS. 59A and 59B. Manufacturing specifications and performance evaluation. The rows shown in graph 3107 of Figure 31C and Figure 59BThe filter manufacturing targets listed in have a first passband center at approximately 450 nm and a half-peak bandwidth of approximately 40 nm, a second passband center at approximately 530 nm and approximately 35 nm A half-peak bandwidth of one meter and a third passband center at about 615 nanometers and a half-peak bandwidth of about 40 nanometers. Optical filter manufacturing specifications can be used to produce optical filters. The optical filter includes an interference filter (q) and a neutral density absorption filter (p), wherein the neutral density absorption filter has a transmittance of about 40%. The filter design is achieved by a linear programming approach as disclosed herein, where the basic filter is a set of approximately 60 rectangular passband filters, each having a single passband width of 10 nanometers and Having center wavelengths in increments of 5 nanometers (this is also the case for all embodiments described below). To improve manufacturability so that interference filter components can be fabricated with a low-order stack of dielectric materials (e.g., less than about 50 material layers), a Gaussian core (k) having a half-maximum width of about 20 nanometers has been used to smooth the filter design (q'). It should further be noted that the resulting filter (f) complies with the minimum transmission limit as shown at 3101 in Figure 31A. The filter design criteria used to produce this embodiment have been configured such that the daylight light transmission is about 18%, which is suitable for the filter to be used in sunglasses with a medium color. Further embodiments disclosed herein may employ the same or nearly the same light transmission. However, the methods disclosed herein are suitable for manufacturing products with any modest light transmission (e.g., as low as about 8% (corresponding to a dark color of sunglasses) or as high as 40% (corresponding to a light color of sunglasses)), or in some In this case, greater than 40%) filter. Additionally, the filter provides a white point that would be considered essentially neutral, as shown in the table of Figure 59A (D65 chromaticity coordinates). Filters with a neutral configuration of the white point are better suited for overall visual comfort and a balanced brightness of all colors. However, other configurations of the white point are possible, but whites with strong chroma should be avoided. This is because these filters generally cannot provide adequate brightness across the entire color gamut. Regarding the white point of this embodiment as viewed over a range of angles of incidence, as demonstrated by the white point displacement plot 3112 in Figure 31E as a function of angle of incidence, the white point moves quite a bit (e.g., at 35 degrees shift greater than 0.03 units), therefore, when such a filter is incorporated into eyeglasses (where the filter is viewed through an angular range), a significant color shift toward the periphery of the lens is observed. Additionally, as shown in graphs 3110 and 3111 in Figure 31D, the color enhancement of the filter is below zero at about 20 degrees, and therefore the filter only provides a relatively narrow field of view in which The desired color enhancement function is effective, for example, green colors in nature (such as leaves) may tend to have a brown appearance at incident angles approaching or exceeding 20 degrees. A further embodiment in Figures 32A-32E, related to the embodiment previously shown in Figures 31A-31E, features the correspondence table in Figures 60A and 60B. This example discloses a filter designed relative to the same conditions as previously described, except that the cost function shown at 3203 in Figure 32A has been modified to further improve color discrimination. The resulting filter design features an alternative passband position that provides better performance. Currently, this configuration is considered to only give the choice of passband position for the best possible performance of any three-passband filter relative to the PGAI metric (however, as will be shown in further discussion, this metric is not necessarily suitable for e.g. glasses Practical applications of these filters). Shown in graph 3207 of Figure 32C and rows of Figure 60BThe filter manufacturing targets listed in have: a first passband at about 440 nanometers with a half-peak bandwidth of about 30 nanometers; a second passband at about 535 nanometers with a half-maximum bandwidth of about 35 nanometers; and a third passband at about 650 nanometers, which has a half-maximum bandwidth of about 80 nanometers. The improved color enhancement effect of this embodiment results in part from the wider separation of the first and third frequency bands. As mentioned previously, color discrimination benefits from a multi-band filter with one of the widest possible spectral apertures, so a filter with a first frequency band having a wavelength shorter than about 450 nanometers can be Preferably, and a filter having a third passband having a center wavelength longer than 610 nanometers is preferred. However, 440 nanometers and 650 nanometers are approximately the maximum outer limits of the band positions in a filter that have this desired effect because band positions above these limits can tend to render blue and red colors unacceptable The dark color. Additionally, this embodiment benefits by locating the mid-passband at a wavelength longer than 530 nanometers. The configuration of the passband at a wavelength less than 530 nanometers can provide a filter that results in an unacceptably dark color for green. The configuration of the passband at exactly 530 nm tends to maximize the PGAI performance measure relative to the Farnsworth D-15 sample and Munsell colors, however, these colors are based on artificial pigments and this filter can tend to cause natural The green color appears unnatural green. The natural color of chlorophyll (as described previously) is more accurately seen as a yellow-green color. The configuration of the mid-passband at approximately 540 nm tends to maximize PAI performance relative to natural samples. The configuration of the passband at about 545 nanometers or longer tends to provide a filter that gives an enhancement of blue-yellow discrimination and a corresponding weakening enhancement of red-green discrimination, and if longer is still selected wavelength, the balance tips towards blue-yellow (discussed in more detail in a further embodiment). Therefore, the configuration of the passband with a center wavelength of about 535 nanometers can achieve one of the best performance balances between artificial color samples and natural color samples, and has a center wavelength of about 545 nanometers. The mid-band is chosen to achieve an optimal performance balance relative to the red-green and blue-yellow axes of the color space. Further embodiments of filters for enhanced red-green discrimination disclosed below are consistent with the selection of centers between about 535 nanometers and about 545 nanometers (if not otherwise specified), however, the examples shown are not It is intended to limit the scope of this invention because the choice of mid-band position can usefully vary between about 530 nanometers and about 545 nanometers for these filters to improve color discrimination. Returning to the discussion of Figures 32A-32E, the performance of the filter relative to the PGAI metric based on the Farnsworth D-15 sample and the natural sample (shown at 3210 and 3211 in Figure 32D, respectively) is shown compared to the previous embodiment. One is significantly improved. In particular, the PGAI is greater than zero for angles of incidence up to about 30 degrees, so the filter can provide a wider field of view giving the desired color enhancement when incorporated into eyeglasses. In addition, the PGAI at normal incidence is significantly larger than that of the previous embodiment. However, in comparison, this embodiment exhibits significantly worse performance with respect to the stability of the white point across multiple angles of incidence, as shown at 3212 in Figure 32E, where the white point displacement at 35 degrees is approximately 0.05 unit. Due to the wide bandwidth of the long wavelength band, the white point tends to shift rapidly towards a red tint. Using available fabrication methods, undesirable white point displacement can be partially mitigated by depositing interference filters so that the layers have a physical thickness that intentionally varies within the area of the lens where the expected viewing angle deviates from the normal, however, Such methods are too costly. For example, relative to manufacturing methods by physical vapor deposition, achieving the required thickness gradient requires highly precise machining configurations that would hinder volume production. Furthermore, even with the appropriate physical distribution of interference coatings on a lens, a filter that is so sensitive to angle of incidence is difficult to reliably align within the frame of a pair of glasses so that the performance of the glasses will depend on frame style and head size. and are robust to changes in similar geometric factors. A further embodiment of Figures 33A-33E, related to the previously shown embodiments of Figures 31A-31E and the embodiment of Figures 32A-32E, is characterized by having the correspondence tables of Figures 61A and 61B. This example discloses a filter designed relative to the same conditions as previously described. However, the design criteria further include a color appearance constraint such that the white point appears substantially constant over a wide angular range, and the cost function is additionally adjusted to maximize the filter's performance over the widest possible angular range. efficacy. The resulting filter design is characterized by a further alternative choice of passband position that provides good performance relative to the PGAI metric but additionally ensures a consistent appearance of color across the entire field of view to thereby incorporate in the filter Delivers robust performance and improved visual comfort when incorporated into glasses. Specifically, the middle passband remains at approximately 535 nm, but the upper passband and lower passband configurations are intermediate between the embodiments of Figures 31A-31E and the embodiments of Figures 32A-32E Location. Graph 3207 of Figure 32C is shown and the line of Figure 60BThe filter manufacturing targets listed in have: a first passband at about 445 nanometers with a half-peak bandwidth of about 25 nanometers; a second passband at about 535 nanometers with a half-maximum bandwidth of approximately 30 nanometers; and a third passband at approximately 630 nanometers, having a half-maximum bandwidth of approximately 40 nanometers. Relative to the efficiency of the filter, it can be observed in Figure 33D that the PGAI is greater than zero for angles of incidence up to approximately 25 degrees. Therefore, the filter can provide a moderately wide field of view giving the desired color enhancement when incorporated into spectacles. Compared to previous embodiments, the performance of the filter with respect to the stability of the white point at multiple angles of incidence is significantly improved. As shown at 3312 in Figure 33E, the white point displacement between 0 degrees and 35 degrees is less than about 0.01 units. In further embodiments, it was demonstrated that the white point displacement can be extended to angles up to 45 degrees while maintaining the same bounds. In all embodiments disclosed below, white point stabilization constraints in some form (if not otherwise specified) are used because such constraints are generally considered beneficial for any system including an interference filter assembly. Manufacturing of this filter. In fact, such filters incorporating a white point stability constraint have been subjectively observed to provide a comfortable field of view without significant color distortion in peripheral vision, regardless of the fact that lenses can be incorporated to give relative A dielectric interference filter whose spectral transmittance changes significantly with the angle of incidence. In general, the methods disclosed herein can be used to find a red-green enhanced multi-band filter having three passbands configured to provide a stabilized white point, where the filter has a wavelength at approximately 440 nm a first passband between about 450 nanometers, a second passband between about 530 nanometers and about 545 nanometers, and a third passband between about 610 nanometers and about 635 nanometers. belt. A preferred embodiment of a red-green enhancement filter is one that has the smallest possible center position of the shortest wavelength passband, the largest possible center position of the longest wavelength passband, the narrowest possible bandwidth, and adjacent passbands and stopbands. The maximum possible contrast ratio between the average transmittances of the bands. However, all such configurations can be adjusted with appropriate constraints to ensure the effectiveness of the filter when incorporated into eyeglasses, for example. Embodiments of optical filters disclosed herein (including, for example, the embodiments disclosed in FIGS. 36A-36E, 37A-37E, 38A-38E, 39A-39E and related embodiments thereof) provide for Obey guidance related to the appropriate maximization of these limitations for practical concerns of intended application. In a further embodiment related to the embodiment of Figures 33A-33E, a blue-yellow enhancement filter is characterized by the correspondence tables of Figures 34A-34E and Figures 62A and 62B. This embodiment discloses a filter designed with respect to essentially the same criteria as those of the related embodiments, except that the cost function (shown at 3403 in Figure 34A) is configured to maximize blue-yellow discrimination rather than red Green identification. These filters can be used by individuals with Type III achromatopsia, a color vision deficiency that makes it difficult to distinguish between blue and yellow. These filters may also be better used in glasses suitable for certain environments where the background is predominantly green (such as golf greens) (where it is desired to suppress the appearance of green to some extent), or better used In an optical aid for locating camouflaged objects in a jungle (where the suppression of changes between greens can reveal previously invisible features). Shown in graph 3407 of Figure 34C and row of Figure 62BThe filter manufacturing targets listed in have a first passband at about 455 nanometers, the first passband having a half-maximum width of about 45 nanometers, a second passband at about 560 nanometers and has a half-maximum width of about 50 nanometers, and a third passband is located at about 675 nanometers and has a half-maximum width of about 60 nanometers. An analysis of the filter's performance relative to the PAGI metric is shown in Figure 34D, where it can be observed that for incident angles up to approximately 20 degrees, the PGAI is predominantly negative. Furthermore, the white point displacement (as shown in Figure 34E) exhibits excellent stability for incident angles up to 45 degrees away from normal incidence with a total displacement of less than about 0.01 units. Additionally, as mentioned in the table of Figure 62A, this filter complies with the chromaticity limits of traffic signals as defined by ANSI Z80.3-2010. Specifically, with respect to these blue-yellow enhancement filters, the amount of color discrimination suppression along the red-green axis is limited by the chromaticity coordinates of the green traffic signal. Relative to the inventive filter that maximizes blue-yellow discrimination and maintains compliance, the green traffic signal chromaticity coordinates are essentially at or nearly at the boundaries of the compliance region such that the green traffic signal appears as allowed by the standard Unsaturated (i.e., white). In another embodiment also related to the embodiments of Figures 33A-33E and 34A-34E, a color enhancement filter is characterized by the correspondence tables of Figures 35A-35E and Figures 63A and 63B, The optical filter is further configured to substantially inhibit the transmission of short wavelength light (eg, light between about 380 nanometers and about 450 nanometers). These filters generally provide a balanced improvement in color discrimination along both the red-green axis and the blue-yellow axis. Furthermore, suppression of short wavelength light improves sharp focusing and reduces the total energy of photons received by the eye, with energy increasing inversely relative to wavelength. This embodiment is difficult to fabricate using a low-order interference filter because the design is preferably characterized by a rapid onset point between reflection and transmission at about 450 nanometers. Therefore, the interference filter assembly (q') is smoothed with a core having a half-maximum width of approximately 10 nanometers. In order to achieve the blue light blocking function, the cost function can be configured with an increasing slope as shown at 3503 in Figure 35A. The filter's white point can be oriented toward a yellow configuration, subject to restrictions that prevent the white point from being considered "strongly colored" according to ANSI Z80.3-2010. Shown in graph 3507 of Figure 35C and line of Figure 63BFilter manufacturing goals are listed in , which assume that the filter incorporates a neutral density absorption filter (p) with a transmission of approximately 50%. The filter fabrication target has a first passband at about 455 nanometers with a half-maximum width of about 15 nanometers; a second passband at about 550 nanometers with a half-maximum width of about 45 nanometers. a half-maximum width; and a third passband located at about 645 nanometers and having a half-maximum width of about 70 nanometers. The filter has a light transmission of about 35% (corresponding to a light-colored sunglasses), but can be made darker by increasing the strength of the absorbing filter element. As shown in Figure 35D, this filter provides a moderately positive value of PAI at angles of incidence up to 30 degrees. Relative to color stability performance, white point displacement is limited to less than 0.01 units between angles of incidence between 0 degrees and 35 degrees, as demonstrated in Figure 35E. Additionally, as indicated in the table of Figure 63A, the solar blue light transmittance (approximately 15%) is less than half of this light transmittance, so the filter can be described as providing an improved blue light blocking function while also maintaining color appearance one of good quality. In a further series of three embodiments discussed below, multi-band filters with enhanced red-green discrimination are disclosed, wherein the filters are configured for use by observers with deuteranomaly, who have difficulty distinguishing green. A group of people with red color vision deficiency. These embodiments provide substantially more enhancement in color discrimination along the red-green axis than previously disclosed embodiments of the red-green enhancement filters herein. The manufacturing specifications disclosed in these embodiments provide for a filter to be produced that is a combination of a neutral density filter and an interference filter, wherein the neutral density filter has from about 40% to about 55% one of transmittance. In addition, interference filters are generally specified as high-order coating stacks because steep transitions between adjacent passbands and stopbands are generally preferred for maximizing color discrimination enhancement. These filters with steep band transitions can provide the unstable color appearance of certain narrowband light sources, such as light emitting diodes and some types of gas discharge lamps, including sodium vapor lamps and some fluorescent lamps. To mitigate these instabilities, these filters incorporate a minimum transmission constraint relative to wavelengths between about 450 nanometers and about 650 nanometers, which is typically specified to be equal to the optical transmission of the filter The rate is about one-fifth of the lower limit. Accordingly, the stopband of these embodiments is limited to this minimum transmittance. These filters also better comply with ANSI Z80.3-2010 related to the chromaticity coordinates of traffic signals provided by the filters, and in particular, such filters that minimize red-green discrimination enhancement Some embodiments of the device may provide chromaticity coordinates of a yellow traffic signal at a restricted position relative to its compliance boundary, where the restricted position provides an appearance of the light as red or nearly red (as permitted). An additional difficulty associated with the design of these filters is that the color matching function for green weak observers is not fully characterized by the CIE standard observer model. Constraints related to white point stability can therefore be calculated better relative to a modified observer model. The details of the calculations are well documented and available to the person of ordinary skill. However, the analysis of white point displacement in this article maintains the use of the CIE 2-degree standard observer. Therefore, the calculated white point displacement as a function of incident angle in these designs is characterized by a wider range (e.g., 0 degrees to 35 about 0.02 units between degrees). The white point displacement functions of these designs typically exhibit a local minimum at an angle between about 20 degrees and about 40 degrees, where the measured white point displacement at the local minimum is typically at most about 0.01 units. A first embodiment of a filter for green-weak observers is disclosed together with the correspondence tables of FIGS. 36A to 36E and FIGS. 64A and 64B. Shown in graph 3607 of Figure 36C and row of Figure 64BThe filter manufacturing targets listed in have: a first passband at about 450 nanometers with a half-maximum width of about 25 nanometers; a second passband at about 535 nanometers with a half-maximum width of about 25 nanometers; having a half-maximum width of about 35 nanometers; and a third passband located at about 635 nanometers and having a half-maximum width of about 35 nanometers. Manufacturing specifications for this filter incorporating a neutral density absorber with approximately 45% transmission are given. For incidence angles up to about 27 degrees, the PGAI provided by this filter is greater than zero, as shown in Figure 36D. As mentioned in the table of Figure 64A, the importance weighted PGAI relative to the Farnsworth D-15 color is at least about 30%, which may work better for an observer with mild deuteranomania. The essentially neutral-toned white point of this filter is stabilized relative to a green-weak observer model and is characterized by a local minimum in the white point shift curve of less than 0.01 units at approximately 32 degrees. , as shown at 3612 in Figure 36E. Together with the correspondence tables of FIGS. 37A to 37E and FIGS. 65A and 65B , a second embodiment of a filter for a green-weak observer is disclosed. Shown in graph 