TWI664454B - Multi-band color vision filters and method by lp-optimization - Google Patents

Abstract

The present invention relates generally to: optical filters that adjust and / or enhance the chromaticity and luminous aspects of the color appearance of light provided by human vision; the therapeutic applications of these optical filters; such optical Filters are used in industrial and safety applications that are incorporated into, for example, radiation protection glasses; methods of designing such optical filters; methods of manufacturing such optical filters; and incorporating such optical filters into Designs and methods in devices including, for example, eyeglasses and luminaires.

Description

Multi-band color vision filter and optimization method using linear programming

The present invention relates generally to: optical filters that adjust and / or enhance the chromaticity and luminous aspects of the color appearance of light provided by human vision; applications of such optical filters; Use of optical filters in ophthalmic lenses; therapeutic applications of these optical filters; industrial and safety applications of these optical filters in, for example, radiation protection glasses; methods of designing such optical filters A method of manufacturing such optical filters; and a design and method of incorporating such optical filters into a device including, for example, eyeglasses and a lighting body.

An optical filter with wavelength selective transmission acting on a light source or light receiver can change the appearance of colors. Optical filters with improved color vision can provide a therapeutic effect to people with color vision defects. Optical filters protect the eyes from high-energy radiation in the ultraviolet, visible, and / or infrared spectrum. A device incorporating an optical filter includes glasses, a window, and a lighting body.

This document discloses a method of producing a filter for designing an optical filter that provides, for example, enhancement and / or adjustment of a color appearance relative to human color perception. The optical filter designs produced by this method can be used as a basis for manufacturing specifications, such as interference filters, by manufacturing such optical filters by physically vapor-depositing multiple layers of dielectric materials onto an optical substrate. The interference filter may further include an absorptive metal material layer. Such metal attenuating coatings can be made, for example, by physical vapor deposition. The optical substrate may be transparent or may incorporate an absorptive, photochromic or polarizing filter material, wherein by doping the substrate with such materials, laminating such materials between multiple substrates, or This incorporation is achieved by coating materials on one or both sides of the substrate. The boundary surface refractive index of both the inside and outside of the assembly can be matched, for example, by incorporating an appropriate anti-reflection filter to reduce transmission loss and substantially improve the optical quality of the assembled filter. These filters may be incorporated, for example, into eyeglasses (e.g. eyepieces, sunglasses, goggles, monocles, safety glasses, contact lenses or any other suitable ophthalmic lens), or may be incorporated into a lighting body (e.g. a lamp assembly )in. The ophthalmic lens is a lens for the eye. An ophthalmic lens may provide optical (focusing) correction to the eye, or it may have zero diopter and not provide 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 program 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 formula of the vector x is solved and the transmittance of the filter as a function of wavelength Calculated by the following expression: , And assuming p, then ,and ; Where, in this method, f is the design of an optical filter, Is the transmittance of f as a function of wavelength λ, and E is a matrix of basic filters such that matrix e _i The behavior is based on 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 is a weighted sum 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. In addition, The combination 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 also generally referred to as a "pre-filter" in the present invention, but generally can be composed of component filters in any order. Linear program constraint 1≥x≥0 is equivalent to constraint 1≥x _i ≥0, where i is between 1 and N. In addition, 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 perception in a desired manner. By c ^T x calculates the total cost associated with the solution, c ^T x represents the inner product of the transpose of c and x. A solution x that provides a lower overall cost is generally better than the desired function of the filter (such as color discrimination enhancement), but other measures of quality can also be used to determine the adequacy 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; one of the white points of the filter Constraints; or constraints on the color appearance of one or more reference lights (such as viewed or illuminated by a transmissive filter); and / or these transmission constraints of filter f at one or more angles of incidence. The wavelength λ as a function of the above expression can be expressed in a table by uniformly sampling according to a wavelength scale (e.g. using a step size of 1 nm) or another scale that is substantially equivalent (e.g. frequency or log wave number) Filter (e _i , p, f) Specifications of transmittance. Sampling can also be defined on an arbitrary scale with uneven intervals between sample points. The filter f (which can be described as a multi-band filter in nature) designed by the method has a spectral transmittance. One of the multi-band filters is a plurality of passbands interleaved with the stop band. In particular, the filter for influencing color perception has three or more passbands separated by two or more stopbands, and each stopband and each passband has a center and a width, where the The center is between about 400 nanometers and about 700 nanometers in the visible spectrum, and the width can be in a range between about 10 nanometers and about 110 nanometers. The lower boundary of a frequency band is defined as the center minus half of the width, and the upper boundary of a frequency band is defined as the center plus half of the width. The average transmittance of a band is the average spectral transmittance of light within the boundaries of those bands. The staggered stopbands share upper and lower boundaries and complementary boundaries of adjacent passbands. A multi-band filter is characterized by one of the smallest contrast ratios to the average transmittance of the stopband and its adjacent passband. For example, a multi-band filter may meet a lower limit of the contrast ratio such that each staggered stopband has an average transmittance that is less than or equal to one-half of the average transmittance of an adjacent passband, for example. A multi-band filter is further characterized by meeting an upper limit of the contrast ratio so that some embodiments of the multi-band filter can be expected to be used with color vision. A filter further incorporated into a device such as an ophthalmic lens is further characterized by a light transmittance, which is defined as the average spectral transmittance of light through the filter weighted by the CIE 1924 photoluminescence function. Filters used in ophthalmic lenses, such as sunglasses, typically have a light transmittance of at least 8%. In addition, the filter white point is defined as the average daylight (i.e., illuminant D65) chromaticity coordinates in a suitable color space, where one (u ', v') chromaticity coordinate means one of the CIELUV color spaces The position and one (x, y) chromaticity coordinate means a position in the CIE xyY color space. The white point of a filter corresponds subjectively to the apparent hue applied by the filter to the field of view, which is described as a neutral white point with a small amount of this hue applied. In some variations, the filter passband is essentially rectangular, that is, the change in transmittance as a function of wavelength within a band boundary is instantaneous or almost 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 measured equivalently according to a frequency scale. In some variations, the filter passband is Gaussian in nature, that is, the change in transmittance as a function of wavelength within 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 boundary and the half-peak transmittance on the long-wavelength boundary (also known as full-width at half maximum (FWHM)). The half-peak bandwidth can be equivalently measured according to 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 it may have a shoulder on one or more sides of the passband, or it may be described as a skewed distribution, where in the 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 non-Gaussian passband changes, such passbands can be smoothed using, for example, a Gaussian core that is just wide enough to essentially eliminate irregular and / or sharp transitions. In this case, the passband can be described as It essentially has a center of a frequency band and a half-peak width corresponding to a smooth passband. The basic filter may be, for example, a single-passband filter having a passband width of about 1 nanometer, and each basic filter has a different center wavelength of the passband. These filters can also be referred to as monochrome filters and are defined as having the following spectral transmittance: ; among them Is the Dirac-delta function and Is the wavelength transmitted by the filter. For a basic set of filters, the wavelength typically varies between about 400 nm and about 700 nm, and the number of these basic filters in the group is about 300. Alternatively, the basic filters may be single-passband filters each having a width greater than about 1 nm, and each basic filter has a different center wavelength of the passband. In some of these changes, the passband may be rectangular (also known as a square pulse function) and the spectral transmittance of a basic filter is defined as follows: ; among them Is the center wavelength, Is the rectangular bandwidth, and H is the Heaviside step function. In these variations, the passband may have, for example, a width of about 10 nanometers and the frequency band position may vary between about 400 nanometers and about 700 nanometers, for example, in steps of about 5 nanometers, so that these basic filters The number of devices is, for example, about 60. In some variations, the passband may have Gaussian or essentially Gaussian spectral transmittance, such as having a spectral transmittance as defined below: ; among them Is the center wavelength, and the half-peak bandwidth is: , among them Is an exponential function, Is the square root function, and Is the natural logarithm. In other variations, the basic filter may be a multi-band filter having two or more passbands, and each basic filter has a center position and / or a bandwidth of two or more passbands One different combination. Any suitable basic filter can be used in the filter design method. For example, the cost vector c may be selected to direct the linear program solver toward one of the filters that improves color discrimination. In some variations, the cost vector is selected to enhance the discrimination between red and green by increasing the apparent color purity of red and green. These red-green enhancement filters can also improve the apparent purity of blue and therefore can generally be described as enhancing color discrimination. Alternatively, the cost vector may be selected to enhance the discrimination between blue and yellow by increasing the apparent color purity of blue and yellow. These blue-yellow enhancement filters also tend to reduce the apparent purity of red and green. 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 the colors provided by the filters 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 based on performance criteria, manufacturing criteria, or 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 Test filter. The cost vector c may be adjusted, for example, to further improve color discrimination (ie, compared to the color discrimination of a trial filter below the current trial filter). Evaluating the performance of the filter may include evaluating the effect of the filter on color discrimination by: determining a first by calculating the area enclosed by a first contour in a chromaticity plane in a color space Color gamut area, where 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 a second contour around a chromaticity plane in a color space A second color gamut area, wherein the second outline corresponds to the appearance of the set of reference colors viewed 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 in addition, evaluating the effectiveness of the filter may include evaluating the effect of the filter on color discrimination by determining one of a first distribution 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 group of reference colors viewed or illuminated by an observer through a test filter; determining one of an axis of the chromaticity plane projected onto 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 viewed or illuminated by an observer through a reference filter; and comparing the first standard deviation with the second standard deviation. The axes useful for analysis include the axes defined by the red blind confusion line, the green blind confusion line, and the third type of color blind confusion line. In some variations, evaluating the performance of a filter may include using an average or a weighted average of the performance of the filter at an angle of incidence that deviates 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 spectral reflectance of a color sample from the Munsell Color Book specifies the color to be adjusted and / or enhanced by a filter. In some changes, instead of or in addition to samples from the Munsell Color Book, the spectral reflectance of the color mask 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 Book, spectroscopic reflectance of natural objects including leaves and flowers, for example, are specified by filters to be adjusted and / or enhanced color. In some variations, at least some of the elements of matrix A and vector b in the above-mentioned linear formula expression are related to: constraints on the appearance of blue, red, green, or yellow traffic signals, as viewed through a transparent filter . Such constraints may be based on, for example, industry or regulatory standards, and, for example, require that when viewing traffic light colors through a filter, the color of the traffic light falls within a particular chromaticity and luminous boundary. The method can provide a filter that meets 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-mentioned linear formula expression are related to: constraints on the stability of the appearance of the color with respect to the change in the angle of incidence with respect to the light on the filter , As viewed through a filter or illuminated. This stability is provided by the constrained configuration 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 total composition of an absorption pre-filter p and an interference filter q, where the change in transmittance of p as a function of the angle of incidence is According to Beer-Lambert's law and the change in the transmittance of Ex as a function of the angle of incidence, according to Snell's law, the transmittance of f at an angle of incidence deviating from the θ radian of the surface normal vector can be expressed as And is approximately expressed by the following expression: ; Where e _i The effective reflectivity is n with one of the values of about 1.85, and the approximation is sufficient for θ between about 0 and about 45 degrees. In some variations, at least some of the elements of the matrix A and the vector b in the above-mentioned linear formula expression are related to: the constraint of the filter on the transmission of blue light between about 380 nm and about 450 nm, such as Minimize this transmission. In some variations, at least some of the elements of the matrix A and the vector b in the above expressions are related to the constraint that a minimum transmittance between about 450 nm and about 650 nm is specified by the filter. In some variations, at least some of the elements of the matrix A and the vector b in the above expressions are related to the constraint that a minimum transmittance between about 580 nm and about 620 nm is specified by the filter. In some variations, at least some of the elements of matrix A and vector b in the above expression are related to: for an electronic visual display (such as a liquid crystal display (LCD) with a light emitting diode (LED) backlight) ) Constraints on light transmission of the emitted primary colors. In some variations, at least some of the elements of the matrix A and the vector b in the above expression are related to: normal colors within a range of incident angles on a filter that is, for example, between about 0 and about 30 degrees Recognize and stabilize the appearance of the color to protect the eye from the radiation of a visible laser (such as a octave Nd: YAG laser (which has laser output power at 532 nm and 1064 nm)). In some variations, at least some of the elements of the matrix A and the vector b in the above expression are related to: a stable color in a range of incident angles on a filter, for example, between about 0 and about 30 degrees The appearance protects the eyes from the radiation of a sodium lighting torch, which has the power concentrated at about 589 nanometers. In some variations, at least some of the elements of matrix A and vector b in the above expression are related to: the constraint to provide a selected illuminant, the color of the illuminant viewed after transmission through the filter The appearance matches the color appearance of the illuminant viewed after being reflected by the filter, and the filtered illuminator transmitted by the filter provides enhanced discrimination of one of the selected reference colors, and none of which is transmitted by the filter Part of the light is reflected by the filter. In another aspect, an equivalent numerical optimization procedure is used to replace the linear program in the method summarized above. In these changes, the equivalent procedure may include: using a table to represent all combinations of band positions and bandwidths within a range of possible values; then evaluating each multi-band filter based on constraint criteria and performance criteria; and then choosing to pass A subset of the filters of the constraint criterion; and then the best performing filter in the subset is selected as the experimental filter. These changes may further include evaluating test filters based on performance criteria, manufacturing criteria, or performance and manufacturing criteria. Some of these changes may also include: adjusting constraint criteria, performance criteria, or any combination of the above; and then performing a numerical optimization procedure again to provide another experimental filter. The constraint criterion or performance criterion may be adjusted, for example, to further improve color discrimination (ie, compared to the color discrimination of an experimental filter below the current experimental filter). In another aspect, a computer-implemented method for evaluating the effect of color perception on an experimental filter includes: using a computer; calculating a first contour from a chromaticity plane in a color space by The enclosed area determines a first color gamut area, where the first contour corresponds to the appearance of a group of reference colors viewed or illuminated by an observer through the test filter; An area enclosed by a second contour in a chromaticity plane to determine a second color gamut area, wherein the second contour corresponds to the appearance of the set of reference colors viewed or illuminated by the observer through a reference filter; And comparing the area of the first color gamut with the area of the second color gamut. In some variations, evaluating the effectiveness of a filter may include using an average or a weighted average of the color gamut area provided by the filter at an angle of incidence that deviates from normal incidence. The angular range may be, for example, from 0 degrees to at least about 20 degrees. In some of these changes, the importance weighting function is derived by estimating the probability that the filter is viewed at a specific angle according to a geometric model of the human eye, and the filter is located on the surface of a typical spectacle frame . In some variations, comparing the area of the first color gamut with the area of the second color gamut includes using a ratio of the area of the first color gamut to the area of the second color gamut. In some variations, at least some of the reference colors are selected from Munsell colors. Alternatively or in addition, at least some of the reference colors are selected from Farnsworth D-15. Alternatively or in addition, at least some of the reference colors are selected from colors present in an environment in which the experimental filter will be used to affect color perception. In the latter case, in some variations, at least some of the reference colors are selected from colors that exist naturally in an outdoor environment. In some variations, the reference color is selected to form a contour that surrounds equal saturation among white points in the chromaticity plane. Additionally or alternatively, the reference color is selected to form a highly saturated contour around white points in the chromaticity plane. For example, the reference filter may be selected to have a wide-band transmittance. In some variations, the reference filter is selected to have the same white point as the test filter relative to the selected illuminant (eg, relative to daylight). In some variations, the Munsell color, which is one of the best 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 of color perception on an experimental filter includes: using a computer; determining a first projection on an axis of a chromaticity plane in a color space; A first standard deviation of a distribution, wherein the first distribution corresponds to the appearance of a group of reference colors viewed or illuminated by an observer through the test filter; the determination is made along the chromaticity plane in the color space. One axis projection one second distribution one second standard deviation, wherein the second distribution corresponds to the appearance of the set of reference colors viewed or illuminated by an observer through a reference filter; comparing the first standard deviation with the Second standard deviation. In some variations, the axis was defined as a red blind confusion line. In some changes, the axis is defined as a green blind confusion line. In some variations, the axis is defined as a third type of color-blind confusion line. In some variations, evaluating the effectiveness of a filter may include using an average or a