3707 of Figure 37C and row of Figure 65BThe filter manufacturing targets listed in have: a first passband at about 445 nanometers with a half-maximum width of about 25 nanometers; a second passband at about 535 nanometers with a half-maximum width of about 25 nanometers; having a half-maximum width of about 35 nanometers; and a third passband located at about 635 nanometers and having a half-maximum width of about 40 nanometers. Manufacturing specifications for this filter incorporating a neutral density absorber of approximately 50% transmission are given. For incidence angles up to about 25 degrees, the PGAI provided by this filter is greater than zero, as shown in Figure 37D. As mentioned in the table of Figure 65A, the importance weighted PGAI relative to the Farnsworth D-15 color is at least about 35%, which may be preferable for an observer with moderate deuteranomaly. The essentially neutral white point of the filter is stabilized relative to a green weak observer model and is characterized by a local minimum in the white point shift curve of less than 0.01 units at approximately 40 degrees. , as shown at 3712 in Figure 37E. A third embodiment of a filter for green-weak observers is disclosed together with the correspondence tables of FIGS. 38A to 38E and FIGS. 66A and 66B. In this embodiment, the filter design criteria are modified such that the minimum spectral transmittance limit (equal to one-fifth of the optical transmittance) is only between yellow wavelengths and red wavelengths (e.g., from about 580 nanometers to about 650 nanometers). m) is mandatory, as shown at 3801 in Figure 38A. The resulting filter design can therefore be described as having a third passband with a "shoulder" on the short wavelength side of the band. Shown in graph 3807 of Figure 38C and row of Figure 65BThe filter manufacturing targets listed in have: a first passband at about 445 nanometers with a half-maximum width of about 20 nanometers; a second passband at about 535 nanometers with a half-maximum width of about 20 nanometers; having a half-maximum width of about 30 nanometers; and a third passband located at about 635 nanometers and having a half-maximum width of about 30 nanometers. Manufacturing specifications for this filter incorporating a neutral density absorber of approximately 55% transmission are given. For incidence angles up to about 25 degrees, the PGAI provided by this filter is greater than zero, as shown in Figure 38D. As mentioned in the table of Figure 66A, the importance weighted PGAI relative to the Farnsworth D-15 color is at least about 40%, which may be preferable for an observer with severe deuteranomaly. The essentially neutral white point of the filter is stabilized relative to a green weak observer model and is characterized by a local minimum in the white point displacement curve of about 0.01 units at about 40 degrees , as shown at 3812 in Figure 38E. A further embodiment related to the series shown in FIGS. 36A to 38E is disclosed together with the correspondence tables of FIGS. 39A to 39E and FIGS. 67A and 67B. This embodiment provides a filter that enhances red-green discrimination for a red-weak observer. Compared to previous examples of red-green enhancement filters, these filters generally prefer one of the shorter wavelength configurations of the second and third passbands when designed for red-weak observers. This is based on the orientation of the line of confusion for color blindness type III and the fact that redness weakness is associated with a blue shift in the spectral absorbance of retinal photopigments in long-wavelength cones. Due to the shorter wavelength configuration of the second and third passbands, the total spectral width of these filters must be relatively reduced so that red appears moderately bright. Shown in graph 3907 of Figure 39C and line of Figure 67BThe filter manufacturing targets listed in have: a first passband at about 440 nanometers with a half-maximum width of about 20 nanometers; a second passband at about 530 nanometers with a half-maximum width of about 20 nanometers; having a half-maximum width of about 25 nanometers; and a third passband located at about 615 nanometers and having a half-maximum width of about 25 nanometers. Manufacturing specifications for this filter incorporating a neutral density absorber of approximately 55% transmission are given. For incidence angles up to about 20 degrees, the PGAI provided by this filter is greater than zero, as shown in Figure 39D. The white point stability of such filters may be additionally considered in the design, however, analysis of the white point stability based on a standard observer model may be inherently inappropriate for the intended use of the filter (e.g., for a red-weak used by observers). In another embodiment, in conjunction with the correspondence table of FIGS. 40A-40E and FIGS. 68A and 68B , it is disclosed to provide color enhancement to normal observers and improve an electronic visual display, such as a liquid crystal display having a light emitting diode backlight. A filter for the light contrast of primary color light in visual displays. The filter is intended for use with electronic displays that typically use three primary colors of light: a red primary color with a peak wavelength between about 610 nanometers and about 630 nanometers and a peak wavelength between about 20 nanometers and about 50 nanometers. A full-width half-maximum of meters; a green primary color, having a peak wavelength of about 530 nanometers to about 535 nanometers and a full-width half-maximum of about 20 nanometers to about 50 nanometers; and a blue primary color, having a peak wavelength of about 530 nanometers to about 535 nanometers. to a peak wavelength between about 460 nanometers and having a full width at half maximum of about 20 nanometers. The filter provides approximately equal light transmission for the red, green, and blue primary colors (thus, preserving the white point of the display). Additionally, the light transmittance is at least about 15% greater than the light transmittance of sunlight provided by the filter. Therefore, the filter may provide an improved contrast ratio when such displays are viewed, for example, under outdoor conditions. Shown in graph 4007 of Figure 40C and row of Figure 68BThe filter manufacturing objectives listed in are characterized by four passbands that provide a stabilized white point up to an angle of incidence of 45 degrees. The filter achieves color stability that provides a white point shift of less than 0.01 units between about 0 degrees and about 45 degrees, as demonstrated by curve 4012 in Figure 40E. Additionally, the filter provides a moderate enhancement of color discrimination, as noted in Table 68A, with an importance weighted percentage of greater than approximately 20% relative to the color gamut area of Farnsworth D-15. It is also possible to design a filter that performs in a similar manner with three passbands, in which the range of the stabilization angle extends to about 35 degrees. Figure 21B shows one variation of a three-pass band filter and another variation of a four-pass band filter, shown at 2105 and 2106 in Figure 21B, each of which achieves this optical contrast gain. Filter 2105 has three passbands, wherein a first passband at approximately 455 nm has a half-maximum width of approximately 15 nm, and a second passband at approximately 535 nm has a half-maximum width of approximately 20 nm. peak width, and a third passband at approximately 620 nanometers with a half-peak width of approximately 25 nanometers. Filter 2106 in FIG. 21B has four passbands, in which a first passband at approximately 455 nm has a half-maximum width of approximately 15 nm, and a second passband at approximately 540 nm has a half-maximum width of approximately 20 nm. A width at half maximum of about 610 nanometers, a third passband at about 610 nanometers having a full width at half maximum of about 20 nanometers, and a fourth passband at about 650 nanometers having a full width at half maximum of about 20 nanometers. Compared to simple three-band filter 2105, filter 2106 provides improved color stability with respect to changes in angle of incidence. Figure 21A shows the spectral radiant flux of daylight 2103 and the spectral radiant flux of blue primary color light 2101, the spectral radiant flux of green primary color light 2102 and the spectral radiant flux of red primary color light 2104, as measured from an LED backlit LCD display . The spectral flux of organic LED-based displays (OLEDs) is very similar, so that the filter of this embodiment will also provide optical contrast gain for these displays. In another embodiment, a multi-band filter for normal observers is designed to provide substantially normal color discrimination and a blocking band between about 530 nanometers and about 560 nanometers. This blocking band protects the eyes from laser radiation at 532 nm, such as that emitted by a frequency-double Nd:YAG laser. These lasers have many applications, including use in a variety of medical procedures. Conventionally designed filters that block visible laser emissions at, for example, about 532 nanometers also typically result in poor quality color discrimination when used in eyeglasses. For example, filters made of absorbing materials cannot achieve sufficient blocking and do not absorb a wide spectral band. Interference filters that include a single stopband (eg, Rugate-type filters) may provide adequate eye protection, but result in significant changes in color appearance and exhibit significant shifts in the white point away from the normal angle of incidence. In contrast, a multi-band interference filter can provide adequate protection against a visible laser, and a multi-band interference filter designed using the filter generation method as previously disclosed can also maintain a normal Color appearance maintains color stability at multiple angles and protects eyes from visible laser radiation over a wide range of angles. An embodiment of a 532 nm blocking filter is disclosed in the correspondence table of FIGS. 41A to 41E and FIGS. 69A and 69B. Shown in graph 4107 of Figure 41C and row of Figure 69BThe characteristics of the filter manufacturing targets listed in are four passbands separated by three stopbands, of which the middle stopband is the laser protection blocking band. The first passband is at about 440 nanometers and has a half-maximum width of about 30 nanometers, the second passband is at about 510 nanometers and has a half-maximum width of about 30 nanometers, and the third passband is at about 570 nanometers. nanometers and having a half-maximum width of about 20 nanometers, and a fourth passband is located at about 630 nanometers and has a half-maximum width of about 30 nanometers. In general, similar filters can be found with frequency bands within +/- 10 nanometers of a given location and with various bandwidths, but all such filters are characterized by at least four passbands. For industrial or medical applications, a blocking passband (between about 530 nanometers and about 560 nanometers) can provide a protection level rated at OD6 or higher (OD6 indicates an optical density of 6, which results in attenuation of transmitted light 10^-6 times). For interference level protection (for example, against a green laser pointer with a 532 nm output), the protection level can be smaller, for example about OD2. This protection may be specified in the filter generator design specification as one of the maximum transmittance constraints 2201 as shown in Figure 22A. Additionally, as shown in Figure 41E, these four passband filters can provide good stability with a white point of less than 0.01 units up to an incident angle of 35 degrees. As shown in Figure 41D, these filters can also provide an essentially normal color appearance over a wide range of angles, as evidenced by the fact that the PGAI is nearly zero for angles of incidence up to about 25 degrees. These filters can be incorporated into safety glasses used in industry or medicine. Specifically, in some applications of laser in medical procedures, it can be beneficial to enable users to accurately perceive the color rendering of biological tissues during surgery and to perceive the correct chromatic appearance of certain colored lights, so that the surgeon can correctly Interpret lights on computer displays and/or equipment. It should be noted that these filters are not compatible for use with illumination sources with narrow-band spectral output, such as some fluorescent lamps or RGB light-emitting diode arrays. Another embodiment related to the embodiment shown in FIGS. 41A to 41E is disclosed in the correspondence table of FIGS. 42A to 42E and FIGS. 70A and 70B. Shown in graph 4207 of Figure 42C and row of Figure 70BThe filter manufacturing objectives listed in are characterized by four passbands separated by three stopbands, the long wavelength stopband being the one that provides protection against a 589 nm sodium emission line. Eye protection from this wavelength may have industrial applications in certain processes such as glass manufacturing or working with lasers that have output power at or near the short wavelength side of the blocking band. Filter design specifications incorporate this blocking band as a spectral transmittance constraint, as shown by maximum transmittance constraint 2301 in Figure 23A. This embodiment may provide similar qualities of color appearance and white point stability as demonstrated by the previous related embodiments. Variations of this embodiment may include only three passbands, however such variations tend to provide a substantial reduction relative to the PGAI metric and are therefore somewhat unsuitable for use in applications where normal color discrimination is desired. Another embodiment related to the embodiment shown in FIGS. 35A to 35E is disclosed in the correspondence table of FIGS. 45A to 45E and FIGS. 71A and 71B . This embodiment also provides a blue light blocking function and a substantially normal color appearance. It is also intended to be suitable for use in dim lighting conditions and especially at night, where illumination by sodium vapor lamps is expected (such as is common in street lamps). Filter design guidelines are incorporated to ensure that 589 nm light is bounded by a minimum transmittance constrained by the filter transmission, as shown at 4501 in Figure 45A. Such a filter and a photochromic element can then be manufactured, for example, such that the filter incorporated into spectacles can be used within a range of lighting levels. This embodiment provides a substantially normal color appearance, as shown in Figure 45D, where the PGAI is not significantly different from zero at angles of incidence up to 45 degrees. Furthermore, as shown in the graph of Figure 43A, the filter complies with the spectral minimum transmittance constraint and the spectral maximum transmittance constraint shown at solid curve 4302 and dashed curve 4301, respectively. The maximum spectral transmittance constraint states that the filter is designed not to transmit light with wavelengths below 450 nanometers. The minimum spectral transmittance constraint stipulates that the filter is designed to transmit at least 15% across the entire stopband between 450 nm and 650 nm; in addition, the filter is designed to pass the filter for wavelengths between 580 nm and 650 nm. The largest possible fraction of light with wavelengths between 610 nanometers passes through. The filter shown in solid curve 4303 of Figure 43B (which is the same as the solid curve shown in Figures 45A-45D) is designed to meet the spectral transmittance constraints of Figure 43A, and the smoothness shown in dashed curve 4304 The filter fully meets the constraints of the intended application; specifically, the filter provides a high-luminosity artificial lamp based on sodium vapor excitation that concentrates energy at approximately 589 nanometers, such as low-pressure sodium lamps and high-pressure sodium lamps commonly used in street lights. . Short-wavelength blue light (e.g., having near-ultraviolet wavelengths between about 380 nanometers and about 450 nanometers) is associated with a family of visual phenomena commonly referred to as glare, the contributing factors of which may include fluorescence (specifically, , the fluorescence of organic materials in the eye that partially react to UV and near-UV light), the dispersion of light through the ocular medium (specifically, due to the degradation of retinal physiology due to age-related effects) and Chromatic aberration of the eyepiece (specifically, the inability of short-wavelength light to focus accurately on the retina). Therefore, a filter that selectively inhibits the transmission of short-wavelength blue light may have utility for reducing glare and improving visual sensitivity. A standard blue light blocking filter (also referred to as a cutoff filter) can be created by incorporating a short wavelength absorber into a lens, such as shown by the transmittance curve at dashed curve 1904 in Figure 19B . However, a multi-band blue light blocking filter can provide improved color discrimination (e.g., as indicated by the solid curve 1902 (providing about 35% light transmittance), the dashed curve 1903 (providing about 60% light transmittance) in Figure 19B shown in the transmittance curve) and the filter design shown in Figures 45A and 43B. The color discrimination provided by these filters is shown in further detail in Figures 44A-44C. The spectral transmittance of a conventional blue light blocking cut-off filter is shown at 4405 of Figure 44C, and the spectral transmittance of a blue light blocking multi-band filter is shown at 4404 of Figure 44C. The color appearance of selected Munsell colors provided by the filters is shown in the chromaticity diagram of Figure 44A, which includes the color appearance provided by the cutoff filter at dashed outline 4401 and the color appearance provided by the solid outline 4402. The multi-band filter provides color appearance. The color appearance provided by the cut filter is inherently dichroic along the red-green axis, that is, the contours are collapsed such that the blue-yellow axis of apparent difference has a length of zero. In comparison, the color appearance provided by the multi-band filter is trichromatic (without collapse). An example configuration of a lens incorporating an attenuating coating and an absorbing optical substrate is depicted in Figures 46A and 46B, where the layers (from front to back) are an antireflective coating 4601, an absorbing optical substrate (e.g., containing Neodymium glass) 4602, multi-layer interference coating 4604 and attenuation coating 4605. In Figure 46B, light incident on the outer side of the lens is shown along arrow 4611. The incident light passes through the anti-reflective coating and absorptive optical substrate, and is then split by an interference filter into a transmitted component that is ultimately received by the eye 4607 and absorbed by the retina 4609 and travels in the opposite direction toward the light source but after a second pass through One of the reflected components 4612 is further absorbed during an attenuating coating. Still referring to Figure 46B, a similar process of reflection-absorption can occur for stray light entering the rear side of the lens (as shown along beam 4606), causing reflected light 4610 to be absorbed before it reaches the eye. In some examples, the attenuating coating is staggered or partially staggered with the dielectric layer of the interference coating. Neodymium-containing glass lenses are known to provide a slightly enhanced color discrimination. For example, the spectral transmittance of a 1.5 mm thick ACE modified lens (manufactured by Barberini GmbH) is shown by solid curve 4705 in Figure 47C. The color discrimination properties of the filter can be analyzed by comparison with one of the best-fit reference filters, Munsell 7.5B 8/4, given by spectral transmittance curve 4704 in Figure 47C. The appearance of selected Munsell colors provided by the ACE modified lens is shown along solid outline 4702 in the chromaticity diagram of Figure 47A, and along dashed outline 4701 is shown the appearance of selected Munsell colors for the reference filter. Neodymium-containing filters produce an increase in the color gamut area enclosed by these contours. However, the increase was mainly clustered around the red sample which was not balanced by one of the apparent purity increases of the green sample. Preferably, a lens including neodymium can be used as an optical substrate for depositing an interference filter and/or attenuating coating, such as described in Figures 46A and 46B. The resulting composite filter can then provide passbands and stopbands by configuring interference filters and narrowband absorption filters to be operated. These composite filters can be designed using linear programming methods as disclosed herein by appropriately configuring the spectral transmittance of the pre-filter p and the optical substrate to be used in the construction. Compared to multi-band filters with passbands provided only by interference filtering, these composite filters can be_IW Measurements provide better performance on average and are generally less sensitive to changes in angle of incidence. Several embodiments of filter designs incorporating a neodymium-containing absorbing element are disclosed below in conjunction with the detailed description of Figures 48A-53E and additionally in Figures 57A-57E. All representations of these embodiments are variations from previously disclosed embodiments and thus require no additional detailed discussion. A general observation related to these changes is that neodymium-containing multi-band filters can provide a slightly improved angular width of the field of view within which color enhancement is provided. For example, for an embodiment that includes only a neutral density type of absorbing filter (where the PGAI is greater than zero up to about 25 degrees), a variation based on additional inclusion of such a filter with neodymium can be used at up to about 30 degrees. Provides a PGAI greater than zero. However, these variations tend to cause compromises in other areas, for example, in some variations, an ophthalmic lens incorporating such a filter may have a greater light reflectivity on the side of the lens facing the eye. The correspondence table of FIGS. 48A to 48E and FIGS. 72A and 72B discloses a first embodiment of an optical filter incorporating a neodymium absorbing element, which is a variation of the design shown in FIGS. 33A to 33E . This filter provides enhanced red-green discrimination to normal observers. This change provides a wider field of view of approximately 5 degrees within which color enhancement is effective. However, the importance weighted percentage of the increase in color gamut area is essentially the same between this variation and its related embodiments. A further embodiment of an optical filter incorporating a neodymium absorbing element is disclosed in Figures 49A-49E and the correspondence table of Figures 73A and 73B, which is a variation of the design shown in Figures 34A-34E. This filter provides enhanced blue-yellow discrimination to normal observers. This change provides a wider field of view of approximately 5 degrees within which color enhancement is