weighted average of the standard deviation of the distribution provided by the filter within a range of incident angles away from normal incidence. The angle range may be, for example, from about 0 degrees to at least about 20 degrees. In some of these changes, the importance weighting function is derived by estimating the probability that the filter is viewed at a specific angle according to a geometric model of the human eye, and 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 using 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 in addition, at least some of the reference colors are selected from Farnsworth D-15. Alternatively or in addition, at least some of the reference colors are selected from colors present in an environment in which the experimental filter will be used to affect color perception. In the latter case, in some variations, at least some of the reference colors are selected from colors that occur naturally in an outdoor environment. In some variations, the reference color is selected to form a contour that surrounds equal saturation among white points in the chromaticity plane. Additionally or alternatively, the reference color is selected to form a highly saturated contour around white points in the chromaticity plane. For example, the reference filter may be selected to have a wide-band transmittance. In some variations, the reference filter is selected to have the same white point as the experimental filter relative to a selected illuminant (such as daylight). In some variations, a Munsell color that is best suited for a test filter is used to define a reference filter, wherein 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 influencing color perception includes a first pass band, a second pass band, and a third pass band separated by two stop bands. The passbands and stopbands are configured to enhance color discrimination for a normal observer (e.g., the functional performance evaluation of the filter may take into account the color of the filter to a 2 degree standard observer of CIE 1931 Effect). The first passband has a center between about 435 nanometers and about 465 nm, the second passband has a center between about 525 nanometers and about 555 nanometers, and the third passband It has a center between about 610 nm and about 660 nm. The widths of the pass bands are each between about 20 nm and about 80 nm, and the widths of the stop bands are each at least about 40 nm. In some variations, the passband is configured (e.g., appropriately positioned and / or shaped) such that the filter provides stable color to an angle of incidence between about 0 degrees and at least about 30 degrees from the surface normal vector Appearance, so that for all or almost all of these angles of incidence, the average white point of daylight is contained in the CIELUV (u ', v') color space and has a radius of about 0.02 units according to the CIE 1931 2-degree standard observer In one of the areas. In some of these variations, the area has a radius of about 0.01 units. In further changes, in addition to or as an alternative to the CIE 1931 2 degree standard observer, the CIE 1964 10 degree standard observer may be used to calculate the chromaticity coordinates. In some variations, the passband is configured such that the filter provides a stable color appearance to an angle of incidence between about 0 degrees and at least about 30 degrees that deviates from the surface normal vector, so that for all or almost all such incidents Angle, the white point of the average daylight is contained in an area having a radius of about 0.02 units according to the CIELUV (u ', v') 1964 2 degree standard observer chromaticity scale. In some of these variations, the area has a radius of about 0.01 units. In some variations, multi-band filters are configured to enhance blue-yellow discrimination. In these changes, the first passband has a center between about 450 nm and about 475 nm, the second passband has a center between about 545 nm and about 580 nm, and the first The three-way band has a center in one of about 650 nm to about 690 nm. In these variations, the passband widths are each between about 20 nanometers and about 60 nanometers. In some of these changes, the filters are configured to provide one of the green traffic signals that has been desaturated or nearly desaturated (as permitted by the standard) as defined by the industry standard ANSI Z80.3-2010. A chromaticity coordinate. In some variations, the multi-band filter has a light transmission of about 8% to about 40%, and the frequency band is configured so that the filter is considered "non-strong" according to the industry standard ANSI Z80.3-2010 color". In some variations, the multi-band filter is configured such that the white point of the filter is neutral or almost neutral, making the filter available in accordance with the industry standard ANSI Z80.3-2010 section 4.6.3.1. And any point on the boundary of the defined average daylight color restricted area is at least about 0.05 units apart (x, y) chromaticity coordinates. In a further variation, the filter is configured so that the white point is located or almost above the average daylight color restricted area. In some variations, the stopband has a minimum transmittance, which is about one fifth of the light transmittance. The minimum transmittance is the lowest value of the spectral transmittance within the boundaries of the stop band. In some variations, the filters are configured to enhance color discrimination and suppress short wavelength light below at least about 440 nanometers. In these variations, the first passband has a center between about 450 nanometers and about 470 nanometers and a width between about 10 nanometers and about 40 nanometers. Meters to a center between about 575 nanometers and a width between about 30 nanometers to about 60 nanometers, the third passband has a central location between about 630 nanometers to about 670 nanometers and about 40 One width between nanometers and about 90 nanometers. In some of these variations, the filter has a light transmission between about 20% and about 35%. In some of these changes, for angles between 0 degrees and at least about 25 degrees, the percentage increase in color gamut area relative to the Farnsworth D-15 color is greater than zero. In some of these changes where the white point is neutral, the weighted percentage of importance relative to the increase in the color gamut area of the Farnsworth D-15 color may be at least 20%. In some variations, the multi-band filter has a light transmittance between about 8% and about 40%, and the frequency band is configured so that the white point of the filter is located or nearly defined as defined by the industry standard ANSI Z80.3 -2010 which is considered to be a non-violent color filter on the boundary. In some variations, filters are manufactured 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, a filter is manufactured by incorporating a neodymium-containing substrate and the interference filter. The filter may further include a neutral density filter. In some variations, the neutral density absorption filter includes a metal attenuating coating that can be incorporated into the layers of the interference filter. Because a neutral density filter has a generally flat spectral transmittance, a filter configured to be used with a neutral density filter may consist of many essentially equivalent options. For example, a circular polarizing filter can be replaced with a metal attenuation coating to achieve a filter with the same or nearly the same spectral transmittance. If appropriate, filters for any of the above changes may be incorporated into the glasses. Such glasses may include, for example, eyepieces (such as sunglasses), goggles, contact lenses, or any other suitable ophthalmic lens. In another aspect, a multi-band filter for influencing color perception includes a first pass band, a second pass band, and a third pass band separated by two stop bands. The passbands and configurations are configured to provide normal color discrimination and reject short wavelengths below about 450 nanometers. In some variations, the filter has three passbands. The first passband has a center wavelength of about 465 nanometers and a half-peak width of about 20 nanometers. The first stopband has a minimum transmittance of about 14%. The second passband has a center wavelength of about 550 nm and a half-peak width of about 40 nm, the second stopband has a minimum transmittance of about 50% between about 580 nm and about 610 nm, and The third passband has a center wavelength of about 660 nanometers and a half-peak width of about 80 nanometers. In some variations, the filter has four passbands. The first passband has a center wavelength of about 465 nanometers and a half-peak width of about 20 nanometers. The first stopband has a minimum transmittance of about 17%. The second pass band has a center wavelength of about 550 nm and a half-peak width of about 35 nm. The second stop band is located at about 560 nm and has a minimum transmittance of about 40%. The third pass band is located at It is at about 595 nanometers and has a half-peak width of about 35 nanometers, and the fourth passband is at about 660 nanometers and has a half-peak width of about 80 nanometers. In some variations, the passband is positioned and / or shaped such that the filter provides a stable color appearance to an angle of incidence between about 0 degrees and about 40 degrees that deviates from the surface normal vector, so that for all or almost all For these angles of incidence, the (u ', v') chromaticity coordinate of the average daylight is included in one of about 0.01 units of the observer's chromaticity (u ', v') scale according to the CIELUV color space 1931 2-degree standard In one of the radii. In some variations, for angles between 0 degrees and at least about 25 degrees, the percentage increase in color gamut area relative to the Farnsworth D-15 color is greater than zero. In some changes in China, the weighting percentage of white points that are neutral and increase in color gamut area relative to Farnsworth D-15 is between about 0% to about 10%. In some variations, the multi-band filter has a light transmittance between about 8% and about 40%, and the frequency band is configured so that the white point of the filter is located or nearly defined as defined by the industry standard ANSI Z80.3 -2010 which is considered to be a non-violent color filter on the boundary. In some variations, filters are manufactured by incorporating a neutral density absorption filter and an interference filter. In some of these variations, the neutral density absorption filter is a linear polarizer. In a further variation, an optical filter without an absorbing element is manufactured. In some variations, filters are manufactured by depositing an interference filter onto a photochromic substrate. If appropriate, filters for any of the above changes may be incorporated into the glasses. Such glasses may include, for example, eyepieces (such as sunglasses), goggles, contact lenses, or any other suitable ophthalmic lens. In another aspect, a multi-band filter for influencing color perception includes a first pass band, a second pass band, and a third pass band separated by two stop bands. The passbands and stopbands are configured to enhance red-green discrimination for an observer with a red-green perception defect. According to this, the evaluation of the performance measure of the filter can consider the physiological characteristics of the observer. The first passband has a center wavelength between about 440 nanometers and about 455 nm, the second passband has a center wavelength between about 530 nanometers and about 545 nanometers, and the third passband It has a center wavelength between about 610 nm and about 640 nm. The widths of the passbands are each between about 10 nm and about 60 nm, and the widths of the stopbands are each at least about 40 nm. The light transmittance of the filter and the white Dot tone and select the width of these frequency bands. In some variations, the passband is positioned and / or shaped such that the filter provides a stable color appearance to an angle of incidence between about 0 degrees and about 30 degrees that deviates from the surface normal vector, so that for all or almost all For these angles of incidence, the white point of daylight is contained in an area having a radius of about 0.02 units, according to 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 to an angle of incidence between about 0 degrees and about 35 degrees that deviates from the surface normal vector, so that for all or almost all For these angles of incidence, the white point of daylight is contained in an area having a radius of about 0.04 units according to the CIELUV 1931 2-degree standard observer chromaticity (u ', v') scale. In some variations, the passband is positioned and / or shaped so that the filter provides a stable color appearance, so that the incident angle-dependent distance at which the white point is shifted from its 0-degree incident angle position is between about 20-degree incident angle to about 40 There is a local minimum at one of the angles between the angles of incidence, where the white point displacement at the local minimum is less than 0.02 units of the observer's chromaticity (u ', v') scale according to the CIELUV 1931 2-degree standard observer. In some variations, the passband is positioned and / or shaped so that the filter provides a stable color appearance so that the incident angle-dependent distance that the white point shifts from its 0-degree incident angle position is between about 20 degrees and about 40 degrees There is a local minimum at one of the angles, wherein the white point displacement at the local minimum is less than 0.01 units of the observer's chromaticity (u ', v') scale according to the CIELUV 1931 2-degree standard observer. In some variations, the multi-band filter has a light transmittance between about 8% and about 40%, and the frequency band is configured such that the filter is considered non-rendering according to the industry standard ANSI Z80.3-2010 Strong colors. In some variations, the multi-band filter has a light transmission between about 8% and about 40%, and the frequency band is configured such that the white point of the filter is neutral or almost neutral, making the white point The (x, y) chromaticity coordinates are within about 0.05 units of (0.31, 0.33) of the observer's color space relative to the illuminant D65 and according to the CIE xyY 1931 2-degree standard observer color space. In some variations, the stopband has a minimum transmittance that is about one fifth of the light transmittance between about 450 nanometers and about 650 nanometers. In some variations, the stopband has a minimum transmittance that is about one fifth of the light transmittance between about 580 nm to about 650 nm. In some variations, one or more of the passbands have a skewed distribution, where the transmittance as a function of wavelength has a slope ratio between the two sides of the passband 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 have a bimodal distribution, where the center wavelengths of the two modes are within +/- 10% and the distributions around these modes partially overlap. This configuration can also be described as dividing the passband into adjacent partially overlapping subbands. In some variations, the first passband has a bimodal distribution, with the first mode at about 435 nm and the second mode at about 455 nm. In these 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 to define the industry standard ANSI Z80.3-2010 relative to an incident angle where the center wavelength of the second passband is between about 525 nm and about 535 nm. A yellow traffic signal that is reddish or almost reddish (as allowed by the standard) provides a chromaticity coordinate. In some variations, the filter is configured to enhance red-green discrimination for an observer with a weak green. In a preferred variation, the third passband has a center wavelength between about 620 nm and about 640 nm. In some of these variations, the first pass band has a center at about 445 nm, the second pass band has a center wavelength at about 535 nm, and the third pass band has a center wavelength at about 635 nm . In some variations, the filter is configured to enhance red-green discrimination for an observer with a mild green weakness. In some of these changes, the weighting percentage of the white point that is neutral and the color gamut area increase relative to the Farnsworth D-15 color is at least about 30%. In further such changes, for angles between 0 degrees and at least about 25 degrees, the percentage increase in the color gamut area relative to the Farnsworth D-15 color is greater than zero. In some variations, the filter is configured to enhance red-green discrimination for one observer with a moderate green weakness. In some of these changes, the weighting percentage of the white point that is neutral and the color gamut area increase relative to the Farnsworth D-15 color is at least about 35%. In further such changes, for angles between 0 degrees and at least about 25 degrees, the percentage increase in the color gamut area relative to the Farnsworth D-15 color is greater than zero. In some variations, the filter is configured to enhance red-green discrimination for an observer with a severe green weakness. In these variations, the stop band may have a minimum transmittance that is one fifth of the light transmittance between about 580 nm to about 650 nm and less than about 475 nm to about 580 nm. The light transmittance is about one-fifth (for example, about one-tenth). In some of these changes, the weighting percentage of the white point that is neutral and the color gamut area increase relative to the Farnsworth D-15 color is at least about 40%. In further such changes, for angles between 0 degrees and at least about 25 degrees, the percentage increase in the color gamut area relative to the Farnsworth D-15 color is greater than zero. In some variations, the filters are configured to enhance red-green discrimination for one observer with weak red. In some of these variations, the third passband has a center wavelength between about 605 nm and about 620 nm. In some of these 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 of these changes, the white point is neutral and the percentage increase in color 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, for angles between 0 degrees and at least about 25 degrees, the percentage increase in the color gamut area relative to the Farnsworth D-15 color is greater than zero. In some variations, filters are manufactured by incorporating a neutral density absorption filter and an interference filter. In a further variation, a filter is manufactured by incorporating a neodymium-containing substrate, the neutral density absorption filter, and an interference filter. If appropriate, filters for any of the above changes may be incorporated into the glasses. Such glasses may include, for example, eyepieces (such as sunglasses), goggles, contact lenses, or any other suitable ophthalmic lens. In another aspect, a multi-band filter includes three or more pass bands separated by two or more stop bands. The passbands and stopbands are configured to transmit the blue primary light, red primary light, and green primary light of an electronic visual display, so that the light appears to have approximately the same luminosity and the light transmittance of the primary light Light transmission is at least about 15% greater than sunlight. In some of these changes, the white point is neutral, and for angles between 0 and at least about 25 degrees, the percentage increase in color gamut area relative to the Farnsworth D-15 color is greater than zero. In some of these changes, the weighted percentage of importance relative to the increase in color 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 frequency band is configured such that the white point of the filter is neutral or almost neutral, making the white point The (x, y) chromaticity coordinates fall within about 0.05 units of the CIE xyY 1931 2-degree standard observer color space relative to (0.31, 0.33) of the illuminant D65. In some variations, the filter has three passbands, and the first passband has a center wavelength of about 450 nm and a width of about 20 nm, and the second pass band has a center wavelength of about 535 nm and A width of about 25 nanometers, and a third passband having a center wavelength of about 615 nanometers and a width of about 30 nanometers. In some variations, the filter has four passbands, the first passband has a center wavelength of about 455 nm and a width of about 20 nm, and the second pass band has a center wavelength of about 540 nm and The third pass band has a center wavelength of about 615 nm and a half-peak width of about 25 nm, and the fourth pass band has a center wavelength of about 680 nm and about 25 nm. One half-peak width. In some variations, the passband is positioned and / or shaped such that the filter provides a stable color appearance to an angle of incidence between about 0 degrees and about 40 degrees that deviates from the surface normal vector, so that for all or almost all For these angles of incidence, the average white point of daylight is contained in an area with a radius of about 0.01 units, according to the CIELUV 1931 2-degree standard observer chromaticity (u ', v') scale. In some variations, a computer display with a filter configured thereon is a liquid crystal display (LCD) with a light emitting diode (LED) backlight. In some variations, the weighting percentage of the white point that is neutral and an increase in the color gamut area of the Farnsworth D-15 color provided by the filter is at least about 20%. In some variations, filters are manufactured by incorporating a neutral density absorption filter and an interference filter. If appropriate, filters for any of the above changes may be incorporated into the glasses. Such glasses may include, for example, eyepieces (such as 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 a 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 light radiation at one or more wavelengths between meters; and to provide blocking at an angle of incidence ranging from about 0 to about 30 degrees 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 frequency band is configured such that the white point of the filter is neutral or almost neutral, making the white point The (x, y) chromaticity coordinates fall within about 0.05 units of the CIE xyY 1931 2-degree standard observer color space relative to (0.31, 0.33) of the illuminant D65. 