effective. However, the importance weighted percentage of the increase in color gamut area is essentially the same between this variation and its related embodiments. A further embodiment of an optical filter incorporating a neodymium absorbing element is disclosed in Figures 50A-50E and the correspondence table of Figures 74A and 74B, which is a variation of the design shown in Figures 36A-36E. This filter provides enhanced red-green discrimination to observers with mild green tint. This change provides a wider field of view of approximately 5 degrees within which color enhancement is effective. However, the importance weighted percentage of the increase in color gamut area is essentially the same between this variation and its related embodiments. A further embodiment of an optical filter incorporating a neodymium absorbing element is disclosed in FIGS. 51A-51E and the correspondence table of FIGS. 75A and 75B, which is a variation of the design shown in FIGS. 37A-37E. This filter provides enhanced red-green discrimination to observers with moderate green tint. This change provides a wider field of view of approximately 5 degrees within which color enhancement is effective. However, the importance weighted percentage of the increase in color gamut area is essentially the same between this variation and its related embodiments. A further embodiment of an optical filter incorporating a neodymium absorbing element is disclosed in Figures 52A-52E and the correspondence table of Figures 76A and 76B, which is a variation of the design shown in Figures 38A-38E. This filter provides enhanced red-green discrimination to observers with severe green tint. This change provides a wider field of view of approximately 5 degrees within which color enhancement is effective. However, the importance weighted percentage of the increase in color gamut area is essentially the same between this variation and its related embodiments. A further embodiment of an optical filter incorporating a neodymium absorbing element is disclosed in Figures 53A to 53E and the correspondence table of Figures 77A and 77B, which is a variation of the design shown in Figures 39A to 39E. This filter provides enhanced red-green discrimination to observers with redness weakness. This change provides a substantially improved color discrimination due to the optimal positioning of the main absorption band providing favorable conditions relative to the displacement stability constraints, whereby the long wavelength passband can be effectively red-shifted by about 10 nanometers, thereby broadening the spectral aperture without compromising other design criteria. One further application of multi-band filters considers their effectiveness in increasing the blue and cyan light absorbed by the eye. Specifically, the reception of light between about 450 nanometers and about 490 nanometers can stimulate retinal ganglion cells. These cells are not involved in color vision, but rather in the suppression of melatonin and the synchronization of circadian rhythms with the phase of daylight. The reception of this light may have therapeutic effects, for example, in treating seasonal affective disorder, sleep disorders, and other health problems. Figure 54A shows the estimated spectral absorption of retinal ganglion cells at 5401, where the absorption profile was obtained by shifting a retinal photopigment template to a peak wavelength of approximately 480 nanometers. To better understand the effect of high-energy stimulation of optical filters on ganglion cells, the example shown in the graph of Figure 54B is instructive. First, a neutral density filter (as shown at 5404) has essentially no effect on ganglion cell absorption - for a moderate range of such light transmittance of a filter (e.g., between about 20% to about 100 %), the dilation or constriction of the pupil ensures that the amount of light reaching the retina (i.e., the number of photons per second) is approximately constant (for example, the area ratio between a dilated pupil and a constricted pupil is approximately 5:1). For example, as shown in 5403, a broadband blue filter has an average transmittance between about 460 nanometers and about 490 nanometers, which is greater than the light transmittance of the filter. The luminosity of light (i.e., daylight) affects pupil dilation, and light sensitivity is maximum at about 555 nanometers, and retinal ganglion cell absorption is maximum between about 460 nanometers and about 490 nanometers, so it is concluded that relative to A filter that transmits substantially more light at about 480 nanometers than at about 555 nanometers can cause the pupil to dilate so that the number of photons absorbed by the ganglion cells increases. However, broadband filters (such as the blue example shown in the figure) do not provide a substantial gain. These blue filters improve ganglion cell stimulation by approximately 30%. However, this increase can be substantially improved by a multi-band filter, such as shown at 5402. This filter improves ganglion cell stimulation by up to approximately 80%. A first embodiment for improving ganglion cell stimulation is disclosed in the correspondence table of FIGS. 55A to 55E and FIGS. 78A and 78B. This embodiment provides an increase in ganglion cell stimulation of about 80%, ie, the ratio of the average transmittance between 460 nm and 490 nm to the light transmittance of the filter is about 1.8. However, this embodiment does not feature a stable white point. As shown by graph 5512 of Figure 55E, the appearance of the white dot shifts rapidly toward blue as the angle of incidence increases. A further embodiment for improving ganglion cell stimulation is disclosed in the correspondence table of Figures 56A to 56E and Figures 79A and 79B. This example provides an increase in ganglion cell stimulation of approximately 50%. This embodiment also features a stable white point, as shown by graph 5612 of Figure 56E. For incidence angles up to about 30 degrees, the white point displacement is less than about 0.01 units. Additionally, as shown in Figure 56D, the PGAI is essentially zero for angles of incidence up to about 30 degrees, demonstrating that the filter provides an essentially normal color appearance. However, the filter design with four passbands is relatively complex and the improvement in ganglion cell stimulation is not significant. A further embodiment for improving ganglion cell stimulation is disclosed in the correspondence table of Figures 57A to 57E and Figures 80A and 80B. This example provides an increase in ganglion cell stimulation of approximately 65% and a stable white spot. Improved performance under these conditions is facilitated by filter designs that incorporate a neodymium absorbing element. As shown by graph 5712 of Figure 57E, the white point displacement is less than about 0.01 units for incident angles up to about 30 degrees. Additionally, as shown in Figure 57D, the PGAI is essentially zero for angles of incidence up to about 30 degrees, demonstrating that the filter provides an essentially normal color appearance. In further embodiments, an optical filter may be designed to be incorporated into a lamp assembly, where the optical filter fabricated, for example, as a multi-layer dielectric coating, provides a beam-splitting function by which the beam-splitting function Function, the transmitted and reflected components of light emitted by a light source within the lamp are configured to have the same white point. The matching of the reflective white point and the transmissive white point allows two beam components to be used for illumination, so no energy is wasted through filtering. Furthermore, the transmitted component of the light beam can be configured to provide a color enhancement effect, such that a lamp assembly can be constructed in which, for example, the central region of the light beam provides an enhanced quality of light (see additional discussion below with respect to Figure 27B). An opposite effect on color appearance can be observed in reflected light, where there can be an opposite effect on the increase in relative color gamut area, as compared to an increase in the relative color gamut area, as exhibited by transmitted illuminants, and a decrease, as exhibited by reflected illuminants. The relative gamut area, ie, the average gamut area of the recombined light beams, is consistent. A lamp assembly containing such a filter preferably includes a broadband illuminator. In one embodiment, light emitting diodes may be preferably used for illumination. If white LEDs including LED driver phosphors alone do not provide a sufficiently wide band emission for good color appearance, white LEDs and red LEDs can typically be combined in a ratio of, for example, about 4:1 to produce a color temperature and spectrum with approximately the same color temperature and spectrum as daylight. The width of a broadband illuminator. Figure 25A shows the spectral radiant flux 2501 of this composite illuminator, the spectral radiant flux 2502 of a white LED, and the spectral radiant flux 2503 of a red LED. Such illuminants may have a color temperature between about 5000 K and about 7000 K and a CRI between about 80 and about 90. In a further example, an illuminator that includes LED-stimulated daylight can include white LEDs, red LEDs, and blue (or cyan) LEDs with a ratio of, for example, about 4:1:2 to produce a light with a temperature of about 5000 K to about 7000 K. A broadband illuminator with a color temperature between K and a CRI between about 90 and about 100. A filter with spectral transmittance 2504 (as shown in Figure 25B) can perform the spectral splitting described. These filters are also called dichroic filters or dichroic reflectors. Design criteria for this filter may include, for example: a cost vector configured to maximize the relative gamut area; an LED mixture as described above as the illuminator; and a reference filter that is The neutral filter makes the white point of the illuminating object under the filter the same as the white point of the illuminating object under the neutral filter and the reflective filter. In addition, the white point constraint can preferably specify the white point at angles of incidence up to about 20 degrees from the normal. This accommodates potential difficulties in perfectly collimating the incident light. A 20 degree beam width can be achieved using a small footprint collimating lens. Additionally, it may be preferable to specify a filter with a minimum spectral transmission of about 10% across visible wavelengths, which can be used to adjust the gamut area increase to reduce the appearance of color when split beams are spatially recombined. The non-uniform appearance in the mixed region of the split beams. The spectral transmittance 2605 of the illuminant beam splitting filter and the spectral transmittance 2606 of its reflectance (reflection) are again presented in Figure 26C. The spectral radiant flux 2604 of a mixture of LED illuminants is again shown in Figure 26B. Point 2603 in the chromaticity diagram of Figure 26A shows the chromaticity coordinates of the white point of the filter and the inverse filter. 2601 is the chromaticity coordinate of the selected Munsell color of the filter, and 2602 is the chromaticity coordinate of the selected Munsell color of the inverse filter. The opposite effect on the gamut area can be easily seen in these profiles, whereby illuminant transmitted through the filter increases the gamut area and illuminant reflected through the filter in turn decreases the gamut area. Small. One possible configuration of components for forming a lamp assembly including such a beam splitting filter is shown in Figures 27A and 27B. Here, the assembly can be configured as a stack that includes a thermally conductive substrate 2701 (such as a metal circuit board), a light emitting diode 2702, a beam forming optical light guide 2703, and a multi-layer interference coating that can be deposited to the surface of an optically transparent substrate (such as glass). Referring specifically to FIG. 27B , in an example configuration, a beam of light emitted by LED 2702 is collimated by optical device (eg, light guide) 2703 to a beam width of approximately 20 degrees, and then incident on interference filter 2704 superior. Thereafter, the transmitted component of light appears in the central portion of output beam 2708, and the reflected portion is redirected by the light guide (e.g., by internal reflection along the boundary indicated by 2709), and is then emitted along the annular portion of output beam 2707 . As shown in the figure, this configuration allows the lamp assembly to incorporate a color-enhancing filter without compromising luminous efficiency because the light not transmitted by the filter is back-radiated into an environment that can still be used for general lighting. , whereas an absorption filter will reduce the efficiency of the lamp, an interference filter has an almost identical efficiency. Such illuminators may be advantageously employed indoors to provide improved color discrimination for green-weak and red-weak observers. In these configurations, the illuminator may also be used with filters incorporated into the glasses (as previously disclosed). For the spectral transmittance as a function of wavelength of any filter disclosed above in this specification, one method for calculating the center position and width of the passband and stopband includes applying a Gaussian smoothing kernel to a spectral transmittance curve (e.g., by convolution of the core and transmission data sequence), where the width of the core is wide enough to substantially eliminate any undesired changes in the curve (e.g., such as those not valued by the filter of interest) transients, ripples, noise, or other artifacts); then normalize the curve so that the maximum transmittance equals 100%; and then round each transmittance value to 0% or 100% so that each adjacent spectral region ( where the rounding value is 0%) corresponds to the frequency band boundary of a stopband, and each adjacent spectral region (where the rounding value is 100%) corresponds to the frequency band boundary of a passband. For band boundaries calculated according to this method, the average transmittance within each passband and each stopband can be calculated relative to the original curve. The width of a passband or stopband is equal to the distance between the lower frequency band boundary and the upper frequency band boundary, and the center of a passband or stopband is equal to the midpoint between the lower frequency band boundary and the upper frequency band boundary. Preferably, for any such calculated set of passband boundaries and stopband boundaries, for each staggered stopband, the average transmission of the stopband is at most half the average transmission of an adjacent passband. If this condition does not apply, then the change between passband and stopband can be essentially useless, in which case the width of the smoothing core can be increased and the calculation iteratively performed until a suitable smoothing width is determined. For most filters of interest in this invention, a smooth core with a half-maximum width of about 20 nanometers is suitable for the purposes of this calculation. For most of the optical filters described in this invention, specified values related to the location of the band boundaries, the location of the band center, and the width of the band can be given in wavelength units rounded to the nearest 5 nanometers. The teachings in this article are sufficient to specify filters with greater spectral resolution. However, a large spectral resolution is not necessarily required to practice the present invention. The foregoing portions of this specification disclose methods for producing multi-band optical filters that affect color vision in a desired manner, including: methods of designing filter specifications that satisfy constraints associated with the filter's intended use; Methods of evaluating the performance of a filter specification and adjusting the design to further improve the performance of the filter specification relative to the desired effect to achieve the specifications of a preferred embodiment of such a filter; manufacturing the filter and/or providing A method suitable for machine specifications with an optical filter made by another method; and one of incorporating the optical filter into an eye lens or a lamp assembly to produce a device that provides the desired effect on color vision Preferred embodiment methods. The scope of the effect on color vision achieved by the present invention includes: maintaining normal color discrimination (which is also referred to in the present invention as providing "good color discrimination"); enhancing color discrimination (which is sometimes also referred to in the present invention as "good color discrimination") Enhanced" or "improved" color discrimination), it can be unconditionally assumed that the improvement in color discrimination between red and green is equivalent to the improvement in color discrimination between blue and yellow; enhanced red-green discrimination, in which the desired effect is such that the improvement in color discrimination between red and green maximizing improvement in discrimination; and enhancing blue-yellow discrimination, wherein the desired effect maximizes improvement in discrimination between blue and yellow. It is generally desirable that filters that also provide additional functionality (such as specified minimum and/or maximum spectral transmittance in one or more regions of the visible spectrum) maintain normal color discrimination, where equivalent spectra are achieved by conventional methods Transmittance limitations will result in a filter providing poor quality color discrimination. For example, a conventional notch filter or cutoff filter that acts as an interference filter can cause significant changes in the chromatic appearance of certain colors, and/or can cause significant changes in the chromatic appearance of certain colors when the filter is incorporated into eyeglasses. Causes the appearance of some colors to change relative to the variable viewing angle in a way that makes the viewer uncomfortable. In a further example, absorption averages that affect spectral transmittance can result in filters with a low optical transmittance and/or a strongly colored white point because the concentration of absorbing material required to achieve the spectral transmittance limit can Significantly affects the transmittance in a wide region of the visible spectrum. The methods disclosed herein enable the design, specification, and fabrication of optical filters that maintain normal color discrimination over a wide range of viewing angles and provide useful constraints on spectral transmittance. Certain variations of the filters and products incorporating the filters disclosed herein include: filters that block blue light between about 380 nanometers and about 450 nanometers; filters that block blue light between about 380 nanometers and about 450 nanometers; A filter that blocks blue light between 450 nanometers and simultaneously ensures high spectral transmittance of light at approximately 589 nanometers within a wide viewing angle range; a filter that blocks green light at approximately 532 nanometers within a wide viewing angle range an optical device; and an optical filter that provides a high average transmittance of light relative to a light transmittance of between about 460 nanometers and about 490 nanometers. The filters in this embodiment family all include three passbands interleaved with two stopbands. However, many of these filters include four passbands interleaved with three stopbands, where one or more of the stopbands and/or one or more of the passbands provide the desired spectral transmittance limitation. Further variations based on the methods disclosed herein enable the design, specification, and manufacture of filters that enhance color discrimination over a wide viewing angle range. These filters include: filters that enhance red-green discrimination; filters that enhance blue-yellow color discrimination. Discrimination enhancement filter; or both. The filters may be configured to enhance color discrimination for observers with normal color vision, or may be configured to enhance color discrimination for observers with color vision deficiencies, including green-tiny color vision deficiency, red-tiny color vision deficiency, and tertiary color vision deficiency. Enhanced color discrimination in observers with achromatopsia. The configuration of a filter intended for use by a particular observer may provide a preferred embodiment of a filter that affects color vision in a desired manner. However, this configuration does not necessarily prevent other observers from experiencing some or all of the desired effects. Applications of filters that enhance red-green discrimination include optical aids for green-weak observers and red-weak observers. These color vision deficient people are characterized by a sensitivity to changes between red and green that is lower than the sensitivity of normal observers. Filters that enhance red-green discrimination may also be used in other applications including general-purpose eyewear for normal observers (such as sunglasses); and event-specific eyewear such as those used when playing certain sports including golf. . Filters that enhance blue-yellow discrimination can be used by type 3 color-deficient observers and also have other applications including enhancing light contrast, stimulating red-green color vision deficiencies, and detecting camouflaged objects. Filters that provide a balanced enhancement of color discrimination between red and green and between blue and yellow may be better used by observers with normal color vision, where such filters are incorporated into eyeglasses Provides general improvements in visual quality. The filters within this family of embodiments all include three passbands interleaved with two stopbands. However, some such filters may include four passbands interleaved with three stopbands. Typically, the fourth passband has a center located at greater than about 660 nanometers and is configured such that the filter maintains a substantially non-whitening point at extreme angles of incidence. Filters configured to enhance color discrimination can be classified according to the center position of the second passband. For the center position between about 520 nanometers and about 540 nanometers, the filter mainly focuses on providing an improvement in discrimination between red and green. For center positions between about 545 nanometers and about 550 nanometers, the filter provides approximately the same improvement in discrimination between red and green and between blue and yellow. For centers between about 555 nanometers and about 580 nanometers, the filter focuses on providing improved discrimination between blue and yellow. For a filter configured to enhance blue-yellow discrimination, the preferred center position of the second passband is approximately 580 nanometers, which corresponds to the monochromatic wavelength that most observers perceive as yellow only. However, a filter with a second passband center position at 580 nm may not be practical as it would cause the colors to appear dichroic and would result in a corresponding loss of all between red and green discern. Therefore, it is useful to constrain these filters, for example by ensuring that the chromaticity coordinates of a green traffic signal are within defined boundaries that give their acceptable limits. Thus, an optimal filter may be found with a second passband position less than or equal to about 560 nanometers that maximizes discrimination between blue and yellow at the expense of color discrimination between red and green. . For a filter configured to enhance discrimination between red and green, the optimal center position of the second passband varies depending on the color group of interest. Relative to Munsell color samples and/or Farnsworth D-15 colors, the optimal center position is approximately 530 nm. However, relative to natural samples, a better location is around 540 nm. Therefore, the choice of 535 nm gives the best average case choice for this filter for use in a mixed environment. Relative to a filter configured to enhance red-green discrimination for a green-weak observer, preferred embodiments may depend on a subclass of this type of observer. For mildly green-weak observers, a moderate contrast ratio between passband average transmission and stopband average transmission may be suitable, for example, about 4:1. For a moderately green-weak observer, a ratio of at least about 6:1 may be preferable. For a severely green-weak observer, a ratio of at least 8:1 may be preferable. For filters having a passband to stopband contrast ratio greater than about 6:1, the filter specifications may be preferably limited to provide between about 580 nanometers and about 620 nanometers and/or between about 560 nanometers and about 560 nanometers. The minimum spectral transmittance is at least about one-fifth of the minimum spectral transmittance of light between about 580 nanometers. This ensures that the filter is suitable for general use, such as the simultaneous operation of a motor vehicle which requires suitable visibility of certain narrow-band yellow lights, including light-emitting diodes and low-pressure sodium lamps. In such a variation, the filter may be preferably constrained to constrain the chromaticity coordinates of a yellow traffic signal within a specific area so that the lights are not mistaken for, for example, orange or red. A variation based on the above range is applied to the second passband center position relative to a filter configured to enhance red-green discrimination for a red-weak observer. Due to retinal physiology associated with the abnormality, the preferred wavelengths were all blue-shifted to about 5 nanometers, for example, the selection of 535 nanometers was modified to about 530 nanometers. Furthermore, it should be noted that relative to the configuration of the filter for red-weak observers, the center of the third passband is preferably at most between about 610 nanometers and about 625 nanometers, due to the relatively small The use of longer wavelengths can result in reduced visibility of red to such observers. The filters within the family of embodiments described above for enhanced color discrimination all include three passbands interleaved with two stopbands. Regarding the configuration of filters used for color vision, such filters generally preferably provide light transmission within a moderate range (e.g., at least about 8%), and also preferably provide light transmission without strong display. The white point of a color (that is, the chromaticity coordinate of average sunlight as viewed through a filter). A constrained white point region may preferably be chosen to provide an essentially neutral hue because filters with a moderately or strongly tinted white point cannot provide the appropriate brightness for some colors. Furthermore, it may be preferable to impose a limit such that the white point remains within a relatively small area within a range of viewing angles, as these filters provide the most comfortable viewing experience when incorporated into eyeglasses and are Achieve tolerance for misalignment and beam divergence when incorporated into the lamp assembly. The CIELUV(u',v') chromaticity coordinates are better used for these calculations because, according to this scale, the ellipse that defines the smallest perceptible difference between colors for the range of the white point of interest is Approximately circular. The (u', v') coordinates can be calculated relative to the CIE 1931 2-degree standard observer or the CIE 1964 10-degree standard observer, where the former gives a better prediction of the apparent color of the object at a distance, and the latter gives A better prediction of the apparent color of an object over a larger portion of the field of view. The white point constraint region may have a radius of approximately 0.02 units on the (u', v') chromaticity diagram relative to a filter configured for use by an observer with normal color vision. More preferably, the region can have a radius of about 0.01 units, and still more preferably, the range of angles of incidence over which the filter white point meets the limit can be expanded from 0 degrees to at least about 25 degrees, and more preferably, Expands from 0 degrees to at least about 35 degrees. With respect to filters configured for use by observers with color vision deficiencies, the constraint region may be preferably defined as an elliptical region, for example, where the long axis of the ellipse corresponds to the type of color vision deficiency Confusing line orientation. Thus, when the properties of these filters are analyzed in terms of a circular constrained region, the properties of these filters are characterized by a white point that leaves the constrained region within a certain range of intermediate angles and is then characterized by a Steeper angles again enter the constraint region, where the steeper angles are typically between about 20 degrees and about 40 degrees. In some embodiments, this may provide a filter that appears to provide good stability of the white point when viewed by an intended observer, but is not perceptible to the same extent by an observer with normal color vision. Stability. The white point constraint area may be better limited to a radius of approximately 0.01 units relative to mild deuteranomaly observers and moderate deuteranomaly observers. Relative to severe green weak observers, an unconstrained region with a radius of approximately 0.02 units may be preferred. Relative to a red-weak observer, the angular range within which the constraints are considered may be reduced to, for example, between about 0 degrees and about 20 degrees. A first method for designing a filter that enhances color discrimination includes: selecting a desired center position of the second passband based on the desired effect as described above; selecting a desired light transmittance appropriate for the filter The minimum required width of one of the second passbands (it should be noted that this preference also implies that the average transmittance of the second passband is as high as possible); and then select the appropriate first and third passbands Center position and width. The center of the first passband is preferably located at the shortest possible wavelength, and the center of the third passband is preferably located at the longest possible wavelength, with the center position and width constrained by constraints related to the white point of the filter. The range of possibilities includes the desired chromaticity coordinates of the white point at normal incidence; and the region within that will contain the chromaticity coordinates of the white point relative to a range of viewing conditions at angles of deviation from normal incidence. Then, the average transmittance within the three passbands is preferably chosen to be the maximum possible value (which can be less than 100% if the filter is specified to incorporate, for example, an absorbing filter), and can be preferably The average transmittance of the staggered stopband is selected within a range of values corresponding to a contrast ratio of the average transmittance between the passband and the stopband of between about 2:1 and about 10:1 or greater. Higher contrast ratios produce stronger color discrimination enhancements. These high ratios may also be associated with the unusual and/or unstable color appearance of certain lamps, such as narrow band lamps. The above description related to the preferred selection of passband positions and passband to stopband contrast ratios and methods of designing the optical filters disclosed herein provides appropriate teachings for designing optical filters that are members of the groups identified above. For example, to achieve such a filter by an exhaustive search procedure, the center position and width of the second passband and the passband may be determined, for example, based on the call range associated with the effect on color vision as described above. Band to stopband contrast ratios, then enumerating all possible combinations of center positions and widths of the first and third passbands, and then using a computer to evaluate each filter within the enumerated group to select the better member. The preferred member satisfies the design constraints required to maximize a performance measure relative to color discrimination. The listed groups may include thousands of members, and the resulting calculations may require significant computational time due to the number of frequency bands considered and the spectral resolution of the calculations. Even better, the methods disclosed herein for designing these filters by solving a linear program can be used, thereby transforming the design constraints into a well-formed linear program that will enable filter design The limit is defined as a geometric abstraction best described as a generalized multidimensional convex polyhedron. Through guidance (which uses a cost vector as described in the teachings of this invention), a linear program solver can quickly position the filter components on the boundaries of the feasible set to maximize along the direction indicated by the cost vector. Given constraints in direction. As disclosed herein, linear programming methods enable nearly instantaneous determination of test filter specifications, allowing best practices for practicing the present invention to interactively guide cost vectors and/or design constraints such that an operator can instantly evaluate an Performance trade-offs involved in specific test filters. The linear programming method also enables the design of, for example, a composite filter including an interference filter and a narrowband absorption filter (such as a neodymium-containing optical substrate), where the linear programming solver determines the interference filter The transmittance specifications of the filter must be specified to produce the desired effect in conjunction with the absorbing filter. Feasible filter sets considered by the linear program solver may include essentially any spectral transmittance curve that is difficult or impossible to achieve by enumerating frequency bands or iterating a local search procedure. Since the linear program solver is not strictly limited to designing a multiband filter (which is a sequence of passbands interleaved with the stopband), it can be used to design a multiband filter that can be achieved when used with another specific filter. A multi-band spectral transmittance filter that includes constraints that consider properties relative to the composite filters over a range of angles of incidence. For any test filter specification (such as produced by the method just described), further methods disclosed herein enable prediction of the effect of the test filter on color discrimination. For example, in one embodiment, a method involves: determining a best-fitting broadband reference filter; then calculating the chromaticity coordinates of a set of reference colors as viewed through the test filter and the reference filter; And compare the ratio of the area enclosed by the coordinates under the two conditions. In another embodiment, a best-fit broadband reference filter is determined, then the chromaticity coordinates of a set of reference colors as viewed through the test filter and the reference filter are calculated, and then these are The chromaticity coordinates are projected onto one axis of the color space, and the relative standard deviations of the sets of coordinates along that axis are compared. Preferably, the axis may comprise one or more of the Line of Confusion for Color Blindness Type 3, the Line of Deuteranopia Confusion, and the Line of Protanopia Confusion, such that the calculated ratio corresponds to the enhancement, weakening, or maintenance of color discrimination along the corresponding direction, where Type III color blindness confusion lines generally correspond to the discrimination between blue and yellow, and deuteranopia confusion lines and protanopia confusion lines generally correspond to the discrimination between red and green. More preferably, these performance analysis calculations are performed relative to the test filter as viewed within a range of angles of incidence from normal, such as between about 0 degrees and at least about 25 degrees. The average efficacy over these angles can be used to estimate the overall efficacy of the product when incorporated into an eye lens, for example, so that filter efficacy must be considered over a wide range of viewing angles. Even better, this analysis may consider the estimated distribution of the curvature and orientation of the lens within a spectacle frame, and/or the geometry of the eye, and/or the orientation of the eye that can be rotated in the eye socket. Preferably, such performance evaluation relative to a reference color may consider a representation of the color under conditions under which the product may be used with, for example, eyeglasses. Such reference color shall include both samples from natural sources as well as artificial pigments, For filters configured for incorporation into interior light assemblies, the reference colors may include only artificial colorants. For a preferred test filter specification, the filter may be fabricated, for example, as an interference filter fabricated by physical vapor deposition of a stack of dielectric materials onto an optical substrate. The test filter specifications may be bounded by a minimum transmittance curve and a maximum transmittance curve to, for example, provide a processing tolerance specification suitable to enable the filter to be manufactured by an operator familiar with such production methods. Some embodiments of the filters disclosed herein may be fabricated, for example, as high-order interference filters that include about 100 layers of dielectric material and have a total thickness of about 6 microns. Relative to implementations of some embodiments, in particular in which only a modest contrast ratio between the average transmission of the passband and the stopband is desired (e.g., having a ratio between about 2:1 to about 4:1) For example), the number of layers and thickness can be significantly reduced such that for example up to about 50 layers are required and/or have a total thickness of about 3 microns, where these limits can be achieved by applying a smooth core to the filter format , for example, the core preferably has a Gaussian shape and a half-peak value of at least about 20 nanometers. The resulting simplified design can then benefit from shorter machining times, compatibility with lower precision procedures, and lower overall production costs. Several of the types represented by the filter embodiments disclosed herein may benefit from being designed as a composite filter (e.g., including an interference filter and an absorption filter, where the absorption filter includes neodymium) Construct. For example, relative to a red-green enhancement filter with a constrained white point within an angular range, these composite designs are feasible at longer wavelengths than would be feasible given the same constraint criteria and without the neodymium absorbing component. Select the position of the third passband at one wavelength. While longer wavelength center locations are preferred, as previously described, this can lead to composite filter designs that further enhance color discrimination. In addition, these composite designs can provide improved stability of color, such as when analyzing performance over an angular range, for high angles that include neodymium, which is 5 degrees greater than the angle of an equivalent filter design that does not include neodymium. A composite design can maintain a gamut area ratio greater than 1:1. However, it was found that the improved angular stability was often compromised by a slightly lower peak efficiency due to an undesired secondary absorption band present in the neodymium-containing filter, resulting in a second pass filter. The band is slightly wider than the optimal passband. However, such composite designs including neodymium may be preferred as filters incorporated into eyeglasses (where overall visual comfort is a consideration). Alternatively or additionally, other narrow band absorbers may be used as neodymium, which include narrow band organic dyes and other rare earth elements such as 鐐鐐 or 鈥, whereby some of these combinations of narrow band absorbers may provide an interference filter. A composite filter designed to exhibit improved angular stability and/or reduced light reflectivity. Such combinations may be designed, for example, using linear stylization methods as disclosed herein. When any of the disclosed filters are fabricated as interference filters, the high reflectivity of these filters must be taken into consideration. When incorporated into eyeglasses, the ratio of light transmittance to light reflectance on the inner surface of the lens is preferably at most about 2:1. Relative to a filter in which the interference filter has a high transmittance (eg, over 60%), the reflectivity of the interference filter may be small enough to be ignored. Preferably, these filters are combined with either a linear polarizer in the form of an absorption filter or a photochromic absorption filter which is combined with an interference filter. Placement will not significantly reduce light reflectivity. With respect to filters in which the interference filter has a light transmission of less than about 60%, management of reflectivity on the inner surface of the lens is a considerable problem. A first approach is to apply a neutral density absorber to the rear side of the lens to facilitate the fact that reflected light must pass through the absorber twice, which can restore the contrast ratio to an acceptable level. However, the neutral density absorber also reduces the maximum spectral transmission of the lens, which in turn implies a required reduction in one of the average transmission contrast ratios between the passband and stopband, which can, for example, reduce the effective color provided Identify improvements. In one embodiment, a circular polarizer can be applied to the inner surface and configured so that the linearly polarizing element absorbs backside reflections. This construction can achieve a very high contrast ratio. Alternatively, a metallic attenuating coating can be incorporated into the interference filter, which includes, for example, titanium dioxide and silicon dioxide (TiO₂ and SiO₂ ) layer, and the metal layer includes pure titanium. Due to the properties of these metal layers when incorporated into interference filters, the configuration can be significantly better than an equivalent neutral density filter with respect to the attenuation of reflectivity. Furthermore, due to the good material compatibility between metal and metal oxide, this configuration can provide a robust product that is also economical to produce and provides the desired effect on color vision. A further concern related to the reflectivity of interference filters concerns the placement of interference filters in ophthalmic lens assemblies, where such filters may be present within the substrate if they are disposed on an interior surface. Visible artifacts caused by reflections; these are preferably mitigated by a high-quality anti-reflective coating on the opposite surface of the lens. Preferred embodiments of the filter may be considered regarding the incorporation into the lamp assembly of a filter configured to provide enhanced color discrimination (where the filter may also be referred to as a dichroic reflector). The efficiency of these assemblies and the quality of color discrimination provided by both the transmitted and reflected components of the illuminant. In some embodiments, the illuminant may be a broadband source, for example, where the transmitted component enhances discrimination between red and green, and the reflected component enhances discrimination between blue and yellow. Preferably, the illuminator can be a multi-band source (such as an array of red LEDs, green LEDs, and blue LEDs) so that the transmitted component provides enhanced color discrimination and the reflected component remains normal. Color discrimination. There are preferred configurations of lamp assemblies in which both transmitted and reflected components of light are used for illumination. The methods disclosed herein may be implemented, for example, using the commercially available computing software program Mathematica® (including its linear program solver) available from Wolfram Research on a computer with a 2.3 GHz Intel Core i7 processor and 8 GB of RAM. Filter design methods. However, those skilled in the art should understand that the methods disclosed herein are not limited to the above implementations and have nothing to do with the computer/system architecture. Accordingly, the methods can be implemented equivalently on other computing platforms, using other computing software (commercially available or specifically coded computing software for filter design methods), and can also be hardwired into a circuit or other computing component . The present invention is illustrative and not restrictive. Further modifications will be apparent to those skilled in the art in view of the present invention. For example, although the methods and steps described above indicate certain events occurring in a certain order, one of ordinary skill will recognize that the order of certain steps may be modified and such modifications are consistent with the invention disclosed herein. Additionally, if feasible, some of the steps may be performed simultaneously in a parallel program, and some of the steps may be performed sequentially as described above. Actions referred to herein as operations of a method or procedure may also be understood as "steps" in the method or procedure. Therefore, in this regard, there are variations of the invention disclosed herein that are within the spirit of the invention or equivalent to the invention disclosed herein, and the invention and its patentable scope are also intended to cover such variations. All publications and patent applications cited in this application are incorporated by reference in their entirety to the same extent as if each individual publication or patent application was specifically and individually indicated to be incorporated by reference.