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 to prevent visible light radiation at about 532 nanometers. In these variations, the filter may include four passbands separated by three stopbands, where the middle stopband is the guard band. The first passband has a center wavelength of about 440 nm and a width of about 20 nm. The second passband has a center wavelength of about 515 nm and a width of about 25 nm. The third pass band has a width of about A center wavelength of 570 nm and a width of about 25 nm, and a fourth passband has a center wavelength of about 635 nm and a width of about 25 nm. In these changes, the weighted percentage of importance relative to the increase in the color gamut area of the Farnsworth D-15 color is approximately zero. In some variations, for angles between 0 degrees and at least about 25 degrees, the percentage increase in color gamut area relative to the Farnsworth D-15 color is about zero. In some variations, the blocking band has a short wavelength boundary at about 585 nm and a long wavelength boundary at about 620 nm, and is therefore protected from visible light radiation at about 589 nm. In these variations, the filter may include four passbands separated by two stopbands, with a long-wavelength stopband providing protection. In some variations, the first passband has a center wavelength of about 455 nm and a width of about 20 nm, and the second pass band has a center wavelength of about 540 nm and a width of about 20 nm. The three-pass band has a center wavelength of about 570 nm and a width of about 20 nm, and the fourth pass band has a center wavelength of about 635 nm and a width of about 30 nm. In some of these changes, the white point is neutral and the importance weighted percentage of the increase in color gamut area relative to the Farnsworth D-15 color is between about 0% to about 15%. In some of these changes, for angles between 0 degrees and at least about 25 degrees, the percentage increase in color gamut area relative to the Farnsworth D-15 color is greater than zero. In some variations, the passband is positioned and / or shaped such that the filter provides a stable color appearance to an angle of incidence between about 0 degrees and about 35 degrees that deviates from the surface normal vector, so that for all or almost all For these angles of incidence, the average white point of daylight is contained in an area with a radius of about 0.01 units, according to the CIELUV 1931 2-degree standard observer chromaticity (u ', v') scale. In some variations, filters are manufactured by incorporating a neutral density absorption filter and an interference filter. If appropriate, filters for any of the above changes may be incorporated into the glasses. Such glasses may include, for example, eyepieces (such as sunglasses), goggles, contact lenses, or any other suitable ophthalmic lens. In another aspect, a multi-band filter for influencing color perception includes three or more pass bands separated by two or more stop bands. The passbands and stopbands are configured to maximize blue light reception by retinal ganglion cells and maximize normal color discrimination. In some variations, the multi-band filter has three passbands separated by two stopbands, where the first passband has a center at about 485 nm and a half-peak width of about 90 nm, and the second The passband has a center wavelength of about 580 nm and a half-peak width of about 25 nm, and the third passband has a center wavelength of about 630 nm and a half-peak width of about 25 nm. In some variations, the multi-band filter has four pass bands separated by three stop bands, where the first pass band has a center wavelength of about 430 nm and a half-peak width of about 30 nm, and the second pass The band has a center wavelength of about 495 nm and a half-peak width of about 50 nm, the third pass band has a center wavelength of about 565 nm and a half-peak width of about 20 nm, and the fourth pass band has about One center wavelength of 630 nm and one half-peak width of about 20 nm. In some variations, the passband is positioned and / or shaped such that the filter provides a stable color appearance to an angle of incidence between about 0 degrees and about 30 degrees from the surface normal vector, making it useful for all or almost For all these angles of incidence, the average white point of daylight is contained in a region with a radius of about 0.01 units according to the CIELUV 1931 2-degree standard observer chromaticity (u ', v') scale. In some changes, the weighting percentage of white points that are neutral and increase in color gamut area relative to the Farnsworth D-15 color is between about 0% and about -10%. In some variations, the multi-band filter has a light transmittance between about 8% and about 40%, and the frequency band is configured so that the white point of the filter is located or nearly defined as defined by the industry standard ANSI Z80.3 -2010 which is considered to be a non-violent color filter on the boundary. In some variations, filters are manufactured by incorporating a neutral density absorption filter and an interference filter. In a further variation, a filter is manufactured by incorporating a neodymium-containing substrate, the neutral density absorption filter, and an interference filter. In some variations, the filter specifications are significantly smoothed, so that the interference filter can be manufactured with less than about 50 layers of material. If appropriate, filters for any of the above changes may be incorporated into the glasses. Such glasses may include, for example, eyepieces (such as sunglasses), goggles, contact lenses, or any other suitable ophthalmic lens. In another aspect, a multiband filter includes three or more passbands and two or more stopbands, and the frequency bands are configured to be adjusted and / or enhanced 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: ; Where in the above expression, Is passband and To adjust the weighting factor of the passband, and Is the minimum transmittance of the filter. The wavelength λ as a function of the above expression can be expressed in a table by uniformly sampling according to a wavelength scale (e.g. using a step size of 1 nm) or another scale that is substantially equivalent (e.g. frequency or log wave number) Filter transmittance (f, u) specifications. Sampling can also be defined on an arbitrary scale with uneven intervals 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 essentially rectangular, that is, the change in transmittance as a function of wavelength at the band boundaries is instantaneous or almost 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 according to a frequency scale. The spectral transmittance of a rectangular passband can be defined by the following expression: ; among them Is the center 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 boundary 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 full-width at half maximum (FWHM)). The half-peak bandwidth can be equivalently measured according to a frequency scale. The spectral transmittance of a Gaussian band can be defined by the following expression: ; among them 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 the transmittance as a function of wavelength, the pass The slope ratio between the two sides of the belt is between about 4: 1 and about 1: 4. In non-Gaussian band changes, these bands can be smoothed with a Gaussian core that is wide enough to essentially eliminate irregular and / or sharp transitions, in which case the band can be described as having Corresponds to the center of a frequency band and the half-peak width of a smooth passband. In some variations, the passband is positioned and / or shaped such that the filter provides a stable color appearance to an angle of incidence between about 0 degrees and about 35 degrees from the surface normal vector, making it useful for all or almost For all such angles of incidence, the white point of daylight is contained in an area with a radius of about 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 to an angle of incidence between about 0 degrees and about 40 degrees from the surface normal vector, making it useful for all or almost For all such angles of incidence, the white point of daylight is contained in an area with a radius of about 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 to incident angles between about 0 degrees and about 45 degrees from the surface normal vector, making it useful for all or almost For all such angles of incidence, the white point of daylight is contained in an area with a radius of about 0.01 units on the CIELUV 1931 2-degree standard observer chromaticity diagram. In some variations, the passband is positioned and / or shaped so that the filter provides a stable color appearance, so that the incident angle-dependent distance that the white point shifts from its 0-degree incident angle position is between about 20-degree incident angle to about 45 There is a local minimum at one of the angles between the angles of incidence, where the white point displacement at the local minimum is less than 0.02 units of the observer's chromaticity (u ', v') scale according to the CIELUV 1931 2-degree standard observer. In some variations, the passband is positioned and / or shaped so that the filter provides a stable color appearance, so that the incident angle-dependent distance that the white point shifts from its 0-degree incident angle position is between about 20-degree incident angle to about 45 There is a local minimum at one of the angles between the angles of incidence, where the white point displacement at the local minimum is less than 0.01 units of the observer's chromaticity (u ', v') scale according to the CIELUV 1931 2-degree standard observer. In some variations, the multi-band filter is manufactured as an interference filter. In some variations, a multi-band filter is manufactured to include an interference filter and one or more neutral density absorption filters, and the interference filter provides a passband and a stopband. In some variations, a multi-band filter is manufactured to include an interference filter and one or more broadband absorption filters, and the interference filter provides a passband and a stopband. In some variations, a multi-band filter is manufactured to include an interference filter and one or more narrow-band absorption filters, wherein the interference filter and the absorption filter are co-configured to provide a passband And stop band. In any of the above changes, the multi-band filter f may include an absorption filter p and an interference filter q, where the change in transmittance of p as a function of the angle of incidence is based on Beer-Lambert's law, And the change in transmittance of q as a function of the angle of incidence is based on Snell's law, so that the transmittance of f at an angle of incidence deviating from the surface normal vector by θ radians can be expressed as And is approximately expressed by the following expression: , Where the effective refractive index of the interference filter q is n having a value of about 1.85, and the spectral transmittance of p at the normal incidence is , The spectral transmittance of f at the normal incidence , The spectral transmittance of q at the normal incidence And approximate values of θ between about 0 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 ; among them Is a coefficient that determines the amount of displacement, and One of the performance criteria selected to maximize the filter over a range of incident angles. In some variations, the filter includes an interference filter, in which the spectral transmittance of the interference filter is significantly smoothed, and the width of the smoothing core is selected so as not to excessively impair the filter's performance, while also making The filter can be manufactured as a low-order stacked dielectric material. If appropriate, filters for any of the above changes may be incorporated into the glasses. Such glasses may include, for example, eyepieces (such as sunglasses), goggles, contact lenses, or any other suitable ophthalmic lens. In another aspect, a computer-implemented method for determining the physical thickness distribution of a filter on a surface includes: using a computer; defining the spectral transmittance of the filter; defining the filter at Spectral transmittance within an incident angle range; define a geometric model of the surface; define a geometric model of a human eye; configure the geometric models to approximate the geometry of a spectacle frame, where the surface is installed in the frame and A lens located in front of the eye; for each position on the surface, calculating the incident angle of light that passes through the position to be imaged on the retina of the eye; and specifies a solid thickness at each position, where the solid thickness is configured such that The spectral transmittance is constant or substantially constant at all or almost all positions on the surface relative to the calculated angle of incidence. In another aspect, a computer-implemented method for determining a physical thickness distribution of a filter on a surface includes: using a computer; defining a spectral transmittance of a filter; defining the filter Spectral transmittance in an incident angle range; a geometric model defining the surface; a geometric model defining the relative solid thickness of the filter deposited on the surface (e.g., as a solid thickness achieved by a specific process The results of the distribution prediction and measurement); define a geometric model of a human eye; configure these geometric models to approximate the geometry of a spectacle frame, where the surface is a lens installed in the frame and located in front of the eye; calculation Corresponds to the position on the surface of the center of the field of view; calculates the incident angle of light passing through the center position; defines an importance distribution of each position relative to the center position; specifies a solid thickness at the center position, where the solid thickness is Select so that light that passes through the center and is imaged onto the retina is filtered based on a defined spectral transmittance; calculates the weight of color perception on the surface of the lens Weighted average effect, which is associated with a range of solid thickness variation within +/- 10% of the specified central solid thickness; and then selecting an offset central solid thickness within that range, so that the importance of color vision is weighted average The effect is maximized. In another aspect, a lens of an eyeglass incorporating a multi-band filter includes an optical substrate, one or more reflective interference filters, and is positioned on one or both sides of the reflective filters One or more absorption filters, wherein the absorption filters are configured to reduce the luminosity of the reflected light on one or both sides of the lens. In some variations, the interference filter includes a low-order stack having one of about 12 to about 50 layers of dielectric material, or is between about 1 to about 3 microns thick, or includes having about 12 to about 50 One of the dielectric material layers is a low-order stack and is between 1 and 3 microns thick. In some variations, the interference filter includes a high-order stack having one of about 50 to at least about 200 layers of dielectric material, or is between about 6 microns to at least about 12 microns thick, or includes having about 50 to at least about One of the 200 dielectric material layers is a high-order stack 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 such as titanium dioxide and silicon dioxide. The material layer can be produced, for example, in a magnetron sputtering machine, for example by physical vapor deposition. Alternatively or in addition, the dielectric material layer may be manufactured, for example, by spin-on deposition. In some variations, a neutral density absorption filter is provided by a metallic attenuation coating. The metallic material layer can be manufactured, for example, by physical vapor deposition. In these variations, the metal layer may be staggered or partially staggered with the dielectric layer of the interference filter. In some variations, a light-activated neutral density absorption filter is provided by incorporating a 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 linear polarization neutral density absorption filter is provided by incorporating a polarizing filter into a laminated composite lens or by coating on the surface of the lens. In these variations, the polarizer may be located between the interference filter and the side of the lens facing the eye. In some variations, an absorption filter is provided by an organic dye in a polymer substrate. The polymer material can be bonded by any suitable method, such as, for example, by incorporating into an optical substrate medium, laminating a film between two optical substrates, or spin coating or dipping the surface of an optical substrate. Into the lens. In some variations, an absorption filter is provided by incorporating an inorganic material into a glass or polymer substrate. In some of these variations, the inorganic materials may include rare earth ions of praseodymium, neodymium, or any mixture of the above. In some variations, one or more absorption filters are configured to affect the color appearance of daylight reflected from the outer surface of the lens (the surface furthest from the eye), where the color appearance is configured for good looking. In some variations, the absorption 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 circle A 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 first Two circular polarizers are configured to transmit light that passes through the interference filter. In some variations, one of the first circular polarizers, which is fixed to one side of the interference filter and configured to absorb light reflected by the interference filter, provides one of the sides closest to the eye's lens Absorptive filter. In a variation incorporating one or more circular polarizers, a circular polarizer includes a linear polarizer and a quarter-wave retarder, and the linear polarizer element can be configured to provide, for example, about 60% Partial polarization efficiency between about 90%. In a variation that includes a linear polarizer, the linear polarizer can be configured to attenuate horizontally polarized light to reduce glare from sunlight reflected from a horizontal surface based on the Brewster 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-reflection coating that reduces the scattering and resonance of reflected light in the optical substrate, and the anti-reflection The luminosity-weighted reflectance of the coating is 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 coated with anti-reflection to reduce the scattering and resonance of the reflected light in the optical substrates. In some variations, the edges of the lens may be sealed with an index-matching absorbing polymer coating that reduces the transmission and scattering of stray light in the optical substrate and also protects the filter layer from contamination (e.g., Avoid penetration of water or solvents into the dielectric or metallic material layer). In some variations, the entire functional layer of the filter is a metal or metal oxide coating compatible with fabrication by physical vapor deposition. In some variations, the optical substrate is chemically toughened glass. In these variations, the glass can absorb, for example, ultraviolet light between about 280 nanometers and about 400 nanometers. 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 filters at the two or more positions differ by at least 20 degrees, and the effective incident angles of the light therein correspond to a beam of light that passes through the lens and is imaged onto the retina of the eye. In some variations, the optical substrate is curved with a radius of curvature between about 50 mm and about 200 mm. In these variations, interference filters and / or attenuation coatings can be positioned on the concave side of the surface. If appropriate, lenses of any of the above changes may be incorporated into spectacles including, for example, eyepieces (such as sunglasses), goggles, or contact lenses. In another aspect, a light source includes an illuminant, a first beam shaping element, a multi-band interference filter, and a second beam shaping element. The light radiated from the illuminating body is substantially collimated by the first beam shaping element. The collimated light beam enters the multi-band filter, wherein the light beam is divided into a transmission part and a reflection part. The transmitting portion and the reflecting portion of the light have the same or substantially the same white point relative to the selected illuminant. The transmitting 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 transmitting portion and the reflecting 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 mainly including light transmitted by the multi-band filter and an external portion mainly including 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 collimation angle of the light from the illuminator incident on the multi-band filter is about 20 degrees. In such changes, the white point of the filter relative to the illuminant for all or almost all positions within the collimated beam may be contained, for example, in the color scale of the observer according to the CIELUV 1931 2-degree standard. 0.01 unit in a radius and an area. In some variations, the multi-band filter includes three passbands separated by two stopbands, where the first passband has a center wavelength of about 450 nm and a bandwidth of about 15 nm, and the second pass The band has a center wavelength of about 535 nm and a bandwidth of about 20 nm, and the third passband has a center wavelength of about 625 nm and a bandwidth of about 30 nm. In some variations, the stopband has a minimum transmittance of about 10%. In a further variation, the stopband has a minimum transmittance 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 wideband combination of light from white light emitting diodes and red light emitting diodes emitted by the illuminator 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 light-emitting diode, a cyan light-emitting diode, and a red light-emitting diode. The light emitted by the combined diode has a broad-band 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 changes, the spectral radiant flux of the illuminant is configured as one of the best approximations of average daylight (D65). In some variations, an ophthalmic lens having a multi-band spectral transmittance is provided. The ophthalmic lens includes an optical substrate and an interference filter, wherein the interference filter has a range between about 30% and about 80%. A light reflectance and a light transmittance between about 8% and about 70%. All methods and variations disclosed herein for designing, evaluating, or otherwise evaluating optical filters, spectacles, ophthalmic lenses, illuminants, and other optical components or devices, and their variations may include the steps of manufacturing the object, manufacturing the object Another step or a step of providing one article's manufacturing specifications to another article, whether or not this step is explicitly stated in a description of a particular method, article or variation thereof. Those skilled in the art will further understand these and other aspects, embodiments, variations, features, and advantages of the present invention when referring to the [embodiments] of the present invention and the drawings briefly described first.

Cross-reference to related applications This application is related to Provisional US Patent Application No. 61 / 449,049, filed on March 3, 2011 and named "MULTI-BAND OPTICAL FILTERS FOR GOOD COLOR APPEARANCE", the entirety of which is incorporated herein by reference. [Embodiments] should be read with reference to the drawings, wherein the same reference numerals refer to the same elements throughout the different drawings. The drawings, which are not necessarily drawn to scale, depict selected embodiments and are not intended to limit the scope of the invention. [Embodiment] The principle of the present invention is illustrated by way of example rather than limitation. [Embodiments] Will enable those skilled in the art to clearly make and use the present invention, and describe several embodiments, adaptations, changes, substitutions, and usages of the present invention, including the best mode for implementing the present invention as currently considered. As used in this specification and the scope of the accompanying patent application, unless the context clearly indicates otherwise, the singular forms "a" and "the" include plural referents. The teachings of the present invention may be usefully read in conjunction with a general understanding of optical science, human color vision science, colorimetry science, and related topics. For general references on these topics, see, for example, "Color Science: Concepts and Methods, Quantitative Data and Formulae" by Günter Wyszecki and WS Stiles (Wiley, 1982, ISBN # 0471021067). In order not to lose the generality, the present invention can assume a conventional configuration of the human visual system: specifically (if not otherwise stated), a human visual system with a photosensitive color vision of a normal human observer with a 2 degree field of view . Photosensitive color vision occurs when the level of illumination is high enough that the rod-shaped photoreceptor cells are not activated, such as when the average surface illumination is about 10 lux or more. In the present invention, unless otherwise stated, the color appearance model is calculated using the CIE 1976 L * u'v '(LUV) color space (which uses a CIE 1931 standard observer with a 2 degree field of view). Details of this calculation are given by the CIE standard S014-5 / E: 2009. The chromaticity diagram is shown in the figure using a color difference table color system (UCS) such as CIE 1976, where the chromaticity coordinates are (u ', v') values, as calculated by the standard. For those of ordinary skill, these teachings introduce a pre-receptor eye assembly (which includes ocular media and Macular pigment) and procedures sufficient to make the teachings applicable to alternative conditions (including, for example, the use of CIE 1964 10-degree observer and changes in observer's eyes and retinal physiology) (e.g., consideration of color vision defects, age, and / or eyes pathology). In the present invention, the illuminant D65 (D65) means light having a typical spectral radiant flux of sunlight and a correlated color temperature of one of 6500 Kelvin, and is a joint ISO / CIE standard ISO 10526: 1999 / CIE S005 / E-1998 definition. In the present invention, the reference to "sunlight", "sunlight" or "average daylight" means the illuminant D65. Illuminant E means an ideal lamp defined as having equal power as a function of wavelength. Illuminant A means a lamp that is usually an incandescent light bulb, which is defined as having a spectral radiant flux of an ideal black body radiator according to Planck's law and a correlated color temperature of 2848 K. A series of lamps including illuminants FL1 to FL12 (which represents the spectral radiant flux of a typical type of fluorescent lamp) is defined by CIE Publication No. 15: 2004. Munsell color is a group of color samples formulated with specific pigments to establish a color standard defined in the spectral domain. Munsell colors can be used in print in the Munsell Colors Book (Glossy Edition, ISBN # 9994678620, 1980). Published by Parkkinen JPS, Hallikainen J., and Jaaskelainen T. "Characteristic spectra of Munsell colors" (Journal of the Optical Society of America A, Vol. 6, No. 2, 1989, p. 318-p. 322) A measurement of the spectral reflectance of a color. Farnsworth D-15 is a standardized color discrimination test that includes forming 15 Munsell color samples with a contour of one of chromaticities between 2 and 4 according to the Munsell scale. Farnsworth D-15 is described by the public case "The Farnsworth dichotomous test for color blindness panel D15 manual" (News York: Psych Corporation; 1947, Farnsworth D). The drawings included in the present invention may be a program flow chart that visually depicts generalized objects and the processes of processing and generating those objects. FIG. 58 depicts an example of a program flowchart for promoting visual language understanding. In this illustration, rounded boxes (eg, 5801 and 5803) depict objects that can be understood as physical entities, virtual entities (such as numerical data), or composite objects containing a heterogeneous collection of component objects. A rounded frame (such as shown at 5808 and 5811) with a double wire frame depicts a composite object containing a heterogeneous assembly of objects. A dashed arrow depicts a component object retrieved from a composite object, such as shown by the connected entities 5801 and 5803. The flow of objects in the program is shown by a solid line arrow, such as shown by connecting entities 5801 and 5802. A square box (such as 5802 and 5805) represents an operation. Operations can produce objects, transform objects, or analyze objects. An arrow pointing away from the frame of an operation shows the output of that operation. The output of an operation depends on the input of the operation that can be tracked by following all the arrows in the box leading to the operation. The operation can be formed as a composite operation by encapsulating another procedure diagram, such as shown at 5806. This construction enables the program flow chart to be expanded on multiple pages, thereby allowing a composite operation defined in another schema to be invoked when referring to one schema. Operations can be connected together in series or in parallel. The details of the sequence in which a particular operation is performed are not necessarily defined by the program flowchart syntax, but must be deduced from the accompanying description. A double-line arrow (shown by connecting 5808 and 5809, for example) indicates the iterative process of multiple homogeneous objects. Use a double-line square box to show repeated operations, such as 5809. Once iterative operation changes its input relative to repeated objects, it can maintain a constant input relative to non-repetitive objects, as shown by the flow arrows connecting 5807 and 5809. A program flowchart for use in the present invention is provided to facilitate understanding when interpreted along with the accompanying detailed description. Color perception can generally be understood as the interaction between the spectral radiant flux of light incident on the retina and the spectral absorptivity of retinal photoreceptor cells. The process flow diagram of FIG. 1 depicts the process of photosensitive color vision and the application of an optical filter for influencing color perception. Herein, an illuminating body 101 such as sunlight is radiated into an optical system 102. The light emitted by an illuminating body can generally be regarded as white light. Within the optical system 102, white light is reflected from a surface of a reference color 104 (103). Then, the reflected light can be described as a colored light, assuming that the reference color is not neutral (ie, non-gray tone). Thereafter, the 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 adhered to, the part of the light that is not transmitted must be reflected or absorbed by the filter at this junction. The reordering of the optical system 102 with respect to its internal operation is unchanged, that is, the filter may be applied equivalently before or after the reference color is illuminated. Subsequently, an observer can perceive the filtered light through a procedure of visual light transduction 115. In visual light transduction under light-sensitive conditions, three retinal photoreceptor cells including short-wavelength cone 108, medium-wavelength cone 110, and long-wavelength cone 112 absorb light at 107, 109, and 111. The total energy absorbed by each cell is converted into nerve stimulation that is transmitted through the optic nerve into the visual cortex to ultimately cause a sense of color. For color appearance modeling, it is fully assumed that the input-output response of the cones is linearly proportional to the energy absorbed. This linear response can be referred to as a tri-color value, which can be viewed as a vector in a three-dimensional space with a non-negative component. As described, the space of three color values is sometimes referred to as the SML color space or the cone excitation space. The distance between the points in the three-color space does not necessarily correspond to the perceived difference between the color stimulus pairs, so it is advantageous to use a color appearance model 118 (as discussed further below with reference to FIG. 3). The color appearance model 118 will The three-dimensional three-color vector is transformed into a one-dimensional component of luminosity 117 (also referred to as brightness or intensity) and a two-dimensional component of chroma 116 (which represents an apparent color that is independent of luminosity). Chroma can be considered as a vector value in two dimensions, in which case the vector value can be referred to as a chroma coordinate. Chroma can be further divided into hue and saturation (also known as purity, which is essentially the perceived difference between a color stimulus and a white stimulus). It should be noted that the spectral absorptivity of retinal photoreceptor cells 108, 110, and 112 (Figure 1) depends on the viewer and varies from person to person. In addition, the formation of a color appearance model 118 may also depend on the observer 113, however, for the sake of generality, a standard model may be used in the subsequent description. FIG. 2A shows a graph of the spectral absorption rate of photosensitive pigments of retinal cone cells (including short-wavelength cone 201, middle-wavelength cone 202, and long-wavelength cone 203) of a normal human eye. However, as mentioned previously, the spectral absorption rate of retinal photoreceptor cells can vary from person to person. These differences are the root cause of color vision defects. For example, individuals with weak green have a medium-wavelength cone photoreceptor pigment that has a spectral absorptance shifted toward longer wavelengths; and individuals with weak red have a long-wavelength cone photoreceptor pigment that has more orientation One of the short-wavelength shifts in spectral absorption. Individuals with weak greens experience more difficulties in distinguishing between red and green than normal individuals. Individuals with weak red also experience more difficulty in distinguishing between red and green than normal individuals, and also tend to regard red as less bright. A photochrome template can be shifted by a log wave number scale (for example, by using the Spectral sensitivities of the middle- and long-wavelength sensitive cones derived from measurements in observers of known by Stockman, A., and Sharpe, LT "genotype." (template published by Vision Research, No. 40, 2000, pp. 1711 to 1737) approximates the spectral absorption rate of abnormal retinal photopigment. The table in Figure 2B lists the associated wavelengths of known genotypic variants and maximum photosensitivity pigment absorption in the population. The leftmost row of the table contains one of the genotype 204 labels (for details, see Asenjo, AB, Rim, J. and Oprian, DD, "Molecular determinants of human red / green color discrimination", Neuron, 1994, Vol. 12, pp. 1131 to 1138), the next line of instructions can be normal, weak green or weak red Class 205 and where the type of abnormality is further classified according to the severity that can be mild, moderate, or severe, and the remaining lines indicate the wavelength (in nanometers) of the maximum absorption rate of short wavelength cone photoreceptor 206, medium The wavelength (in nanometers) of the maximum absorption rate of wavelength cone photoreceptor pigments 207 and the wavelength of the maximum absorption rate (in nanometers) of long wavelength cone photoreceptor pigment 208. This table contains the most common types of genetic color vision defects: green weak has a global prevalence of about 4% (and about 8% is male and less than 1% is female); red weak has a prevalence of about 0.5% (about 1% are male and less than 0.1% are female). The higher prevalence of color vision defects in men is due to the X recessiveness of genetic abnormality genes. The abnormality of light-sensitive pigments in short-wave cone cells is called type III color weakness. Hereditary type 3 color weakness is rare, however, when cone cells (specifically, short-wavelength cones) are destroyed, for example, by exposure to certain toxins such as mercury, acquired type 3 color weakness . Individuals with Type III color weakness experience more difficulties in distinguishing between blue and yellow than normal people. The standard observer model of color vision can be conceived to best fit a normal population and does not necessarily provide a good model of color perception for any particular individual or subgroup. However, if the physiological characteristics of any individual can be fully obtained, then any individual physiologically relevant observer model 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 axis of the graph corresponds to the neural excitation of short-wave cones 310, the neural excitation of medium-wave cones 306, The neural excitation 301 of the long-wavelength cone cells and the tri-color value correspond to a point 302 of the color appearance of a specific light (for example, reflected by a reference color or emitted by an illuminant). The three-color value is a three-dimensional point, and its dimension corresponds to the portion of light energy absorbed by various cone cells. Light itself can be regarded as a vector of essentially infinite dimensions, and its spectrum can be measured using a spectrophotometer, however, the trichromatic value is only three-dimensional. Therefore, many different lights can be mapped to the same point in the three-color space, and a group of lights mapped to the same point in the three-color space is called a color change pair. The projection from the spectral domain of light to the three color domains of the color appearance is a linear mapping, therefore, the addition and scalar multiplication of light are retained. This property implies a geometric shape with three color values. For example, if a composite light is formed by a non-negative addition mixture of a set of light (that is, a convex linear combination), the three color values of the composite light must be contained in a convex polyhedron, and the corners of the convex body are three Color value. Referring again to FIG. 3, the origin 307 of the axis corresponds to the appearance of black (ie, there is no light and zero nerve excitation). The spectral trajectory is a set of three color values that form a contour 309 corresponding to the color appearance of the set of monochromatic light (ie, ideal light with only a single wavelength of energy). Since any light can be regarded as a convex linear combination of the set of monochromatic lights, the tri-color value is always contained in a generalized cone whose vertex is the origin 307 and its boundary is defined by the spectral locus 309. For subsequent analysis of the optical filter, and as briefly discussed above, the three-color representation can be usefully divided into one-dimensional component of luminosity and two-dimensional component of chromaticity. These transformations are also linear mappings. The luminosity response is a line in a three-color space that is consistent with the three-color values of the origin and the illuminant E. The perceived luminosity of a light can be calculated by projecting the three color values onto the luminosity response line 303 and then measuring the vector norm of the projection 305. The luminosity line (which is also drawn by the spectral trace 309 in this figure) is also orthogonal (vertical) to a plane of the three color values of the equivalent illuminant, and can be calculated by projecting the three color values onto this plane 304 The perceived chromaticity of a light. Subsequently, the chromaticity projection can be further transformed by an affine mapping to generate a chromaticity coordinate (which is a two-dimensional value in a space), where the distance between the chromaticity coordinates and the equivalent light source light The perceived difference is approximately proportional, and it is called a color difference table color system such as one of the color difference table color systems (UCS) such as CIE 1974. In the first-order chromatic aberration color system, it can be observed that the distance from white light (such as illuminant E) to the spectral locus varies with the wavelength. Specifically, yellow monochromatic light (e.g., having a spectral radiant flux at a single wavelength (585 nm nominally)) and cyan monochromatic light (e.g., having one of the characteristic wavelengths of about 490 nanometers) (Monochromatic light) seems to be more subjectively more similar to white light than blue, green, or red monochromatic light and correspondingly closer to white light on the UCS diagram. Therefore, filters that substantially block yellow and / or cyan wavelengths can improve the apparent purity of color, and the general form of these filters includes at least three passbands and at least two stopbands. Spectral transmittance of multi-band filter f as a function of wavelength λ It can be approximated by the following expression: ; Where in the above expression, For passband and To 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 wavelength λ in the above expression can be expressed in a table by uniformly sampling according to a wavelength scale (for example, using a step size of 1 nanometer) or another scale that is substantially equivalent (for example, frequency or log wave number). Specification of the transmittance (f, d) of a function filter. Sampling can also be defined on an arbitrary scale with uneven intervals 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 boundary is instantaneous or almost 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 measured equivalently according to a frequency scale. The spectral transmittance of a rectangular passband can be defined by the following expression: ; among them Is the center 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 boundary 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 full-width at half maximum (FWHM)). The half-peak bandwidth can be equivalently measured according to a frequency scale. The spectral transmittance of a Gaussian band can be defined by the following expression: ; among them 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 in which the passband is a function of wavelength as a function of transmittance. The slope ratio between the two sides is between about 4: 1 and about 1: 4. In the changes regarding non-Gaussian passbands, a passband that is sufficiently wide to essentially eliminate irregular and / or sharp transitions can be used to smooth these passbands. In this case, the passband can be described as ( In essence) has a center of a frequency band and a half-peak width corresponding to a smooth passband. A general method for evaluating the effectiveness of a filter is used to determine which filter configurations are possible for a particular application involving color vision. This grading method can be performed by measuring the relative color 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, so the area of the color gamut is also filter-dependent. A flowchart of a procedure for calculating the relative color gamut area is presented in FIG. 4. In the method depicted in FIG. 4, the relative color gamut area is 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, that is, the three color values of the filtered illuminant are the same for the two filters. This limitation eliminates the need for a chroma adaptation model (such as the von Kries model) that can bias the results. The method may benefit from a suitable selection of one of the set of reference colors, as described later with reference to FIGS. 6A and 6B of