101‧‧‧Illuminating body 102‧‧‧Optical system 103‧‧‧Light reflection 104‧‧‧Reference color 105‧‧‧Light transmission 106‧‧‧Optical Filter 107‧‧‧Light absorption 108‧‧‧Short wavelength cones 109‧‧‧Light absorption 110‧‧‧Medium wavelength cones 111‧‧‧Light absorption 112‧‧‧Long wavelength cones 113‧‧‧Observer 115‧‧‧Visual phototransduction operation 116‧‧‧Chroma 117‧‧‧Luminosity 118‧‧‧Color Appearance Model 201‧‧‧Curve of spectral absorbance of short-wavelength cone photopigments 202‧‧‧Curve of spectral absorbance of medium-wavelength cone photopigments 203‧‧‧Curve of spectral absorbance of long-wavelength cone photopigments 204‧‧‧Genotype 205‧‧‧Classification 206‧‧‧The wavelength of the maximum absorption rate of short-wavelength cone photopigments 207‧‧‧The wavelength of the maximum absorption rate of medium-wavelength cone photoreceptor photopigments 208‧‧‧The wavelength of the maximum absorption rate of long-wavelength cone photoreceptor photopigments 301‧‧‧Neural excitation of long-wavelength cones 302‧‧‧points 303‧‧‧Luminosity response line 304‧‧‧Plane 305‧‧‧Projection 306‧‧‧Neural excitation of medium-wavelength cones 307‧‧‧Axis/origin 309‧‧‧Contour/Spectral Trajectory 310‧‧‧Neural excitation of short-wavelength cone cells 401‧‧‧Test filter 402‧‧‧Illuminating body 403‧‧‧Reference color 404‧‧‧Observer 405‧‧‧Reference Filter 406‧‧‧Operation 407‧‧‧Operation 408‧‧‧Color gamut area 409‧‧‧Color gamut area 410‧‧‧ratio 411‧‧‧Relative color gamut area 501‧‧‧Reference color 502‧‧‧Illuminating body 503‧‧‧Optical filter 505‧‧‧Optical interaction 506‧‧‧Visual phototransduction 507‧‧‧Observer 508‧‧‧Color Appearance Model 509‧‧‧Chromaticity coordinates 510‧‧‧Delaunay Triangulation Algorithm 512‧‧‧Color gamut area 601‧‧‧Munsell 5B 5/4 spectral reflectance 602‧‧‧Munsell 5G 5/4 spectral reflectance 603‧‧‧Munsell 5Y 5/4 spectral reflectance 604‧‧‧Munsell 5R 5/4 spectral reflectance 605‧‧‧Munsell 5P 5/4 spectral reflectance 606‧‧‧Spectral reflectance of blue flower 607‧‧‧Spectral reflectance of green leaves 608‧‧‧Spectral reflectance of yellow flower 609‧‧‧Spectral reflectance of safflower 610‧‧‧Spectral reflectance of purple flower 701‧‧‧Dotted outline 702‧‧‧Solid outline 703‧‧‧Solid outline 704‧‧‧points 705‧‧‧Dotted outline 706‧‧‧points 708‧‧‧Line segment 709‧‧‧Enclosed solid line 710‧‧‧Spectral radiant flux of illuminant D65 711‧‧‧Spectral transmittance of reference filter 712‧‧‧Test filter white point 802‧‧‧Solid outline 803‧‧‧Solid outline 804‧‧‧white spot 807‧‧‧Dot/dashed outline 808‧‧‧Dotted Line Wheel 809‧‧‧Spectral radiant flux 810‧‧‧Spectral transmittance of reference filter 811‧‧‧Spectral transmittance of test filter 901‧‧‧Cost Vector 902‧‧‧Spectral transmittance constraint 903‧‧‧Filter Generator 904‧‧‧Illuminating body 905‧‧‧Linear program solver 906‧‧‧Constraint projection limit/Constraint projection limit vector 907‧‧‧Linear Program 908‧‧‧Filter white point constraint 909‧‧‧Constrained projection norm/constrained projection norm matrix 910‧‧‧Three-color constraint calculation operation 911‧‧‧Solution vector 912‧‧‧Reference Filter 913‧‧‧Basic Filter 914‧‧‧Weighted sum operation 915‧‧‧Color Appearance Constraints 916‧‧‧Smooth operation 917‧‧‧Filter assembly operation 918‧‧‧Observer 919‧‧‧Pre-filter 920‧‧‧Smooth core 921‧‧‧Filter specifications/composite design filters 922‧‧‧Offset 923‧‧‧Offset coefficient 1001‧‧‧Convex polyhedron 1002‧‧‧Convex polyhedron 1003‧‧‧Trichromatic value 1004‧‧‧iso-bright plane 1005‧‧‧Wall-like surface/cone 1006‧‧‧Upper luminosity limit 1007‧‧‧lower luminosity limit 1101‧‧‧Color Appearance Constraints 1102‧‧‧Three-color constraint calculation 1103‧‧‧Observer 1104‧‧‧Luminance limit interval 1105‧‧‧Reference light 1106‧‧‧Chroma Boundary 1107‧‧‧Basic Filter 1108‧‧‧Light transmission 1109‧‧‧Operation 1111‧‧‧Light transmission 1112‧‧‧Matrix 1113‧‧‧Surface 1114‧‧‧Observer 1115‧‧‧Retinal photopigment absorption rate/visual phototransduction 1116‧‧‧Matrix-vector product 1117‧‧‧Trichromatic value 1118‧‧‧Boundary 1119‧‧‧Vector length/norm 1201‧‧‧Cost function 1202‧‧‧Cost function 1203‧‧‧Nature Filter 1204‧‧‧Munsell Color Filter 1301‧‧‧Optical Filter Design Guidelines/Reference Colors 1302‧‧‧Optical Filter Design Program/Optical Filter Design and Analysis Program 1303‧‧‧Filter Generator 1304‧‧‧Reference filter 1305‧‧‧Test filter/test function 1306‧‧‧Illuminating body 1307‧‧‧Performance analysis operation 1308‧‧‧Manufacturing Analysis Procedures/Operations 1309‧‧‧Additional information 1311‧‧‧Manufacturing Specifications 1312‧‧‧Manufacturing cost 1313‧‧‧Results of standard compliance analysis 1314‧‧‧Relative color gamut area 1315‧‧‧Operation 1316‧‧‧Operation 1317‧‧‧Operation 1401‧‧‧Chroma Boundary/Point 1402‧‧‧points 1403‧‧‧points 1404‧‧‧points 1405‧‧‧Chroma Boundary/Area 1406‧‧‧Chroma Boundary 1407‧‧‧Curve of spectral radiant flux of green traffic signal 1408‧‧‧Curve of spectral radiant flux of sunlight 1409‧‧‧Curve of spectral radiant flux of yellow traffic signal 1410‧‧‧Transmittance of filter/constrained filter 1411‧‧‧Transmittance of Unconstrained Filter 1501‧‧‧curve 1502‧‧‧curve 1503‧‧‧curve 1504‧‧‧Optical Filter/Spectral Transmittance Curve 1601‧‧‧Curve 1603‧‧‧curve 1604‧‧‧Curve 1605‧‧‧curve 1701‧‧‧Contour 1702‧‧‧Contour 1703‧‧‧Contour 1705‧‧‧Curve 1706‧‧‧Curve 1707‧‧‧Curve 1801‧‧‧Contour 1802‧‧‧Contour 1803‧‧‧Chromaticity coordinates 1804‧‧‧Curve 1805‧‧‧Reference Number 1806‧‧‧Curve 1807‧‧‧Curve 1902‧‧‧Solid curve 1903‧‧‧Dotted curve 1904‧‧‧Dotted curve 2001‧‧‧Solid curve/dashed curve 2002‧‧‧Solid curve/dashed curve 2101‧‧‧Spectral radiation flux of blue primary color light 2102‧‧‧Spectral radiation flux of green primary color light 2103‧‧‧Spectral radiant flux of sunlight 2104‧‧‧Spectral radiation flux of red primary color light 2105‧‧‧Tri-band filter 2106‧‧‧Optical filter 2201‧‧‧Maximum transmittance constraint 2301‧‧‧Maximum transmittance constraint 2401‧‧‧Linear Polarizer 2402‧‧‧Quarter Wave Retarder/Circular Polarizer 2403‧‧‧Optical transparent substrate 2404‧‧‧Multilayer interference coating/interference filter 2405‧‧‧Quarter Wave Retarder 2406‧‧‧Polarizer 2408‧‧‧Beam 2409‧‧‧eyes 2411‧‧‧Reflected light 2412‧‧‧Retina 2413‧‧‧arrow 2414‧‧‧Reflection component 2501‧‧‧Spectral radiant flux of composite illuminator 2502‧‧‧Spectral radiant flux of white LED 2503‧‧‧Spectral radiant flux of red LED 2504‧‧‧Spectral transmittance 2601‧‧‧Chromaticity coordinates 2602‧‧‧Chromaticity coordinates 2603‧‧‧points 2604‧‧‧Spectral radiant flux of mixture of LED illuminants 2605‧‧‧Spectral transmittance 2606‧‧‧Spectral transmittance 2701‧‧‧Thermal conductive substrate 2702‧‧‧Light-emitting diode 2703‧‧‧Beam forming optical light guide/optical device 2707‧‧‧Output beam 2801‧‧‧Anti-reflective coating 2802‧‧‧Optical substrate 2803‧‧‧First attenuation coating 2804‧‧‧Multi-layer interference coating 2805‧‧‧Second attenuation coating 2806‧‧‧Beam 2807‧‧‧eyes 2809‧‧‧Retina 2810‧‧‧Reflected light 2811‧‧‧arrow 2812‧‧‧Reflection component 2815‧‧‧First attenuation coating 2901‧‧‧Spherical Section 2902‧‧‧Spherical Section 2904‧‧‧Hemisphere 2905‧‧‧Hemisphere 2906‧‧‧Dotted arrow 2909‧‧‧Dotted arrow 3001‧‧‧Contour 3002‧‧‧Contour 3003‧‧‧Contour 3004‧‧‧Border/Interference Filter 3005‧‧‧points 3006‧‧‧Contour 3007‧‧‧Curve 3008‧‧‧Output beam/curve 3009‧‧‧Curve 3101‧‧‧Solid curve 3102‧‧‧Dotted curve 3103‧‧‧Dotted curve 3104‧‧‧Solid curve 3105‧‧‧Dotted curve 3106‧‧‧Dotted curve 3107‧‧‧Solid curve 3108‧‧‧Dotted curve 3109‧‧‧Dotted curve 3110‧‧‧Solid curve 3111‧‧‧Dotted curve 3112‧‧‧White point displacement diagram 4301‧‧‧Dotted curve 4302‧‧‧Solid curve 4303‧‧‧Solid curve 4304‧‧‧Dotted curve 4401‧‧‧Dotted outline 4402‧‧‧Solid outline 4404‧‧‧Spectral transmittance of blue light blocking multi-band filter 4405‧‧‧Spectral transmittance of blue light blocking filter 4601‧‧‧Anti-reflective coating 4602‧‧‧Absorbent optical substrate 4604‧‧‧Multi-layer interference coating 4606‧‧‧Beam 4607‧‧‧eyes 4609‧‧‧Retina 4610‧‧‧Reflected light 4611‧‧‧arrow 4612‧‧‧Reflection component 4701‧‧‧Dotted outline 4702‧‧‧Solid outline 4704‧‧‧Spectral transmittance curve 4705‧‧‧Solid curve 5801‧‧‧Rounded corner frame/entity 5802‧‧‧Solid/square frame 5803‧‧‧Rounded corner box/entity 5805‧‧‧square frame 5806‧‧‧Composite operation 5808‧‧‧Composite object 5811‧‧‧Composite object

Figure 1: Process flow chart depicting photosensitive observation and color perception of the human eye. Figure 2A, Figure 2B: A curve graph of the spectral absorbance of retinal photopigments in normal people (Fig. 2A); and a table of peak variables of the spectral absorbance of retinal photopigments corresponding to known genotypes in the population (Fig. 2B ). Figure 3: A trichromatic diagram showing the tristimulus values corresponding to a color appearance and their projection into the luminescence and chrominance components. Figure 4: Process flow chart for relative gamut area calculation for comparing the effect on color discrimination of two filters. Figure 5: Process flow chart for calculation of color gamut area relative to a specific set of reference colors, an illuminant, a filter and an observer. Figure 6A, Figure 6B: A graph of spectral reflectance of selected Munsell colors (Fig. 6A); and a graph of spectral reflectance of selected colors from natural objects (Fig. 6B). Figures 7A to 7C: Chromaticity diagrams of the color appearance of selected Munsell colors under daylight illumination (as viewed through a first filter and a second filter) (Figure 7A); Spectral radiation of daylight A graph of flux (Fig. 7B); and a graph of spectral transmittance of these filters (Fig. 7C). Figures 8A to 8C: Chromaticity diagrams of the color appearance of selected natural colors under sunlight (as viewed through a first filter and a second filter) (Figure 8A); Spectral radiation of sunlight A graph of flux (Fig. 8B); and a graph of spectral transmittance of these filters (Fig. 8C). Figure 9: Process flow chart of filter generation by linear programming method. Figure 10A, Figure 10B: A trichromatic diagram showing the trichromatic value corresponding to a color appearance and the boundary of a constrained convex polyhedron (Fig. 10A); an expanded view of the trichromatic value and the boundary of the constrained convex polyhedron (Fig. 10B) . Figure 11: Constrained projection norms with respect to a specific reference light, a convex chromaticity boundary, a luminosity boundary, a first observer, a basic filter, a pre-filter and a second observer Program flow chart for calculating constrained projection limits. Figure 12A, Figure 12B: A graph of a cost function designed to enhance the red-green discrimination of Munsell colors and a graph of a cost function designed to enhance the red-green discrimination of natural colors (Fig. 12A); and the designs have corresponding A graph of the spectral transmittance of the two filters as a function of cost (Figure 12B). Figure 13: Process flow chart of the iterative filter design process considering design criteria, usage criteria, and manufacturing criteria. Figure 14A to Figure 14C: Chromaticity diagram of the color appearance of green and yellow traffic signals and daylight viewed through a first filter and a second filter (Figure 14A); A graph of spectral radiant flux (Fig. 14B); and a graph of spectral transmittance of the filter (Fig. 14C). Figure 15A to Figure 15B: A graph of two variables of a minimum spectral transmittance constraint (Fig. 15A); and a graph of the spectral transmittance of the corresponding color enhancement filter that satisfies the constraint (Fig. 15B). Figure 16A, Figure 16B: Graph of the displacement of wavelength percentage as a function of incident angle for an interference filter with a refractive index of 1.85 according to Snell's law (Figure 16A); and a filter that provides enhanced red-green discrimination A graph of the spectral transmittance of an optical device and a graph of the spectral transmittance of an optical filter that additionally provides a stable color appearance over a range of wavelength shifts (Figure 16B). Figures 17A to 17C: Chromaticity diagrams of the color appearance of selected Munsell colors under daylight illumination (as viewed through a filter and as determined by the same filter with wavelength shifts of -2.5% and -5% View) (Figure 17A); a curve of the spectral radiant flux of sunlight (Figure 17B); and a curve of the spectral transmittance of the filter and the filter with wavelength shifts of -2.5% and -5% Figure (Fig. 17C). Figures 18A to 18C: Chromaticity diagrams of the color appearance of selected Munsell colors under daylight illumination (as viewed through a filter and as viewed through the same filter with a wavelength shift of -2.5%) (Figure 18A); a graph of the spectral radiant flux of sunlight (Fig. 18B); and a graph of the spectral transmittance of the filter and the filter with a wavelength shift of -2.5% (Fig. 18C). Figure 19A, Figure 19B: Graph of the blue light risk function as a function of wavelength (Figure 19A); and the spectral transmittance of two multi-band filters that provide blue light blocking and a conventional cut-off filter that provides blue light blocking. Graph (Figure 19B). Figure 20A, Figure 20B: Curves of spectral transmittance of two narrow-band selective absorption filters (Fig. 20A); and spectral transmittance of two multi-band interference filters and absorption filters that provide red and green discrimination enhancement Rate curve (Figure 20B). Figure 21A, Figure 21B: Curves of the spectral radiant flux of sunlight and primary color light of a liquid crystal display with a light-emitting diode backlight (Figure 21A); and providing an enhancement of display primary colors relative to the luminosity of sunlight A graph of spectral transmittance of a filter as a function of luminosity (Figure 21B). Figure 22A, Figure 22B: Curves of spectral transmittance constraints for a filter that protects the eye from 532 nm radiation emitted by a frequency-octaved Nd:YAG laser with an incident angle between 0 degrees and about 30 degrees. Figure (Figure 22A); and a graph of the spectral transmittance of this filter (Figure 22B). Figures 23A, 23B: Graph of spectral transmittance constraints of a filter that protects the eye from 589 nanometer radiation emitted by a sodium illumination torch with incident angles between 0 degrees and about 30 degrees (Figure 23A ); and a graph of the spectral transmittance of this filter (Figure 23B). Figure 24A, Figure 24B: Schematic diagram of a composite lens containing an interference filter and a circular polarizer that absorbs light reflected by the interference filter (Fig. 24A); and showing the operation of the composite filter A schema (Fig. 24B). Figure 25A, Figure 25B: Curves of the spectral radiant flux of white light formed by combining a phosphor-based white light-emitting diode and a red light-emitting diode (Figure 25A); and designed to enhance the transmission of a The spectral transmittance of a filter that imparts a good color appearance to objects illuminated by light transmitted by the filter and provides a good color appearance to objects illuminated by light reflected by the filter (Figure 25B). Figures 26A to 26C: Chromaticity diagrams of the color appearance of selected Munsell colors under illumination of a combination of white LEDs and red LEDs (as viewed when the illuminant is transmitted through a filter and as when the illuminant is transmitted through a filter) (as viewed when the filter reflects) (Figure 26A); the spectral radiant flux of the illuminant (Figure 26B); and the graph of the spectral transmittance of these filters (Figure 26C). Figure 27A, Figure 27B: Contains a light-emitting diode, an interference filter and provides a composite light beam (wherein the central area of the light beam includes the light transmitted through the filter and the annular area of the light beam includes the light transmitted by the filter) A schematic diagram of a lamp assembly (Fig. 27A) as a beam forming element (light reflected by a filter); and a diagram showing the operation of the lamp assembly incorporating the filter (Fig. 27B). Figure 28A, Figure 28B: Schematic diagram of a composite filter containing an interference filter and an absorption filter (where the absorption filters attenuate the light reflected by the interference filter) (Figure 28A); and a diagram showing the operation of the composite filter incorporated into eyeglasses (Fig. 28B). Figure 29A, Figure 29B: Diagrams showing the geometry of a lens in glasses relative to the eye and two beams of light passing through the lens at different positions and being imaged on the retina of the eye; top view (Figure 29A) and Angular view (Fig. 29B). Figure 30A, Figure 30B: Contour diagrams of the effective incident angle of light passing through a position on the surface of a lens, where the effective incident angle corresponds to the surface normal of the lens at a position and the angle passing through the position. The angle between the lens and a beam of light imaged onto the retina (Fig. 30A); and a graph of relative importance and components of the relative importance function as a function of effective angle of incidence (Fig. 30B). Figures 31A to 31E: Plots of transmittance constraints and cost functions for a filter designed to enhance color discrimination for a normal observer (Figure 31A); plots of spectral transmittance of components of the filter Figure (Figure 31B); Plot of one manufacturing specification of this filter (Figure 31C); Relative to the Farnsworth D-15 reference color as a function of angle of incidence and relative to the selected color provided by the filter A graph of the percentage increase in gamut area of a natural reference color (Fig. 31D); a graph of the white point shift of daylight provided by the filter as a function of angle of incidence (Fig. 31E). Figures 32A to 32E: Graphs of transmittance constraints and cost functions for designing a filter that enhances red-green discrimination for a normal observer (Figure 32A); spectral transmittance of components of the filter Graph (Fig. 32B); Graph of one manufacturing specification of this filter (Fig. 32C); relative to Farnsworth D-15 reference color as a function of angle of incidence and relative to selected colors provided by this filter A graph of the percentage increase in gamut area of a natural reference color (Fig. 32D); a graph of the white point shift of daylight provided by the filter as a function of incident angle (Fig. 32E). Figures 33A to 33E: Graphs of transmittance constraints and cost functions for designing a filter that enhances red-green discrimination for a normal observer and provides a stable color appearance over a range of incident angles (Figure 33A); A graph of the spectral transmittance of components of the filter (Figure 33B); a graph of one of the manufacturing specifications of the filter (Figure 33C); relative to the Farnsworth D-15 reference color as a function of angle of incidence and Plot of percentage increase in gamut area relative to selected natural reference colors provided by the filter (Fig. 33D); white point shift of daylight provided by the filter as a function of angle of incidence Graph (Figure 33E). Figures 34A to 34E: Graphs of transmittance constraints and cost functions for designing a filter that enhances blue-yellow discrimination for a normal observer and provides a stable color appearance over a range of incident angles (Figure 34A); A graph of the spectral transmittance of components of the filter (Figure 34B); a graph of one of the manufacturing specifications of the filter (Figure 34C); relative to the Farnsworth D-15 reference color as a function of angle of incidence and Plot of percent increase in gamut area relative to selected natural reference colors provided by the filter (Fig. 34D); white point shift of daylight provided by the filter as a function of angle of incidence Graph (Figure 34E). Figures 35A to 35E: Curves of transmittance constraints and cost functions for designing a filter that enhances red-green discrimination in a normal observer and provides suppression of short-wavelength blue light and stable color appearance over a range of incident angles. Figure (Figure 35A); a graph of the spectral transmittance of components of the filter (Figure 35B); a graph of one of the manufacturing specifications of the filter (Figure 35C); versus Farnsworth as a function of incident angle Plot of D-15 reference color and percent increase in gamut area relative to selected natural reference colors provided by the filter (Fig. 35D); as a function of angle of incidence provided by the filter Curve of daylight white point displacement (Figure 35E). Figures 36A-36E: Plots of transmittance constraints and cost functions for designing a filter that enhances red-green discrimination and provides stable color appearance over a range of incidence angles for an observer with mild deuteranomania. (Figure 36A); a graph of spectral transmittance of components of the filter (Figure 36B); a graph of one of the manufacturing specifications of the filter (Figure 36C); versus Farnsworth D as a function of incident angle - Graph of 15 reference colors and percent increase in gamut area relative to selected natural reference colors provided by the filter (Fig. 36D); daylight provided by the filter as a function of angle of incidence The white point displacement curve (Figure 36E). Figures 37A-37E: Plots of transmittance constraints and cost functions for designing a filter that enhances red-green discrimination and provides stable color appearance over a range of incidence angles for an observer with moderate green tint. (Figure 37A); a graph of spectral transmittance of components of the filter (Figure 37B); a graph of one of the manufacturing specifications of the filter (Figure 37C); versus Farnsworth D as a function of incident angle - Graph of 15 reference colors and percent increase in gamut area relative to selected natural reference colors provided by the filter (Fig. 37D); daylight provided by the filter as a function of angle of incidence The white point displacement curve (Figure 37E). Figures 38A to 38E: Graphs of transmittance constraints and cost functions for designing a filter that enhances red-green discrimination for an observer with severe deuteranomania and provides stable color appearance over a range of incidence angles ( Figure 38A); a graph of the spectral transmittance of components of the filter (Figure 38B); a graph of one of the manufacturing specifications of the filter (Figure 38C); versus Farnsworth D- as a function of incident angle 15 Plot of reference color and percent increase in gamut area relative to selected natural reference colors provided by the filter (Fig. 38D); daylight provided by the filter as a function of angle of incidence Curve of white point displacement (Figure 38E). Figures 39A-39E: Plots of transmittance constraints and cost functions for designing a filter that enhances red-green discrimination for an observer with redness weakness and provides stable color appearance over a range of incidence angles (Fig. 39A); a graph of the spectral transmittance of components of the filter (Fig. 39B); a graph of one of the manufacturing specifications of the filter (Fig. 39C); relative to Farnsworth D-15 as a function of incident angle Graph of reference color and percent increase in gamut area relative to selected natural reference colors provided by the filter (Fig. 39D); daylight whiteness provided by the filter as a function of angle of incidence Point displacement curve (Figure 39E). Figures 40A-40E: Transmission constraints and costs for designing a filter that enhances the luminosity of primary color light emitted by an electronic visual display to a normal observer and provides a stable color appearance over a range of incidence angles. The graph of the function (Fig. 40A); the graph of the spectral transmittance of the filter component (Fig. 40B); the graph of one of the manufacturing specifications of the filter (Fig. 40C); the incident angle as a function Plot of percent increase in gamut area relative to Farnsworth D-15 reference color and relative to selected natural reference colors provided by this filter (Fig. 40D); The curve of the white point displacement of sunlight provided by the device (Figure 40E). Figures 41A to 41E: Transmittance constraints and cost functions for designing a filter that protects the eye from a 532 nm frequency doubled Nd:YAG laser and provides a stable color appearance over a range of incident angles. The graph of the spectral transmittance of the filter component (Fig. 41B); the graph of one of the manufacturing specifications of the filter (Fig. 41C); the relative Plot of Farnsworth D-15 reference color and percent increase in gamut area relative to selected natural reference colors provided by this filter (Fig. 41D); A graph of the white point displacement of daylight is provided (Figure 41E). Figures 42A-42E: Plots of transmittance constraints and cost functions for designing a filter that protects the eye from a 589 nm sodium illumination torch and provides stable color appearance over a range of incidence angles ( Figure 42A); a graph of the spectral transmittance of components of the filter (Figure 42B); a graph of one of the manufacturing specifications of the filter (Figure 42C); versus Farnsworth D- as a function of incident angle 15 Plot of reference color and percent increase in gamut area relative to selected natural reference colors provided by the filter (Fig. 42D); daylight provided by the filter as a function of angle of incidence Curve of white point displacement (Figure 42E). Figure 43A, Figure 43B: Curves of spectral transmittance constraints of a filter that