the present invention. In addition, the reference filter is preferably selected to have a wide-band spectral transmittance, so that the reference filter provides minimal or little distortion in color appearance. For any given test filter, the test filter can be compared, for example, by a spectral reflectance set according to the Munsell color and then the Munsell color (e.g., having a relative to Select the most similar white point color of the illuminant) 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 obtained color gamut areas 408 and 409 to obtain a relative color gamut area 411. One of the relative color gamut areas of 1.0 implies that the test filter does not provide distortion of color appearance, and the test filter It is said to provide normal color discrimination. Implicit in a relative color gamut area greater than 1.0: the test filter increases the perceived difference between the reference colors. In general, the increase in these differences is greater between red and green, so the test filter is said to provide enhanced red-green discrimination. Implicit in one of the relative color gamut areas less than 1.0: the test filter reduces the perceived difference between the reference colors. Generally, this effect is associated with an increase in one of the differences between blue and yellow, Therefore, the test filter is said to provide enhanced blue-yellow discrimination. It should be understood that the relative color gamut area measurement based on the analysis of chromaticity coordinates of reference colors is independent of the perceived luminosity of those reference colors, for example, the increase in apparent differences between color stimuli is not based on a color presentation The fact that it is a rare dark color and another color appears as a rare bright color. Instead, these increase or decrease the percentage increase in available color gamut area (PGAI) is expressed by the following expression: ,and ,and ; among them Calculated for the color gamut area relative to the test filter f, reference color S, illuminant I, and observer O (as described below in conjunction with FIG. 5), and Relative to the reference filter And similar color gamut areas. To evaluate the filters in the following of the invention, one or the other of two methods for calculating the percentage increase in color gamut area is used. In one method, the illuminant I is defined as the illuminant D65, and the observer O is defined as a CIE 1931 2-degree standard observer combined with a color difference table color system such as CIELUV (u ', v'), and the reference color S is specified For any color of the Farnsworth D-15 panel, and the percentage increase in color gamut area is given by the following expression: . In another method, the reference color is given by a selected natural sample (as described in conjunction with Figure 6B), and the percentage increase in color gamut area is given by the following expression: . In the above two expressions, the color gamut area is calculated with respect to a given condition. The calculation of the color gamut area in operations 406 and 407 of FIG. 4 may be implemented, for example, as detailed in the program flowchart of FIG. 5. For a specific illuminant 502, a filter 503, and a set of reference colors 501, each reference color undergoes an optical interaction 505. As explained above with respect to operation 102 of FIG. 1, the optical interaction may be, for example: the reference color reflects filtered light from the illuminant; or the filter filters the light from the illuminator 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 (ie, the observer model) and converted to a set of three color values by visual light transduction 506, as described above, for example, with respect to the figure 1 operation 115 is explained. The set of three color values is further transformed by a color appearance model 508 and is 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 obtained mesh can be converted into an area by summing the areas of the triangles in the mesh, and the final result of the calculation is the color gamut area of 512. The calculation of the color gamut area benefits from a suitable 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, and their chromaticity coordinates form a triangle enclosing the white point (ie, the chromaticity coordinates of the illuminant). Preferably, the reference color set includes a sufficient number (e.g., at least 5) and a sufficient variety of spectral reflectances, so that the calculation of the color gamut area is stable with respect to the change in the transmittance of the filter, and its reduction makes one The risk of filter designs being too specialized. 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 color gamut area calculations such that their chromaticity coordinates approximately form a circle around an equal saturation among white points. The spectral reflectance of these Munsell colors is wideband and varies with respect to hue in a controlled manner. This is obvious in the graph of FIG. 6A, which shows that includes Munsell 5B 5/4 at 601, Munsell 5G 5/4 at 602, Munsell 5Y 5/4 at 603, Munsell 5R 5/4 and 605 at 604 A selection of Munsell colors from Munsell 5P 5/4. In a further variation, a group of Munsell colors with high saturation may be better selected. Alternatively or in addition, part or all of the reference color 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, which form an outline that is saturated around the white point. A filter that provides an increase in the color gamut area relative to these D-15 colors will also tend to provide an increase in score based on the D-15 cap configuration test when an observer performs a test and views a sample through the filter. Alternatively or in addition, part or all of the reference color may be directly sampled from the environment in which the filter will be used. In particular, several of the embodiments shown later can be usefully incorporated into sunglasses, and because sunglasses are generally worn outdoors under daylight, the spectral reflection of natural colored objects such as leaves and flowers can be measured Rate and better find the reference color. The graph of FIG. 6B shows the spectral reflectance of these natural objects, including the spectral reflectance 606 of blue flowers, the spectral reflectance 607 of green leaves, the spectral reflectance 608 of yellow flowers, the spectral reflectance 609 of red flowers, and the spectral reflection of purple flowers Rate 610. These natural colors are free from the "Spectral representation of color images" of 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 218 measured samples published. It can be easily observed from the graphs of FIGS. 6A and 6B that the colors in nature have a more diverse distribution than the Munsell colors, and further contain certain significant features: for example, green 607 in nature depends on The spectral reflectance of chlorophyll with a characteristic peak at the meter, and the color described as green relative to the Munsell color (which is an artificial color) usually has a peak reflectance at about 525 nm. As shown in the diagrams of FIGS. 7A to 7C and FIGS. 8A to 8C, the calculation of the relative color gamut area (as described above) and the chromaticity appearance of the color appearance of the multi-band filter can be conveniently visualized. The effect. In FIG. 7C, the spectral transmittance of a reference filter is shown at 711, which is also one of the Munsell colors selected to best match the white point of the experimental filter shown at 712. The illuminating body is designated as the illuminating body D65, and its spectral radiant flux 710 is represented by a graph in FIG. 7B. In FIG. 7A, a chromaticity diagram is used to plot the chromaticity coordinates of the selected Munsell color, as viewed under a given illuminant and different filter conditions. In the chromaticity diagram, the enclosed solid line 709 is a spectral locus corresponding to the chromaticity coordinates of the monochromatic spectral light, and the line segment 708 is referred to as a purple light connecting line. The white points of the filters are substantially the same and are shown at point 706. The chromaticity coordinates of the selected Munsell color are shown along the hollow circles along the dotted outlines 701 and 705 (as viewed through the reference filter 711). The chromaticity coordinates of the selected Munsell colors are shown along the solid circles along the solid outlines 702 and 703 (as viewed through the experimental filter 712). The inner contour corresponds to the selected saturated Munsell color, and the outer contour corresponds to the selected saturated Munsell color. By examining the contours, it should be understood that the chromaticity coordinates of the colors (as viewed through a test filter) cover a larger area of the chromaticity diagram, and in particular, the chromaticity coordinates show along the One of the separations of the chromaticity coordinates of the red-to-green axis has increased significantly (green mainly appears near the "front end" of the upper left corner of the track (approximately at (0, 0.5)) and red essentially appears at the upper right corner of the track (0.5, 0.5)). Therefore, an experimental filter (which has a relative color gamut area greater than 1.0 compared to a reference filter) can be described as enhancing red-green discrimination. In the example of FIG. 7A, the reference color of the inner contour starting at point 704 and traveling clockwise is: 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 outer contours starting at point 707 and moving 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 the visualization of the color gamut area, the graphs of FIGS. 8A to 8C show the effects of the same experimental filter and reference filter relative to the color of nature. In FIG. 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 FIG. 8A, the white point of the filter is shown at 804. The dotted outlines 807 and 808 correspond to the chromaticity coordinates of the selected natural color (as viewed through a reference filter), and the solid outlines 802 and 803 correspond to the chromaticity coordinates of the same natural color (such as through a test filter). Watched). 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 from point 807 at 606, 607, 608, 609, and 610, respectively, in the graph of FIG. 6B. The outer contour corresponds to the appearance of the most saturated instance of natural color available in the previously cited database. While natural colors can be a better choice for analyzing the effectiveness of a filter in an outdoor background (for example, for incorporation into sunglasses), Munsell colors provide a more easily interpreted visualization, so The remaining pictures in the present invention use Munsell colors for this purpose. Heretofore, examples of the multi-band filter for enhancing the color appearance, such as in FIGS. 7C and 8C, have a structure including three rectangular passbands and two stopbands. This filter can be uniquely specified by enumerating the starting and ending wavelengths of each frequency band giving 6 degrees of freedom. Thus, a computer can be used to: completely enumerate the entire set of possible filters; then use the relevant color gamut area metric as described above to rank the performance of each of these filters; and then select the best for a desired effect A good filter (such as for enhancing red-green discrimination, or enhancing blue-yellow discrimination or maintaining normal color discrimination). The increase in the number of degrees of freedom characterized by filters can, for example, extend the search to a larger group by allowing the transmittance to vary within a frequency band or by increasing the number of possible frequency bands. Along these lines, a computer-implemented method for designing an optical filter that affects color perception in a desired manner is listed below. It is assumed that the desired filter includes a pre-filter and a multi-band interference filter in the overall optical composition. First, specify the following: the transmittance of the pre-filter over the entire visible spectrum; the desired white point of one of the optical filters; the minimum total light transmission of one of the optical filters; an illuminant; a plurality Reference colors; and an initial test multi-band interference filter, which includes a plurality of adjacent blocking wavelength bands and pass wavelength bands covering the visible spectrum. Next, one or more new experimental multi-band interference filters are generated by changing the stop wavelength band stop and the pass band, transmittance, or boundary and transmittance of the initial test multi-band interference filter. Device. Next, the white point and total light transmission of the optical filter are determined for each combination of the pre-filter and one of the new experimental multi-band interference filters. Next, the effect of the optical filter on the color perception of each combination of the pre-filter and one of the new experimental multi-band filters is evaluated using the specified illuminant and reference colors. Next, one of the new experimental multi-band interference filters (for this new experimental multi-band interference filter, the optical filter satisfies a specified white point and a specified minimum total light transmission and affects color vision in a desired manner) It is selected as the multi-band interference filter in the optical filter. In this method, the pre-filter may have a transmission of about 100% over the entire visible spectrum. That is, the pre-filter is optional. The initial test interference filter may include, for example, five or more stop bands and pass bands in total. Creating a new experimental interference filter may include, for example, varying the number of passbands, stopbands, or number of passbands and the number of stopbands in the initial experimental interference filter. Additionally or alternatively, generating a new experimental interference filter may include varying the shape of one or more of the stopband or passband. The effect of evaluation on color vision may include any of the evaluation methods disclosed in this specification. The method also includes: specifying a color constraint that constrains the appearance of a reference color, such as viewed or illuminated through an optical filter; evaluating each combination of a pre-filter and one of the new experimental multi-band filters against the reference The effect of color appearance of color; and one of the new experimental multi-band interference filters (for this new experimental multi-band interference filter, the optical filter meets the specified color constraints) is used in the optical filter as Multi-band interference filter. Any of the color constraints disclosed in this specification can be used with this method. As one of the possible disadvantages of the above method, the optimal filter for achieving the desired effect may not be a member of the filter group under study in some cases. In addition, the strategy described above becomes unmanageable due to the multiplication of the number of possible filters to be evaluated and each additional free variable. Another related method is to use a quasi-Newton adaptation method to search through a subset of possible filters and move incrementally toward the desired filter in an evaluated optimal direction. However, in some cases, solutions found by this type of method may be only locally optimal. One of the further difficulties of these methods, including direct enumeration and local search, is that it is difficult or impossible to impose constraints on the filter, such as, for example, the specifications of the filter's white point relative to a selected illuminant. Instead, each test filter must usually be evaluated to determine whether it meets these constraints. To constrain the white point, a filter can be expressed as a linear combination of the color change pairs of the white point, such as a weighted combination within a three-color color change pair group (that is, essentially including three different wavelengths of light) However, this requires one representation with thousands of degrees of freedom, because the number of these color-changing pairs is large, and when the search space has so many dimensions, the quasi-Newton search method is generally excessively slow. In addition, this method cannot easily achieve the specifications of additional constraints beyond the white point of the filter. One method of designing filters that are computationally efficient and implement multiple constraint criteria specifications (described in detail below) is to use a linear programming approach. This method can have many different advantages: a linear program solver uses a sequence of incremental steps to quickly locate the best solution, however, a linear program solution is unique and globally optimal (relative to the input). In addition, the solution can be constrained to meet useful criteria related to chromaticity appearance and luminous appearance of color appearance. Commercially available linear program solvers can quickly determine whether a given set of constraints has no solution (i.e., not feasible), and these solvers can also quickly determine linear programs with thousands of free variables and hundreds of constraints The best solution. Linear programming 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, the details related to how to design a filter that affects color vision and how to translate the design rule into a linear program are explained in detail. The filter generation method disclosed below incorporates a linear program solver (abbreviated as LP), which can generally be described as the best method for determining a resource allocation problem that is subject to a linear constraint relative to a linear cost function One solution. When applied to the problem of designing color vision filters, the resources to be allocated can be understood as the transmittance of the filter as a function of wavelength. The linear constraint is derived from the use requirements of the filter and the linear cost function Essentially a mechanism by which a linear program solver can lead to a better solution within the scope of a feasible solution. The method of generating a filter by linear programming can be practiced by using a computer to solve a linear program given by the following expression: Minimize 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 formula of the vector x is solved, and the transmittance of the filter as a function of wavelength Calculated by the following expression: , And if p, then ,and ; Wherein, in this method, f is a designed optical filter, Is the transmittance of f as a function of wavelength λ. E is a matrix of one of the basic filters such that the matrix e _i The behavior is based on the transmittance of light as a function of the wavelength of each elementary filter, and the number of elementary filters is N. definition The expression is a weighted sum of one of the basic filters, where the weighting factor 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. In addition, The combination 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 also generally referred to as a "pre-filter" in the present invention, but these filters can be composed in any order. Linear program constraint 1≥x≥0 is equivalent to constraint 1≥x _i ≥0, where i is between 1 and N. In addition, 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 a desired manner. By c ^T x calculates the total cost associated with the solution, c ^T x represents the inner product of the transpose of c and x. A solution x that provides a lower total cost is generally better than the desired function, but other measures of quality can also be used to determine the adequacy 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; one of the white points of the filter Constraints; or constraints on the color appearance of one or more reference lights, such as viewed or illuminated by a transmissive filter; and / or these transmission constraints of filter f at one or more angles of incidence. The wavelength λ as a function of the above expression can be expressed in a table by uniformly sampling according to a wavelength scale (e.g. using a step size of 1 nm) or another scale that is substantially equivalent (e.g. frequency or log wave number) Transmittance of the filter (e _i , p, f) specifications. Sampling can also be defined on an arbitrary scale with uneven intervals between sample points. The basic filter may be, for example, a single-passband filter having a passband width of about 1 nanometer, and each filter has a different center wavelength of the passband. These filters can also be referred to as monochrome filters and are defined as having the following spectral transmittance: ; among them As a Dirac Δ function, and Is the wavelength transmitted by the filter. For the basic filter group of the entire group, the wavelength usually varies between 400 nm and 700 nm. In this case, the basic filter matrix E is essentially a unit matrix of 301 × 301. Alternatively, the basic filters may be single-passband filters each having a width greater than about 1 nm, and each basic filter has a different center wavelength of the passband. In some of these changes, the passband may be rectangular (also known as a square pulse function) and the spectral transmittance of a basic filter is defined as follows: ; among them Is the center wavelength, Is the rectangular bandwidth, and H is the Heaviside step function. One typical choice of rectangular bandwidth is about 10 nanometers. In this case, the number of basic filters can also be reduced, so that there is a 5 nanometer gap between adjacent filters. In some variations, the passband may have Gaussian or one of Gaussian spectral transmittances, as defined by the following expression: ; among them Is 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. One different combination of widths, in which case the number of basic filters can be larger (e.g. thousands of combinations). A multi-passband basic filter can be configured, for example, by adjusting the bandwidth and / or band transmittance levels to color-changing pairs with respect to the illuminator 904 and the reference filter 912 (FIG. 9). Any suitable set of basic filters can be used in the filter design method. One suitable basic filter must have at least one physically achievable transmittance spectrum (for example, a transmittance value between 0 and 1), And the calculation of a cost associated with the filter must be further realized, which will be described later together with the discussion of FIG. 12A and FIG. 12B. Preferably, the basic filter has a compact support (that is, a transmittance is 0 outside a finite interval), so that a numerical calculation method of sparse linear algebra can be applied, which includes an interior point method for solving a linear equation . It should be observed that f as defined in the above expression includes a weighted summation of one of the basic filters, where the basic filter is typically a single-pass or multi-pass filter (for example, including One or more rectangular or Gaussian pass bands), it can be inferred that the designed filter f can be understood as a multi-band filter, however, the number of pass bands is very large in nature (for example, 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 and multi-band filters with more complex transmittance curves. In reality, however, the figure will show that the most useful filter designs usually have three or four characteristics that can be described essentially as frequency bands, but the essential shape of these frequency bands can be irregular in some cases, ie, 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 in which the wavelength at In the transmittance of the function, the slope ratio between the two sides of the passband is between about 4: 1 and about 1: 4. In changes regarding non-Gaussian passbands, such passbands can be smoothed, for example, by a Gaussian core that is only wide enough to essentially eliminate irregular and / or sharp transitions, in which case the passband can be described It essentially has a center of a frequency band and a half-peak width corresponding to a smooth passband. Figure 9 contains a flow chart describing a procedure for generating a filter (according to a specification of a design criterion). Box 903 presents a computer-implemented filter generator operation described in more detail below. 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 formula expression provided above), spectral transmittance constraint 902, color appearance constraint 915, filter white point constraint 908, illuminant 904, reference filter 912, observer 918, basic filter 913 (matrix E in the expression provided above), optional pre-filter (top The p in the expression provided in the text can be set as a whole to be effectively skipped) 919, the smoothing core 920 is selected, and the bias coefficient 923 is selected. Still referring to FIG. 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 FIG. 11), and the three-color constraint calculation operation 910 generates a constraint projection limit 906 (a linear program expression Vector b) and Constrained Projection Norm 909 (Matrix A in Linear Formula Expressions). Next, a linear equation 907 is represented by a constraint projection bound 906, a constraint projection norm 909, and a cost vector 901 (as described by the linear equation expression provided above). Then, the linear program is solved by a linear program solver 905. The linear program solver 905 provides a solution of the linear program as a one-to-one solution vector 911. The solution vector 911 is the best vector x in the linear programming expression provided above. The elements of the solution vector 911 are coefficients x _i , Which gives the corresponding basic filter e _i (These are the rows of the matrix E representing the basic filter set 913.) A weighting factor is provided. Next, operation 914 performs a summation of one of the basic filters weighted by corresponding elements of the solution vector 911 to provide a first filter. , The first filter It is then smoothed at 916 (optional), then biased at 922 (optional) and combined with a second filter (pre-filter) 919 combination to produce engineered filter specifications 921. For example, by combining an absorption pre-filter With an interference filter And manufacture composite filters 921, wherein the interference filter assembly is specified by an 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 wide band transmittance (i.e., It fluctuates smoothly and slowly depending on the wavelength), or may have a narrow-band or multi-band transmittance. Methodological considerations These properties of p in the specifications make the resulting filter f meet the input design criteria. 24A, FIG. 24B, FIG. 28A, and FIG. 28B to describe a preferred pre-filter in detail Of choice. In particular, the use of a pre-filter with a narrow band absorption rate can be better used for some applications and demonstrated and described in detail in conjunction with Figures 20A and 20B. Contemporaneous methods for designing and manufacturing interference filters (such as using non-quarter-wavelength optical monitoring) can make one filter with almost any spectral transmittance curve. However, the number of dielectric material layers required to implement a particular filter specification varies. Any desired limitation on the total number of dielectric material layers requires, for example, that the spectral transmittance curve has a limited 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 summing operation 914. For example, a smoothing core 920 can be applied to the best filter provided at operation 914 by frequency domain maneuvers in 916. The smooth core may be, for example, a Gaussian core having a half-peak width (which is 2% of the center wavelength). In a further example, the smooth core may be a Gaussian core with a half-peak width (which is about 10% of the center wavelength) such that the filter may be implemented with a low-order dielectric stack (e.g., less than about 50 material layers). specification. Alternatively or in addition, the basic filter can be smoothed (for example, by the specification as a Gaussian filter instead of a rectangular filter). The smoothed filter type output from the smoothing operation 916 can then be used as a specification for manufacturing an (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 (such as its effect on color perception) is not significantly degraded by smoothing. For example, the width of the smooth core may be selected as the widest core so that the peak transmission in the passband of the filter is not significantly reduced. Although smoothing is selected, all of the filter embodiments described herein (as designed by the linear programming method described above) use a smoothing core with a half-peak width between about 10 nm and about 25 nm. In particular, in order to improve the filter performance, under the condition that the incident angle of the light passing through the filter varies within a certain range, an offset coefficient 923 can be used to bias the filter specifications toward a longer wavelength ( 922). The selection of the bias coefficient is described in further detail together with FIGS. 29A to 29B and 30A to 30B. Now returning to the various inputs of the filter generator operation 903 (FIG. 9), a cost vector 901 (c in the above linear stylized expression) must be specified so that a cost can be associated with each basic filter. For example, if the basic filters are each a single-pass band filter, then a function Specifying the 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-pass band filter (where each basic filter has three or more passbands), the cost function 901 may be, for example, one of the relative color gamut areas of the basic filter A function, for example, the cost associated with a basic filter can be defined as follows: ; among them Is the gamut area provided by the basic filter, and Is the 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 changed further 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, a process described in more detail below with respect to FIG. 12. The specification of a cost vector provides a way for the filter generation method to direct the linear program solver towards a better filter design, because the linear program solver will avoid basic filtering with a relatively high cost Incorporation of optical devices (ie, positive weighting) (if one or more constraints must not be met). The preferred filter design can be changed according to the target application of the filter, so the specifications of the cost function should also be changed appropriately. For example, FIG. 12A shows two functions of cost as a function of wavelength (e.g., for use with a set of single-passband basic filters as previously described), where the cost functions are selected to maximize filtering The relative color gamut area of the optical device design, which leads to a method design that filters one of the red and green discriminators. To design a filter that enhances the blue-yellow discrimination, these cost functions can be inverted, for example, by multiplying by a negative one. The cost function 1201 is configured to maximize the relative color gamut area relative to the selected Munsell color, as shown at 601, 602, 603, 604, and 605 in FIG. 6A. The cost function 1202 is configured to maximize the relative color gamut area relative to the selected natural color, as shown at 606, 607, 608, 609, and 610 in FIG. 6B. For other identical design criteria, the cost function of Munsell color results in filter 1204 (FIG. 12B) and the cost function of natural color results in filter 1203 (see also FIG. 12B). It should be noted that the passband of the natural filter 1203 is about 10 nm red compared to the filter 1204 of the Munsell color, and a similar preference for a longer wavelength is also found in the short-wavelength passband. These details are not trivial. For example, the natural filter 1203 causes less distortion of the green hue. The spectral reflectance of green is mainly determined by the content of chlorophyll in the plant, and the leaf green has one significantly longer than the artificial green pigment. The reflectance peak wavelength is consistent with the analysis of the reference colors of the two different groups as previously discussed in conjunction with Figures 6A and 6B. Referring again to FIG. 9, the observer 918 is generally a standard observer with normal vision. If the filter design is intended to correct a very extreme defect, a specific defect observer can be selected. The lighting body 904 is selected according to the intended use and environment of the filter, and may be, for example, any suitable lighting body disclosed herein. The reference filter 912 is selected to set the intended white point of the designed filter, where the white point is the chromaticity coordinates of the selected illuminant as viewed through the reference filter, and the designed filter will be based on The same white point is characteristic. The reference filter has also been used in a relative color gamut area calculation (as described above) to compare the designed filter with a reference filter, such as described below with respect to FIG. 13. The remaining design criteria inputs shown in FIG. 9 are spectral transmittance constraint 902, filter white point constraint 908, and color appearance constraint 915. Each color appearance constraint includes: a reference light (defined by its spectral radiant flux); a luminosity constraint such that the resulting filter must specify the luminosity of the reference light as viewed through the filter at a marginal interval And a selection of chromaticity constraints, which makes the resulting filter must specify that the chromaticity coordinates of the reference light as viewed by the transmissive filter are contained within the convex hull of the bounded chromaticity coordinates. The viewing conditions mentioned above are also specified relative to the observer 918 and the pre-filter 919. In addition, the spectral transmittance constraint 902 and the filter white point constraint 908 are special cases of a color appearance constraint 915 as indicated by a 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 limited to a certain luminosity interval (note that a (The chromaticity of monochromatic light cannot be changed by any filter). Some spectral transmittance constraints are necessary, for example, the transmittance must be limited between 0.0% and 100.0% at each visible wavelength to produce a passive optical filter. The white point constraint of the filter includes a reference light (which is a selected illuminant), and further provides a luminescent equation constraint and a chromaticity boundary. In general, the chromaticity boundary may have a size that is essentially infinitely small, so that the white point is accurately set. Alternatively, the chromaticity boundary may have a wider boundary, which includes, for example, an approximately circular area centered on the white point of the reference filter. For color vision needs, the filter white point is generally set or otherwise constrained within a central area of a chromaticity diagram corresponding to a color that is not considered to be a strong color. For the design of the filter to be used in sunglasses, the illuminating body preferably represents daylight (eg, illuminating body D65), and the luminosity based on the limit of the illuminating body is between about 8% and about 40%. As mentioned above, a color appearance constraint is specified as a margin interval based on a boundary of chromaticity coordinates and a luminosity based on the color appearance of a reference light. This data can be geometrically understood as a constrained polyhedron in one of the three-color models, 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 three color values of the reference light as viewed through the filter are contained in a convex polyhedron that is essentially conical ( 1001, 1002), wherein the chromaticity boundary forms a closed contour of a wall-like surface (eg, 1005), and the luminosity limit interval defines two cover-like surfaces including a lower luminosity limit 1007 and an upper luminosity limit 1006. The cover-like surfaces are parallel to the iso-brightness plane 1004 and each is contained in a plane that is shifted from the origin to the corresponding upper and lower luminosity limits, respectively. Each of these wall-like surfaces is contained in a plane that intersects the origin. The chromaticity boundary is specified by a convex hull of a set of chromaticity coordinates that define the wall of the cone 1005 when converted to three-color values. If and only if the vector norm of the projection on the surface normal vector (not shown in the figure) pointing inward from all three colors to all walls is non-negative, then the example three color value 1003 satisfies the chromaticity boundary. In addition, if and only if the vector norm of the projection on the surface normal vector (not shown in the figure) of the three-color value to the inwardly pointing surface of the upper and lower covers is greater than / less than the lower and upper luminosity limits, The example tricolor value 1003 then meets the luminosity limit. The surface normal vectors are vectors in a three-color space, which are, by definition, perpendicular to a plane containing a surface. If the lower limit of the luminosity is zero, the cone reaches a vertex at the origin. If there is no upper limit for the luminosity, the cone extends indefinitely 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's linear constraint, as described in additional detail below. Referring again to FIG. 9, the color appearance constraint 915 is converted into a set of linear constraints through calculation at 910, and the operation at 910 is repeatedly performed with respect to each color appearance constraint 915 and each basic filter 913 to cause the linear constraint projection limit 906 Vector and matrix of constrained projection norm 909. The conversion of a color appearance constraint to a system's linear constraint is further detailed from the program flowchart of FIG. 11, where the three-color constraint calculation 1102 corresponds to operation 910 in FIG. 9. Herein, a color appearance constraint 1101 may be designated as a reference light 1105, a chroma boundary 1106, and a luminosity limit interval 1104. These bounds can be converted into a generalized polyhedral cone in the three-color space of the observer 1103 (operation 1109), as explained in conjunction with the description of FIGS. 10A and 10B. From the obtained geometry, operation 1109 provides: a matrix 1112 comprising a vector orthogonal (perpendicular) to the surface of the polyhedron and pointing inward from the surface of the polyhedron; and an origin offset from each plane containing a surface 1113 A one-shift vector that is zero for a wall-like surface and equal to the upper and lower luminosity limits for a cap-like surface as previously described. Then, the interaction between the bounded geometry of the color constraint and each basic 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, and then calculate the filtered retinal photoreceptor pigment absorption 1115 received by the observer 1114 ( That is, visual light transduction), resulting in a three-color value 1117 corresponding to the reference light as viewed through a basic filter and a pre-filter. Next, a matrix-vector product 1116 is used to project the tri-color value 1117 onto the surface normal vector (in matrix 1112) of the constrained polyhedron, resulting in a set of vector lengths (range Number) 1119 and the corresponding limit 1118 that will ensure restraint against color appearance constraints. These constraint projection norms are the linear properties of the basic filter relative to the constraint. For example, if the three color values projected onto a surface normal vector have a length of zero, the basic filter is effectively orthogonal to the constraint and any number of filters can be incorporated without violating that particular boundary In the solution. If the constraint projection norm is non-zero, the magnitude of the norm gives the ratio that causes the designed filter to move towards or away from the constraint boundary, as a function of the linear weighting of the basic filter. Referring again to FIG. 9, these results are accumulated in a constrained projection norm matrix (A in the above-mentioned linear program expression) 909 and a constrained projection limit vector (b) in the above-mentioned linear program expression, where the results are One suitable format that is compatible when incorporated in the linear program 907. In some embodiments, a color appearance constraint 1101 (FIG. 11) may also include an incident angle of the reference light 1105 with respect to the basic filter 1107. In this case, an appropriate transformation may be applied to correctly calculate 1108 and 1111 The resulting transmission of the light in the medium allows the three-color value of the reference light, as viewed through the basic filter and the pre-filter, to also take into account the incident angle of the reference light. For example, if the filter is to be manufactured as an interference filter, this angle of incidence can be used to shift the basic filter (based