blocks short-wavelength light and allows narrow-band light of 589 nanometers to pass through (Figure 43A); a filter that obeys these constraints and the A graph of this filter smoothed by a smoothing kernel (Fig. 43B). Figures 44A to 44C: Chromaticity diagrams of the color appearance of selected Munsell colors under sunlight, as viewed through a blue-blocking multi-band filter and a blue-blocking cutoff filter (Fig. 44A); Spectrum of Daylight Radiant flux (Figure 44B); and a graph of spectral transmittance of these filters (Figure 44C). Figures 45A to 45E: Graphs of transmittance constraints and cost functions for designing a filter that provides suppression of short-wavelength blue light and high light transmittance (Figure 45A); spectral transmittance of components of the filter Graph (Fig. 45B); Graph of one manufacturing specification of this filter (Fig. 45C); relative to Farnsworth D-15 reference color as a function of angle of incidence and relative to selected colors provided by this filter A graph of the percentage increase in gamut area of a natural reference color (Fig. 45D); a graph of the white point shift of daylight provided by the filter as a function of incident angle (Fig. 45E). Figure 46A, Figure 46B: Schematic diagram of a composite filter containing an interference filter and an absorption filter (wherein the absorption filters attenuate the light reflected by the interference filter) (Figure 46A); and a diagram showing the operation of the composite filter incorporated into eyeglasses (Fig. 46B). Figures 47A to 47C: Chromaticity diagrams of the color appearance of selected Munsell colors under daylight illumination, as viewed through a reference filter and a neodymium glass filter (Figure 47A); Spectral radiant flux of daylight (Figure 47B); and a graph of the spectral transmittance of these filters (Figure 47C). Figures 48A to 48E: Graphs of transmittance constraints and cost functions for a neodymium-containing filter designed to enhance red-green discrimination for a normal observer and provide stable color appearance over a range of incidence angles (Figure 48A ); a graph of the spectral transmittance of components of the filter (Figure 48B); a graph of one of the manufacturing specifications of the filter (Figure 48C); relative to the Farnsworth D-15 reference as a function of angle of incidence Plot of color and percent increase in gamut area relative to selected natural reference colors provided by the filter (Fig. 48D); white point of daylight provided by the filter as a function of angle of incidence Displacement curve (Figure 48E). Figures 49A to 49E: Graphs of transmittance constraints and cost functions for a neodymium-containing filter designed to enhance blue-yellow discrimination for a normal observer and provide stable color appearance over a range of incidence angles (Figure 49A ); a graph of the spectral transmittance of components of the filter (Figure 49B); a graph of one of the manufacturing specifications of the filter (Figure 49C); relative to the Farnsworth D-15 reference as a function of angle of incidence Plot of color and percent increase in gamut area relative to selected natural reference colors provided by the filter (Figure 49D); white point of daylight provided by the filter as a function of angle of incidence Displacement curve (Figure 49E). Figures 50A to 50E: Transmittance constraints and cost functions for designing a neodymium-containing filter that enhances red-green discrimination for an observer with mild green tint and provides stable color appearance over a range of incidence angles. Curve (Fig. 50A); Curve of spectral transmittance of components of the filter (Fig. 50B); Curve of one of the manufacturing specifications of the filter (Fig. 50C); Relative to Plot of Farnsworth D-15 reference color and percent increase in gamut area relative to selected natural reference colors provided by this filter (Fig. 50D); as a function of angle of incidence provided by this filter The curve of the white point displacement of sunlight (Figure 50E). Figures 51A-51E: Transmittance constraints and cost functions for designing a neodymium-containing filter that enhances red-green discrimination for an observer with moderate green tint and provides stable color appearance over a range of incidence angles. Curve graph (Fig. 51A); Curve graph of spectral transmittance of components of the filter (Fig. 51B); Curve graph of one of the manufacturing specifications of the filter (Fig. 51C); Relative to Plot of Farnsworth D-15 reference color and percent increase in gamut area relative to selected natural reference colors provided by this filter (Fig. 51D); as a function of angle of incidence provided by this filter The curve of the white point displacement of sunlight (Figure 51E). Figures 52A to 52E: Curves of transmittance constraints and cost functions for designing a neodymium-containing filter that enhances red-green discrimination and provides stable color appearance over a range of incident angles for an observer with severe deuteranomania. Figure (Figure 52A); a graph of the spectral transmittance of components of the filter (Figure 52B); a graph of one of the manufacturing specifications of the filter (Figure 52C); versus Farnsworth as a function of incident angle Plot of D-15 reference color and percent increase in gamut area relative to selected natural reference colors provided by the filter (Fig. 52D); as a function of angle of incidence provided by the filter Curve of daylight white point displacement (Fig. 52E). Figures 53A-53E: Graphs of transmittance constraints and cost functions for designing a neodymium-containing filter that enhances red-green discrimination for an observer with redness weakness and provides stable color appearance over a range of incident angles. (Figure 53A); a graph of the spectral transmittance of components of the filter (Figure 53B); a graph of one of the manufacturing specifications of the filter (Figure 53C); versus Farnsworth D as a function of incident angle - Graph of 15 reference colors and percent increase in gamut area relative to selected natural reference colors provided by the filter (Fig. 53D); daylight provided by the filter as a function of angle of incidence The white point displacement curve (Figure 53E). Figure 54A, Figure 54B: Graph of approximate spectral absorbance of retinal ganglion cells (Figure 54A); a blue broadband reference filter and a multi-band filter that maximizes photon energy absorbed by retinal ganglion cells Curve diagram of optical device (Fig. 54B). Figures 55A to 55E: Plots of transmittance constraints and cost functions for designing a filter that enhances optical power received by retinal ganglion cells (Figure 55A); spectral transmittance of components of the filter A graph of one of the manufacturing specifications of this filter (Fig. 55C); a graph of reference color as a function of angle of incidence relative to the Farnsworth D-15 and relative to the experience provided by the filter A graph of the percentage increase in gamut area for selected natural reference colors (Fig. 55D); a graph of the white point shift of daylight provided by the filter as a function of angle of incidence (Fig. 55E). Figures 56A-56E: Plots of transmittance constraints and cost functions for designing a filter that enhances the optical power absorbed by retinal ganglion cells and provides a stable color appearance over a range of incident angles (Figure 56A) ; Graph of spectral transmittance of components of the filter (Fig. 56B); Graph of one of the manufacturing specifications of the filter (Fig. 56C); Relative to Farnsworth D-15 reference color as a function of angle of incidence and a plot of percent increase in gamut area relative to selected natural reference colors provided by the filter (Fig. 56D); white point shift for daylight provided by the filter as a function of angle of incidence Graph (Figure 56E). Figures 57A-57E: Plots of transmittance constraints and cost functions for designing a neodymium-containing filter that enhances the optical power received by retinal ganglion cells and provides stable color appearance over a range of incidence angles (Fig. 57A); a graph of the spectral transmittance of components of the filter (Fig. 57B); a graph of one of the manufacturing specifications of the filter (Fig. 57C); relative to Farnsworth D-15 as a function of angle of incidence Graph of reference color and percent increase in gamut area relative to selected natural reference colors provided by the filter (Fig. 57D); daylight whiteness provided by the filter as a function of angle of incidence Point displacement curve (Figure 57E). Figure 58: An example program flow diagram used to describe and demonstrate the syntax and structure of the program flow diagram as presented in other figures. Figures 59A, 59B: Table of evaluated performance criteria for the filters of Figures 31A to 31E for enhancing color discrimination for a normal observer (Figure 59A); transmittance, cost function of the filter assembly , transmittance constraints and filter manufacturing specifications table (Figure 59B). Figure 60A, Figure 60B: Table of evaluated performance criteria for the optical filter of Figures 32A to 32E for enhancing the red-green discrimination of a normal observer (Figure 60A); transmittance, cost of the filter assembly Table of functions, transmittance constraints, and filter manufacturing specifications (Figure 60B). Figures 61A, 61B: Table of evaluated performance criteria for the optical filters of Figures 33A to 33E for enhancing red-green discrimination in a normal observer and providing stable color appearance over a range of incident angles (Figure 61A ); table of transmittance, cost function, transmittance constraints and manufacturing specifications of the filter assembly (Figure 61B). Figures 62A, 62B: Table of evaluated performance criteria for the filters of Figures 34A to 34E for enhancing blue-yellow discrimination in a normal observer and providing stable color appearance over a range of incidence angles (Figure 62A ); table of transmittance, cost function, transmittance constraints and manufacturing specifications of the filter assembly (Figure 62B). Figures 63A, 63B: Evaluated performance of the optical filters of Figures 35A to 35E for enhancing red-green discrimination in a normal observer and providing suppression of short-wavelength blue light and stable color appearance over a range of incident angles. Table of criteria (Figure 63A); table of transmittance, cost function, transmittance constraints and filter manufacturing specifications of the filter assembly (Figure 63B). Figures 64A, 64B: Evaluated performance criteria for the filters of Figures 36A to 36E for enhanced red-green discrimination and providing stable color appearance over a range of incident angles for an observer with mild deuteranomania. Table (Figure 64A); table of transmittance, cost function, transmittance constraints and filter manufacturing specifications of the filter assembly (Figure 64B). Figures 65A, 65B: Evaluated performance criteria for the filters of Figures 37A to 37E for enhanced red-green discrimination and providing stable color appearance over a range of incident angles for an observer with moderate deuteranomaly. Table (Figure 65A); table of transmittance, cost function, transmittance constraints of the filter assembly and manufacturing specifications of the filter (Figure 65B). Figures 66A, 66B: Evaluated performance criteria for the filters of Figures 38A to 38E for enhanced red-green discrimination and providing stable color appearance over a range of incident angles for an observer with severe deuteranomaly. Table (Fig. 66A); Table of transmittance, cost function, transmittance constraints of the filter assembly and manufacturing specifications of the filter (Fig. 66B). Figures 67A, 67B: Table of evaluated performance criteria for the filters of Figures 39A to 39E for enhanced red-green discrimination for an observer with redness weakness and providing stable color appearance over a range of incidence angles (Figure 67A); a table of transmittance, cost function, transmittance constraints and manufacturing specifications of the filter assembly (Figure 67B). Figures 68A, 68B: Schematics of the optical filters of Figures 40A to 40E for enhancing the luminosity of primary color light emitted by an electronic visual display to a normal observer and providing a stable color appearance within a range of incident angles. Table of performance criteria for evaluation (Figure 68A); table of transmittance, cost function, transmittance constraints and filter manufacturing specifications of the filter assembly (Figure 68B). Figure 69A, Figure 69B: Evaluation of the optical filter of Figures 41A to 41E for protecting the eye from a 532 nm frequency doubled Nd:YAG laser and providing a stable color appearance over a range of incident angles Table of performance criteria (Figure 69A); table of transmittance, cost function, transmittance constraints and filter manufacturing specifications of the filter assembly (Figure 69B). Figures 70A, 70B: Evaluated performance criteria for the filters of Figures 42A to 42E for protecting the eye from a 589 nm sodium illuminator and providing a stable color appearance over a range of angles of incidence. Table (Figure 70A); Table of transmittance, cost function, transmittance constraints of the filter assembly, and manufacturing specifications of the filter (Figure 70B). Figure 71A, Figure 71B: Table of evaluated performance criteria for the optical filter of Figures 45A to 45E for providing suppression of short-wavelength blue light and high light transmittance (Figure 71A); transmittance, cost of the filter assembly Table of functions, transmittance constraints, and filter manufacturing specifications (Figure 71B). Figures 72A, 72B: Table of evaluated performance criteria for the neodymium-containing filters of Figures 48A to 48E for enhancing red-green discrimination in a normal observer and providing stable color appearance over a range of incident angles ( Figure 72A); a table of transmittance, cost function, transmittance constraints and filter manufacturing specifications of the filter assembly (Figure 72B). Figures 73A, 73B: Table of evaluated performance criteria for the neodymium-containing filters of Figures 49A to 49E for enhancing blue-yellow discrimination by a normal observer and providing stable color appearance over a range of incident angles ( Figure 73A); a table of transmittance, cost function, transmittance constraints and filter manufacturing specifications of the filter assembly (Figure 73B). Figures 74A, 74B: Evaluation of the neodymium-containing filters of Figures 50A to 50E for enhanced red-green discrimination and providing stable color appearance over a range of incident angles for an observer with mild deuteranomania. Table of performance criteria (Figure 74A); table of transmittance, cost function, transmittance constraints and filter manufacturing specifications of the filter assembly (Figure 74B). Figures 75A, 75B: Evaluation of the neodymium-containing filters of Figures 51A to 51E for enhanced red-green discrimination and providing stable color appearance over a range of incident angles for an observer with moderate green tint. Table of performance criteria (Figure 75A); table of transmittance, cost function, transmittance constraints and filter manufacturing specifications of the filter assembly (Figure 75B). Figures 76A, 76B: Evaluated performance of the neodymium-containing filters of Figures 52A to 52E for enhanced red-green discrimination and providing stable color appearance over a range of incident angles for an observer with severe deuteranomaly. Table of criteria (Figure 76A); table of transmittance, cost function, transmittance constraints and filter manufacturing specifications of the filter assembly (Figure 76B). Figures 77A, 77B: Evaluated performance criteria for the neodymium-containing filters of Figures 53A to 53E for enhanced red-green discrimination for an observer with redness weakness and providing stable color appearance over a range of incident angles. Table (Figure 77A); table of transmittance, cost function, transmittance constraints and filter manufacturing specifications of the filter assembly (Figure 77B). Figures 78A, 78B: Table of evaluated performance criteria for the three-pass band filter of Figures 55A to 55E for enhancing optical power received by retinal ganglion cells (Figure 78A); filter assembly Table of transmittance, cost function, transmittance constraints, and filter manufacturing specifications (Figure 78B). Figures 79A, 79B: Evaluated performance criteria for the four-pass band filter of Figures 56A to 56E for enhancing the optical power received by retinal ganglion cells and providing a stable color appearance over a range of incident angles. Table (Figure 79A); Table of transmittance, cost function, transmittance constraints and filter manufacturing specifications of the filter assembly (Figure 79B). Figures 80A, 80B: Evaluated performance of the neodymium-containing three-pass band filter of Figures 57A to 57E for enhancing the optical power received by retinal ganglion cells and providing a stable color appearance over a range of incident angles. Table of criteria (Figure 80A); table of transmittance, cost function, transmittance constraints and filter manufacturing specifications of the filter assembly (Figure 80B).