on the percentage of wavelength) according to Snell's law. (See, for example, curve 1601 in FIG. 16A). In addition, if the pre-filter is an absorption type, the calculation can consider the path length difference according to Beer-Lambert's law. Next, the composite filter f can be expressed by the total composition of the components q = Ex and p, so that the transmittance of f at an angle of incidence that deviates from θ radians of the surface normal vector can be expressed as And is approximately expressed by the following expression: ; Where e _i The effective refractive index is n having a value of about 1.85, and for approx. Θ between about 0 and about 45 degrees, this approximation is sufficient. Incorporating color appearance constraints at non-zero incident angles is particularly useful for providing filter designs with improved color stability under non-ideal viewing conditions. In order to evaluate the filter in the present invention, the white point displacement of a filter f relative to the incident angle θ is defined by the following expression: , Where, in the above expression, (u ₀ , v ₀ ) And (u ₀ , v ₀ ) Is the CIELUV (u ', v') chromaticity coordinate (relative to CIE 1931 2 degree standard observer) of the illuminating body D65 as viewed through a filter with normal incidence and θ degree deviation from the incidence. Instead, the white point displacement is calculated relative to a CIE 1964 10 degree standard observer. Referring now to the flow chart of FIG. 13, in some embodiments, a filter design process is repeated. This iterative process may begin with an initial specification of one of the filter design criteria 1301 input into the filter generator 1303 of the design process 1302. The design criteria 1301 may, for example, include some or all of the design inputs shown in FIG. 9. Process-related additional information 1309 can also be entered into the optional manufacturing analysis program 1308 (also described further below) in the design process 1302. This manufacturing information may, for example, include: time constraints on the use of manufacturing equipment; manufacturing costs or budgets; and physical restrictions on the filter structure, such as, for example, thickness, thickness uniformity, composition, or Limitation of the uniformity of the composition of the material layer of the filter. The filter generator 1303 may be, for example, the same or substantially the same as the filter generator 903 described above with reference to FIG. 9. The filter generator 1303 generates a test filter 1305, which may be, for example: an optimal filter type, which is related to transmission as a function of wavelength or frequency (e.g., output by operation 914 in FIG. 9); A smooth optimal filter type that is related to transmission as a function of wavelength or frequency (e.g., output by operation 916 in FIG. 9); or a composite filter design that incorporates an optional pre-filter (E.g., output from operation 917 in FIG. 9). The optical performance of the test filter 1305 (Figure 13) can be analyzed as appropriate at operation 1307. This performance analysis may include, for example, calculating a relative color gamut area 1314 relative to a reference filter 1304, an illuminant 1306, and a set of reference colors 1301 (all of which are optional inputs to the design process 1302). The relative color gamut area can be calculated, for example, using the procedure described above with reference to FIG. 4. If the relative color gamut area is not desirable (ie, too high or too low), the cost function can be adjusted at operation 1315 and the filter design criteria 1301 can be updated accordingly before another iteration through the design process 1302. In the embodiment in which the cost function is adjusted as just described, the first iteration of the design procedure 1302 may utilize, for example, a (for example, two) Gaussian functions (each of which is characterized by a center wavelength, a width, and an amplitude). The sum of the initial cost functions as a function of wavelength. The cost function may further include a monotonic offset incorporated by addition or multiplication with any monotonic function. For example, a monotonic function may be linear. When iterating the design process and calculating the relative color gamut area in each iteration, the cost function may be adjusted using any suitable conventional maximizing method that adjusts the cost function to increase (or alternatively, decrease) the color gamut area. Adjusting the cost function may, for example, include: changing a parameter characterized by Gauss; changing a parameter characterized by any monotonic offset; or changing a parameter characterized by Gauss and changing a parameter characterized by an offset. The cost function or any other suitable form of 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 the relative color gamut area to evaluate the effectiveness of an experimental filter with respect to color discrimination, in some embodiments, the distribution of the reference color in the chromaticity space is characterized by one or more standard deviations of the calculated distribution . These standard deviations can be calculated along the red-green axis and the blue-yellow axis in the chromaticity space or along any other suitable choice of projection distribution along the axis. The projection onto the green blind obfuscation line can be better used to evaluate the filter to be used by the weak green observer. The projection onto the red blind confusion line can be better used to evaluate the filter to be used by the weak red observer. The projections on the third type of colorblind obfuscation line can be better used to evaluate filters to be used by the third type of color-blind observers, or they can be used to evaluate filters to ensure that one of the red or green discriminations is vertical or almost vertical The complementary increase of the standard deviation will not negatively affect the blue-yellow discrimination. An experimental filter that adds one or more of these standard deviations compared to a reference filter can be considered to enhance color discrimination along one or more corresponding directions in the chromaticity space. A test filter that reduces one or more of these standard deviations compared to a reference filter can be considered as attenuating color discrimination along one or more corresponding directions in the chromaticity space. Similar to the description above with respect to the relative color gamut area, in some embodiments, the cost function used in the design process 1302 may be repeatedly adjusted to maximize or minimize the chromaticity space as viewed through the experimental filter One or more standard deviations of the reference color distribution. Now return to the performance analysis operation 1307 (Figure 13) in the design procedure 1302. Operation 1307 can also be assessed as conforming to 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 text of these two standards are incorporated herein by reference). This analysis can be performed, for example, to ensure that the test filter is intended for safe use by a human observer in intended applications, such as when operating a motor vehicle. Based on the result 1313 of this standard compliance analysis, operation 1316 may contemplate additional or modified color appearance constraints for the filter design criteria 1301 to guide the filter design process 1302 to conform to the standard. In addition to or instead of the performance analysis 1307, the manufacturability of the test function 1305 can be analyzed at operation 1308. This operation may result in, for example, an estimated manufacturing cost 1312 and a manufacturing specification 1311 that provides one of the tolerances and / or processing procedures. The estimated manufacturing cost 1312 may be expressed as, for example, a total manufacturing time, a total financial cost, or both. Based on the estimated manufacturing cost 1312, operation 1317 may optionally adjust color constraints, smoothing (e.g., operation 916 in FIG. 9) or color constraints and smoothing to direct the filter design process 1302 toward one of the lower estimated manufacturing costs. Filter. For example, the width of the smooth core 920 (FIG. 9) can be increased, or the constraints on the spectral transmittance in certain regions can be relaxed or tightened appropriately. A linear program solver (such as 905 in Figure 9) can detect this if the constraints added or modified at operation 1316 or 1317 result in an infeasible design criterion (that is, a design criterion that cannot solve a linear programming problem) . The constraints can then be relaxed or revised until feasibility is restored. The entire filter design and analysis procedure 1302 may be repeated until a satisfactory (eg, optimal) filter design is reached. At this time, the manufacturing specification 1311 may be adopted and used to manufacture the optical filter. A filter as described herein may filter light based on, for example, absorption, reflection, or absorption and reflection of light. The filters may include, for example, any suitable combination of interference filters, absorption filters, and polarization filters (polarization filters typically include a pair of linear polarizers enclosing a wavelength-selective polarization rotator). The interference filter portion of the interference filter and the composite filter (as disclosed herein) can be manufactured, for example, using about 12 to 200 layers and having a total thickness of about 6 microns per 100 layers and having a thickness of about 6 microns. A dielectric coating with a typical effective refractive index between 1.8 and about 1.9. Such multilayer interference coatings can be applied, for example, to glass or optical polymer substrates having a base arc between 0 and about 10 diopters, where diopters are defined as being calibrated to a refractive index of 1.523 by a lens gauge Measured spherical curvature. The interference filter designs disclosed herein and intended for eyewear can 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. The further design of the interference filter disclosed herein and intended for spectacles can also be specified for use in combination with a neutral density absorber or a wideband absorber or a narrowband absorber, the details of which are shown in the figure 28A and FIG. 28B and specific examples given in the accompanying description and the like are disclosed in conjunction with the discussion of FIGS. 20A and 20B. In general, in the following, it is assumed that the process (at least) involves physical vapor deposition of a dielectric material into a coating having a sequence of different thicknesses and refractive indices to form an interference filter. Industrial machines and programs can easily obtain and implement high-throughput and high-precision manufacturing of these filters, which include filters with irregular configurations of areas with partial transmittance and / or passbands. Any other suitable process may be used instead, or any other suitable process may be used in combination with this physical vapor deposition process. If not otherwise constrained, filters designed to enhance red-green discrimination may tend to reduce transmission of yellow light, which may cause a yellow traffic signal to appear darker and more similar to red (eg, orange or reddish). Similarly, filters that enhance blue-yellow discrimination can tend to cause green light to look more like blue or white (eg, unsaturated). To avoid this and similar potential problems, filters incorporated in general purpose glasses, such as sunglasses, may be configured such that the resulting glasses provide one of certain colors (specifically, the color of average daylight and traffic signal light). Adjust appearance. For certain glasses, this needs to meet, for example, industrial or government regulatory standards. The methods described above (eg, by applying suitable constraints to the filter design) can be used to design a compliant configuration. A luminosity constraint ensures that these lights (such as daylight, traffic signal light) appear to be moderately brighter when viewed through filter glasses. A chromaticity constraint, designated as one of the convex boundaries in chromaticity coordinates, ensures that such light falls within the bounds of the boundary and therefore treats the observer as one of the hue with the correct standard color name, ie, ensures that daylight is essentially White; and the traffic signal is correctly identified as, for example, a traffic light green light, a traffic light yellow light, and a traffic light red light. Figure 14A shows an example of this "general purpose" constraint for general purpose glasses. An example chromaticity boundary 1401 specifies that yellow traffic lights are not orange or red. Point 1402 shows the chromaticity of the yellow traffic light as viewed through an unrestricted red-green discrimination enhancement filter, and point 1401 shows the chromaticity of the yellow traffic light under the red-green discrimination enhancement filter. An example chromaticity boundary 1406 provides that the green traffic light is not yellow, blue, or excessively unsaturated. Point 1404 shows the chromaticity of the green traffic light, which is essentially the same under both filters. An example chromaticity boundary 1405 specifies that daylight does not exhibit strong colors. Point 1403 shows the chromaticity of substantially the same daylight under the two filters. FIG. 14B shows a curve 1408 of spectral radiant flux of sunlight, a curve 1407 of spectral radiant flux of green traffic signals, and a curve 1409 of spectral radiant flux of yellow traffic signals. FIG. 14C shows the transmittance 1411 of the unconstrained filter and the transmittance 1410 of the constrained filter. In the filter 1410, the effect of the constraint is obviously that the long passband has been essentially divided into two passbands to form a four-passband filter. As shown in this example, the constraint is on the reddest side of the yellow chroma boundary. However, as shown in the further description in conjunction with FIG. 15A and FIG. 15B, the split pass band may be better forced to have an irregular shape (such as having a shoulder on the short wavelength side to replace one of the split sub-bands) A single pass band, or a core that is wide enough to merge the subbands essentially into a single pass band to smooth the split pass band. One further concern related to the incorporation of multi-band filters into glasses is that the stop band can significantly suppress the luminosity of some narrow-band light, such as from light emitting diodes, lasers, and sodium vapor lamps. In some embodiments, a lower limit of a minimum transmittance of a filter may be preferably set to ensure a minimum brightness of all monochromatic light. For example, in FIG. 15A, a graph 1501 shows a lower limit of the spectral transmittance of about 7% between about 450 nm and about 650 nm. One filter incorporating constraints is shown by its spectral transmittance graph 1504 in FIG. 15B. The filter 1504 is a four-pass band filter in which a fourth pass band has been added to satisfy a yellow traffic light constraint (as described in conjunction with FIGS. 14A to 14C). In some embodiments, this additional passband may be better converted to a frequency band shoulder on the short wavelength side of the long wavelength passband. This change may be better because the resulting filter can provide a more stable appearance with respect to one of the yellow light (specifically, narrow-band yellow light) that varies with the angle of incidence, assuming that the multi-band filter is incorporated into the An interference filter characterized by a blue shift of the spectral transmittance at an angle of incidence other than normal incidence is described further below. Replacing the fourth passband with a shoulder can be accomplished, for example, by increasing a minimum spectral transmittance constraint in the desired region (such as shown by graph 1502 in FIG. 15A). In the graph 1502, the minimum transmittance has been set to about 18% between about 580 nm and about 635 nm. The resulting modified filter transmittance is shown by graph 1503 (FIG. 15B), and graph 1503 shows the described shoulder on the short wavelength side of the long wavelength passband. A passband with a shoulder as just described can also be used at other locations within a three-pass 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 narrow-band fluorescent lamps under the blue shift induced by the angle of incidence ( (Such as FL10 to FL12). In a further example, some embodiments have a shoulder on the short wavelength side or the long wavelength side of the short wavelength passband, which is described in more detail in conjunction with FIGS. 16A and 16B. In a further example, the passband may have an irregular shape (i.e., non-rectangular and non-Gaussian) having a configuration that is essentially a bimodal distribution, where the two modes at least partially overlap; or the passband may be Has a shoulder on one or more sides of the passband; or the passband can be described as a skewed distribution, where in the transmittance as a function of wavelength, the slope ratio between the two sides of the passband is about 4 : 1 to about 1: 4. One further constraint applicable to these filters is the white point, that is, the chromaticity coordinates of a typical illuminant, such as daylight. If the white point is within a moderate radius of the neutral point (ie, the chromaticity coordinate corresponding to unfiltered daylight), the filter can be considered non-strongly colored. Therefore, the visual mechanism of chromaticity adjustment will enable the observer to adjust to the new color balance after wearing glasses for several minutes. In some embodiments, this adjustment may preferably be minimized, for example, by configuring the white point to be neutral (i.e., so that the chromaticity coordinates of daylight are at or near the center of region 1405 (Figure 14)). waiting time. In these cases where the white point can be expected to be neutral, a restricted area can be given for the appearance of daylight, for example, the (x, y) chromaticity coordinate of the illuminant D65 is about (0.31, 0.33), and The best filter provides a white point within about 0.05 units of this point. In some cases, in particular, for example, when the cost function is configured to maximize or minimize the transmission of blue light, it may be better to allow the white point to be in a larger area (e.g., area 1405 (FIG. 14)). Anywhere). In further cases, specific shades of white point may be specified for other reasons that include good looking. As mentioned above, the transmission spectrum of a multi-band interference filter is sensitive to the deviation of the incident angle of incident light. Specifically, as the effective optical thickness of an interference filter (i.e., the wavelength at which the destructive interference occurs at the refractive index boundary within the filter) decreases as the angle of incident light deviating from normal incidence increases At hours, the spectral transmission suffers a shift (one blue shift) towards one of the shorter wavelengths. The normal incidence is defined by a vector perpendicular to the surface on which the interference filter is deposited. In this context, a normal incidence may be referred to as a zero-degree angle of incidence, that is, an angle means an angle of deviation from the normal vector. In addition, a multi-band filter incorporating an absorption filter can change transmittance according to Beer-Lambert's law, where absorption tends to be attributed to transmission when the angle of incident light deviating from normal incidence increases. The larger effective path length of the absorbing medium increases. In any of the above changes, the multi-band filter f may include an absorption filter p and an interference filter q, where the change in the transmittance of p as a function of angle is based on Beer-Lambert's law, and The change in the transmittance of q as a function of angle is based on Snell's law, so that the transmittance of f at an angle of incidence that deviates from θ radians of the surface normal vector can be expressed as And is approximately expressed by the following expression: , Where, 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 the normal incidence , The spectral transmittance of f at the normal incidence , The spectral transmittance of q at the normal incidence , And for θ between about 0 and about 45 degrees, this approximation is sufficient. The incident angle sensitivity of a filter has implications associated with the incorporation of the filter into devices such as eyeglasses, where the