901‧‧‧Cost Vector

902‧‧‧Spectral transmittance constraint

903‧‧‧Filter Generator

904‧‧‧Illuminating body

905‧‧‧Linear program solver

906‧‧‧Constraint projection limit/Constraint projection limit vector

907‧‧‧Linear Program

908‧‧‧Filter white point constraint

909‧‧‧Constrained projection norm/constrained projection norm matrix

910‧‧‧Three-color constraint calculation operation

911‧‧‧Solution vector

912‧‧‧Reference Filter

913‧‧‧Basic Filter

914‧‧‧Weighted sum operation

915‧‧‧Color Appearance Constraints

916‧‧‧Smooth operation

917‧‧‧Filter assembly operation

918‧‧‧Observer

919‧‧‧Pre-filter

920‧‧‧Smooth core

921‧‧‧Filter specifications/composite design filters

922‧‧‧Offset

923‧‧‧Offset coefficient

Claims (42)

A method for enhancing red-green discrimination (discrimination) for observers with deuteranomalous or protanomalous color vision defects. The method includes providing a multi-band optical filter (multi-band optical filter) for the observer. filter to view colored objects through the multi-band optical filter. The multi-band optical filter includes: a plurality of pass-bands and stop bands that partition the visible spectrum. -bands), including: three or more passbands, which are interleaved with two or more stopbands, wherein each passband has a center and a width equal to the center minus the width. One-half the lower band boundary is equal to the center plus one-half the width of the upper band boundary and a mean transmittance. Each stopband has a center, a width equal to The center minus a lower band boundary of half the width is equal to the center plus an upper band boundary of half the width and an average transmittance, the lower band boundary of each staggered stopband being equal to the lower band boundary of an adjacent passband The upper frequency band boundary is the same, the upper frequency band boundary of each staggered stopband is the same as the lower frequency band boundary of an adjacent passband, the center of each passband is between about 400 nanometers and about 700 nanometers, and the width of each passband is between Between about 10 nanometers and about 110 nanometers, Each stop band center is between about 410 nanometers and about 690 nanometers, and each stop band width is between about 10 nanometers and about 80 nanometers, and each of the staggered stop bands has an average transmittance Less than half the average transmittance of an adjacent passband. The method of claim 1, wherein the multi-band optical filter is configured to enhance red-green discrimination for observers with green-weak color vision deficiency, and a first passband of the plurality of passbands has a wavelength at about 440 A center between about 455 nanometers and about 455 nanometers, and a width between about 20 nanometers and about 40 nanometers, a second passband of the plurality of passbands having a center between about 525 nanometers and about 545 nanometers with a center between about 20 nanometers and about 50 nanometers, and a third passband of the plurality of passbands having a center between about 610 nanometers and about 640 nanometers , and a width between about 30 nanometers and about 80 nanometers, each of the staggered stop bands having a width of at least about 40 nanometers, and less than about one quarter of the average transmittance of an adjacent pass band One of the average transmittances, the minimum spectral transmittance of the multi-band optical filter between about 475 nanometers and about 580 nanometers is at most one of the luminous transmittance of the multi-band optical filter About one-fifth, and the spectral transmittance of the multi-band optical filter between about 580 nanometers and about 610 nanometers is at least about one-fifth of the light transmittance of the multi-band optical filter . The method of claim 2, wherein the first passband center is located at less than or equal to about 450 nanometers. The method of claim 2, wherein the first passband center is located at less than or equal to about 445 nanometers. The method of claim 2, wherein the third passband center is located at greater than or equal to about 625 nanometers. The method of claim 2, wherein the third passband center is located at greater than or equal to about 635 nanometers. The method of claim 2, wherein the second passbandwidth is at most about 40 nanometers. The method of claim 2, wherein the second passbandwidth is at most about 35 nanometers. The method of claim 2, wherein the second passbandwidth is at most about 30 nanometers. The method of claim 2, wherein the second passband center is located between about 535 nanometers and about 540 nanometers. The method of claim 2, wherein the second passband center is located at approximately 535 nanometers. The method of claim 2, wherein the minimum spectral transmittance of the multi-band optical filter between about 475 nanometers and about 580 nanometers is less than about one-fifth of the light transmittance. The method of claim 2, wherein the minimum spectral transmittance of the multi-band optical filter between about 475 nanometers and about 580 nanometers is less than about one-tenth of the light transmittance. The method of any one of claims 2 to 13, wherein each of the staggered stopbands has an average transmittance less than about one-eighth of the average transmittance of an adjacent passband. The method of any one of claims 2 to 13, wherein each of the staggered stopbands has an average transmittance less than about one-tenth of the average transmittance of an adjacent passband. The method of claims 2 to 13, wherein each of the staggered stopbands has an average transmittance greater than about one sixteenth of the average transmittance of an adjacent passband. The method of claim 2, wherein the first passband has a center at about 445 nanometers and a width of about 25 nanometers, the second passband has a center at about 530 nanometers, and A width of approximately 45 nanometers, the third passband having a center located at approximately 635 nanometers, and a width of approximately 50 nanometers, each of the staggered stopbands having an average transmittance of approximately The average transmittance of the passband is about one-sixth. The method of claim 17, wherein the multi-band optical filter is configured to enhance red-green discrimination for observers with mild green color vision deficiency. The method of claim 2, wherein the first passband has a center at about 445 nanometers and a width of about 25 nanometers, the second passband has a center at about 530 nanometers, and A width of approximately 40 nanometers, the third passband having a center located at approximately 640 nanometers, and a width of approximately 50 nanometers, each of the staggered stopbands having an average transmittance of approximately The average transmittance of the passband is about one-eighth. The method of claim 19, wherein the multi-band optical filter is configured to enhance red-green discrimination for observers with moderate green-weak color vision deficiency. The method of claim 2, wherein the first passband has a center at about 440 nanometers and a width of about 25 nanometers, the second passband has a center at about 530 nanometers, and a width of approximately 45 nanometers, the third passband having a center located at approximately 640 nanometers, and a width of approximately 50 nanometers, Each of the staggered stopbands has an average transmission that is approximately one-eighth of the average transmission of an adjacent passband. The method of claim 21, wherein the multi-band optical filter is configured to enhance red-green discrimination for observers with severe green-weak color vision deficiency. The method of claim 1, wherein the multi-band optical filter is configured to enhance red-green discrimination for observers with red-weak color vision deficiencies, and a first passband of the plurality of passbands has a wavelength at about 440 A center between about 455 nanometers and about 455 nanometers, and a width between about 20 nanometers and about 40 nanometers, a second passband of the plurality of passbands having a center between about 525 nanometers and about 545 nanometers with a center between about 20 nanometers and about 45 nanometers, and a third passband of the plurality of passbands having a center between about 610 nanometers and about 640 nanometers , and a width between about 30 nanometers and about 80 nanometers, and each of the staggered stop bands has a width of at least about 30 nanometers and less than about four times the average transmittance of an adjacent pass band One-third of the average transmittance, the minimum spectral transmittance of the multi-band optical filter between about 475 nanometers and about 580 nanometers is at most about five times the light transmittance of the multi-band optical filter one-fifth of the light transmittance of the multi-band optical filter between about 580 nanometers and about 610 nanometers. The method of claim 23, wherein the first passband center is located at less than or equal to about 450 nanometers. The method of claim 23, wherein the first passband center is located at less than or equal to about 445 nanometers. The method of claim 23, wherein the first passband center is located at less than or equal to about 440 nanometers. The method of claim 23, wherein the third passband center is located at greater than or equal to about 615 nanometers. The method of claim 23, wherein the third passband center is located at greater than or equal to about 625 nanometers. The method of claim 23, wherein the second passbandwidth is at most about 40 nanometers. The method of claim 23, wherein the second passbandwidth is at most about 35 nanometers. The method of claim 23, wherein the second passbandwidth is at most about 30 nanometers. The method of claim 23, wherein the second passband center is between about 525 nanometers and about 535 nanometers. The method of claim 23, wherein the second passband center is located at about 530 nanometers. The method of claim 23, wherein the minimum spectral transmittance of the multi-band optical filter between about 475 nanometers and about 580 nanometers is less than about one-fifth of the light transmittance. The method of claim 23, wherein the minimum spectral transmittance of the multi-band optical filter between about 475 nanometers and about 580 nanometers is less than about one-tenth of the light transmittance. The method of any one of claims 23 to 35, wherein each of the staggered stopbands has an average transmission less than about one-eighth of the average transmission of an adjacent passband. The method of any one of claims 23 to 35, wherein each of the staggered stopbands has an average transmission less than about one-tenth of the average transmission of an adjacent passband. The method of any one of claims 23 to 35, wherein each of the staggered stopbands has an average transmittance greater than about one sixteenth of the average transmittance of an adjacent passband. The method of claim 23, wherein the first passband has a center at about 445 nanometers and a width of about 20 nanometers, the second passband has a center at about 525 nanometers, and a width of approximately 40 nanometers, the third passband having a center located at approximately 630 nanometers, and a width of approximately 55 nanometers, Each of the staggered stopbands has an average transmission that is approximately one-eighth of the average transmission of an adjacent passband. The method of claim 39, wherein the multi-band optical filter is configured to enhance red-green discrimination for observers with red-weak color vision deficiencies. The method of any one of claims 2 to 13 and 23 to 35, wherein the multi-band optical filter provides a (x, y) chromaticity coordinate that is consistent with industry standard ANSI Z80.3-2010 Any points on the boundary of the mean daylight color-limited area defined in Section 4.6.3.1 are at least approximately 0.05 units apart. The method of any one of claims 2 to 13 and 23 to 35, wherein the multi-band optical filter provides an (x, y) chromaticity coordinate of a yellow traffic signal as determined by industry standard ANSI Z80.3 -Within approximately 0.05 units of the points (0.313, 0.620) defined in Sections 5.6.3.1 and 4.6.3.1 of 2005.