effective incident angle of light has a significant change in position on the surface of the lens as a function of position (along with Figure 29A To FIG. 29B and FIG. 30A to FIG. 30B and describe them in detail), and also has the implication related to incorporating such filters into a device such as a lamp assembly, in which a perfect beam of an illuminating body cannot be achieved Collimation. A change in the spectral transmittance of a filter that is a function of the angle of incidence is a physical property of the filter. However, the main concern is the perceptual implication of these changes, which can be quantified by measuring the change in chromaticity and luminosity of a reference light as a function of the angle of incidence as viewed through the filter. In particular, it is useful to consider these changes with respect to the chromaticity coordinates of the illuminant (i.e., the white point of the filter) because the change in the white point as a function of the angle of incidence is generally the same as that under the illuminant. These changes in the entire set of reference colors viewed are related. In addition, two or more angles of incidence (e.g., 0 degrees and 25 degrees off the normal axis or 0) can be constrained by employing additional color appearance constraints in the filter generation method as previously described. Degrees, 25 degrees, and 35 degrees), the chromaticity coordinates of the illuminating body are substantially unchanged at the specified angle and the intermediate angle. In FIG. 17C, graph 1707 (similar to graph 811 of FIG. 8C) shows the spectral transmission of one 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 filter's (blue) off-normal incidence at about 20 and 30 degrees, respectively. Shift) spectral transmission. FIG. 17A also shows the effect on the appearance of a selected contour of Munsell colors as viewed through three filters. Contour 1703 corresponds to a normal filter (0 degree incident angle), contour 1702 corresponds to a first displacement filter (approximately 20 degrees of incidence), and outline 1701 corresponds to a second displacement filter (approximately 30 degrees of incidence) ). It should be understood from these contours that the appearance of the color under the filter is not stable with respect to these changes in the angle of incidence. Furthermore, we have observed that the filter with the greatest red-green discrimination enhancement tends to locate the passband, with one or more of the retinal photopigment pigments having the largest change in absorption as a function of wavelength. Therefore, the best filter for enhancing color discrimination (specifically, for red-green discrimination) is also the worst filter for providing a stable color appearance. In FIG. 16B, graph 1603 (similar to graph 1503 of FIG. 15B) shows the spectral transmission of one 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 so that it is substantially the same at normal incidence and about 30 degrees off normal incidence. Transmission of the optical filter. Multi-band filters that provide a stable color appearance can be stabilized, for example, by having frequency bands that are positioned and / or shaped such that when viewing stable reference light, the stimulus changes of each of the three cone cells It is approximately linear in the angular range and the change between the three cells essentially describes a system with at most one degree of freedom, where the degree of freedom acts only in the direction of luminosity. For example, in some embodiments, these frequency bands may preferably be located near the wavelength of the peak sensitivity of one or more of the retinal photopigment absorption rates, or may have a doublet as a function of the angle of incidence within the desired range Or other irregular shapes (which are used to make the stimulus change constant or almost constant). In a further embodiment, the shape of a passband (such as a long wavelength passband) can be configured such that the stimulus change of the long wavelength cones is inversely proportional to the stimulus change of the wavelength cones as a function of the angle of incidence, thus ensuring The required limit on the degree of freedom to maintain a constant chromaticity. However, I have found that these frequency band locations and / or shapes are generally the next best for enhancing color discrimination, so one utility of the linear programming method can be based on the fact that it provides a solution that satisfies a color stability constraint, This solution maximizes color discrimination enhancement. Specifically, such changes in the position of the filter band preferably occur on the outermost band. For example, the stimulus change rate of short-wavelength cones can be made substantially constant by positioning the short-wavelength band at about 450 nm. Alternatively, in some cases, it may be preferable to split the short wavelength pass band near the peak of the absorptance of the short wavelength cone cells (e.g., shown in graph 1605), whereby the pass band can be described as having a double Peak distribution (it has 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 having one of the first mode at about 620 nm and the second mode at about 650 nm, or may have a skewed distribution, a convex Shoulder (usually on the short wavelength side) or other irregular (ie, non-Gaussian) distribution. The graphs of FIGS. 18A to 18C show the behavior of a filter having a stable white point relative to a range of incident angles. FIG. 18C shows the transmittance of the filter at normal incidence in graph 1807 and the transmittance of the filter at about 20 degrees of incidence in graph 1806. It can be observed in these graphs that the splitting sub-band structure in the short wavelength region identified by reference number 1805 essentially functions as a comb filter that is tuned to stabilize when performing wavelength shifts. The illuminating body whose color appearance has been stabilized is the illuminating body of daylight, as shown in the graph 1804 in FIG. 18B. In the chromaticity diagram of FIG. 18A, the chromaticity coordinates 1803 of the illuminant are the same at two incident angles. Figure 18A also shows the effect on the appearance of the selected contour of the Munsell color. The profile 1801 corresponds to a normal filter (0 degree incident angle), and the profile 1802 corresponds to a shifted filter (about 30 degree incident angle). As can be understood from the position of these contours, the filter provides a moderately stable appearance of one of these reference colors, with most of the loss of saturation mainly associated with the highest saturated color (e.g., Munsell contours as previously described in conjunction with Figure 8A) Associated. The chromaticity stability demonstrated by the filter can significantly reduce the appearance of a "hot spot" in the center of the lens (caused by the blue shift induced by the angle of incidence) and generally contribute to improved visual comfort. As shown in FIG. 18C, a filter that provides color stability can provide weaker red-green discrimination enhancement due to the effect of the imposed constraints. In some embodiments, it may be better to incorporate a pre-filter with a narrow band absorption rate, where the absorption band (s) are located near the location where the stop band in the filter design is expected. 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 these filters are shown in FIGS. 20A and 20B. In FIG. 20A, the solid line curve at 2001 shows the spectral transmittance of an absorption filter including neodymium in a glass substrate. Neodymium is a rare earth material, which is characterized by a strong absorption band at about 590 nm and a secondary absorption band at about 520 nm. In FIG. 20B, the solid line curve at 2002 shows the transmittance of an interference filter that, when combined with the neodymium absorption filter, provides enhanced red-green discrimination and an angle of incidence of 0 to 30 degrees The stable color appearance. Referring again to FIG. 20A, the dashed curve at 2001 shows the spectral transmittance of an absorption filter including one of the narrow-band organic pigments Exciton P491 and Exciton ABS584 in a polymer substrate. Exciton P491 is characterized by a strong absorption band at about 491 nanometers, and Exciton ABS584 is characterized by a strong absorption band at about 584 nanometers. In FIG. 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 an angle of incidence between 0 and 30 degrees. Stable color appearance. These examples can be designed by a linearly stylized method as previously described, by incorporating the absorption filter as a pre-filter. 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 the constraint is relative to about 0 degrees to about CIE 1931 2 degree observer at an angle between 35 degrees. In some cases, the angular range can be increased to about 0 degrees to about 45 degrees. For observers with green weakness, the displacement tolerance can be increased to about 0.02 units, and for observers with weak red or severe green weakness, the tolerance can be further increased to about 0.04 units because of this. Two observers are not sensitive to color shift and their equal color perception may not be fully characterized by a standard observer model. In addition, for these anomalous observers (their color matching functions are significantly different from the CIE 1931 2-degree standard observer's color matching functions), an observer-specific color matching function can be used to calculate the constraint criteria for achieving color stability. In these cases, the obtained filter may have the following properties when analyzing the white point displacement stability according to a CIE 1931 2-degree observer: the white point displacement function is at an angle between about 20 degrees and about 40 degrees of incidence Has a local minimum at; and the distance from the local minimum to the normal white point is less than about 0.02 units. To characterize the relative importance of the performance of filters at normal incidence and deviation from normal incidence when these filters are incorporated into a pair of glasses, a lens and one geometric model of the eye (for example, 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. Thus, the effective incident angle is defined as the angle between the normal vector of a lens at a lens position and the normal vector of a beam of light that passes through the lens position to be imaged on the retina of the eye. Figures 29A (top view) and Figure 29B (perspective view) show the geometric model as previously mentioned. Here, the geometric shapes of the left eye and the right eye are represented by hemispheres 2904 and 2905, respectively. The human eye (typically an adult's eye) has a radius of curvature of about 12.5 millimeters and an interpupillary distance of about 60 millimeters. The sense of color is mainly derived from the vision of 10 degrees in the center. However, the eyes can also rotate in their eye sockets, 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 glasses) are represented by spherical segments 2901 and 2902. A dotted arrow 2906 illustrates a light beam passing through a center position on the lens, and a dotted arrow 2909 illustrates a light beam passing through a distal position on the lens. These beams are also generally imaged at the central and distal positions of the retina. 2907 and 2908 show the surface normal vectors of the lens at the locations where the beams pass through. The lens in the glasses may have a radius of curvature between about 50 millimeters and about 150 millimeters (in this example, the radius of curvature is 87 millimeters). 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 Figures 29A and 29B by 2908 and 2909. The increase in the angle between them (compared to the angle between 2907 and 2906) is shown. For any frame pattern (for example, the edge contour of a lens and the positioning of the lens relative to the eye) and any lens curvature, it can be calculated from the geometric model just described (for example, using a computer) with the lens position as The effective angle of incidence of the function: repeatedly points on the lens; constructing the surface normal vector and the retinal image beam; and then calculating the angle between the two vectors at the surface position. The result of this calculation is shown in the contour diagram of FIG. 30A, where the boundary 3004 indicates the edge of a lens, and the internal contour shows the effective incidence angle as previously described, for example, the effective incidence angle is about 10 degrees along the contour 3001, It is about 20 degrees at the outline 3002 and about 30 degrees at the outline 3003. Next, it is useful to calculate the relative importance as a function of the effective angle of incidence. Referring now to FIG. 30B, one of the relevant importance functions as a function of the effective angle of incidence includes the product of two parts: first, an estimate of the ratio of the surface area of the lens viewed at a specific angle; and second, oriented along an axis One of the possibilities that the eye makes it see through the lens at a particular angle is estimated. In this paper, a Gaussian statistical model is used to estimate the directional distribution, as shown, for example, by a curve 3007 having a standard deviation of about 10 degrees. Therefore, the eye is most likely to be viewed at a normal incident angle. However, it should be noted that only a single point of incidence on the lens is normal (e.g., point 3005 in FIG. 30A), and the surface area of the lens is, for example, between 10 and 15 degrees (e.g., between the figures 30A between 3001 and 3006). On the surface of a typical lens, the incident angle is at most 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 FIG. 30B Indicated. The product of the area weighted curve and the directional distribution curve gives an importance weighting function, such as shown at curve 3008. Therefore, the importance weighted PGAI can be defined by the following expression: ,and , among them Is an exponential function, θ is an effective angle of incidence having a range of 0 degrees to 30 degrees, Test filter f and reference filter as viewed or illuminated at the angle of incidence θ PGAI, Is the standard deviation of the eye orientation distribution, which usually has a value of about 10 degrees, and k is a weighted normalization factor. In order to evaluate the filter in the present invention, two specific column equations are given which are weighted percentages of the importance of the increased color gamut area, in which the standard deviation of the eye orientation angle is set to about = 10 degrees and the reference color is designated as D15 or nature sample. The column equations are given by the following expressions: , ,and Which has previously been specified in the invention for calculation and Condition. In particular, the expression above The defined performance metric can be used to classify the properties of a filter f, and if the white point of the filter is neutral and the white point remains neutral within a moderate range of incidence, then these filters can be The percentage of comparative absolute power between one group increases or decreases. in the text, The use of calculations is limited to filters with a white point that is neutral and stable with respect to these angle changes. For between about -10% to about 10% Filters can be described as providing color discrimination that is inherently normal. 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 above assume that the filter provides a white point that is essentially neutral, that is, (x, y) of the illuminant D65 for all or almost all angles of incidence between 0 and about 30 degrees. The chromaticity coordinates are about (0.31, 0.33). As mentioned previously, the evaluation of the color gamut area can vary with the white point, so it is not possible to use a weighted PGAI metric to meaningfully evaluate filters that are not stabilized by the white point displacement. In addition, some hue (specifically, green) of the white point may provide a larger value of PGAI, however, such increase does not necessarily correspond to enhanced color discrimination. In a further embodiment, the calculation may also take into account changes in the thickness of the entity due to a process. For example, in physical vapor deposition onto a curved substrate, the thickness of the coating tends to decrease with distance from the sputtering source and / or the effective incident angle between the spray particles and the surface normal of the curved substrate. In a further embodiment, the calculation of the effective incident angle as just described can be used as the basis of a manufacturing specification, so that the filter is manufactured on a curved substrate, so that the filter has a solid thickness profile, such as The effective incidence angle is compensated by having a distribution that increases the thickness toward the edge of the lens (eg, linearly increases the thickness of the normal solid from the center to approximately + 10% of the solid thickness at the edge of the lens). An interference filter can be manufactured to achieve a constant or substantially constant optical thickness relative to the effective incidence angle at all or nearly all positions on the lens. In some embodiments, the performance analysis of a filter may include using relevant importance data to determine the importance-weighted average performance of a filter when incorporated in the glasses. The importance-weighted average performance can be improved by adjusting the spectral transmittance specifications of the filter (specifically, by red-shifting the specifications). E.g, The spectral transmittance can be shifted towards longer wavelengths, as calculated by the following expression: ,and ; among them Is a factor that determines the amount of displacement, and A weighted average relative color gamut area selected to maximize importance along one axis of the color space is increased and / or decreased and / or standard deviation. Instead, It may be selected to improve some other performance measures to, for example, reduce the importance weighted average solar blue light transmittance. Because the typical offset required is usually about 1% to about 4% ( = 1.01 to 1.04), so you can effectively determine the optimal bias coefficient by expressing a 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 can preferably be red-shifted to about 535 nanometers ( = 1.01) weighted average relative color gamut area with improved importance. Another aspect related to the incorporation of multi-band filters into spectacles (specifically, these filters include an interference filter) is the management of the reflectivity on one or both sides of the lens. With transmittance The reflectivity of an ideal interference filter is transmittance Complement Is defined by the following expression: . For example, a filter incorporated in a sunglasses may have a light transmittance of about 20%. Therefore, if the filter is manufactured with only one interference filter, the filter will have about 80% A light reflectance. 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 own eye reflected in the lens. For general use, the light reflectivity on the inner surface of the lens should be at most about one fifth of the light transmittance of the lens, but in some cases, light reflectances up to about one half of the light transmittance are also acceptable. The high reflectivity can be partially reduced by improving the shielding around the frame (for example, using a side shield on the temple arm). An absorption filter (e.g. a component as previously described The incorporation of) can significantly improve the reflectivity on one or both sides of the lens, for example, on one side of the lens In terms of this, the reflectivity on this side is significantly reduced, because the reflected light must pass through the absorption filter twice, as used in the calculation by the interference filter The reflectivity of the filter f, which is one of the filters f and the absorption filter p, is shown in the following expression: ,and ; Where in the above expression, Is the spectral reflectance of the filter. The ratio between the peak transmittance and the average transmittance of the composite filter f should preferably be as high as possible relative to these composite filters for enhancing color discrimination. In a further example, the Broken down into two constituent absorption filters, which are then on opposite sides of the lens, for example, ,and ,and ; Where in the above expression, Give the spectral reflectance on one side of the lens (such as the outer surface), and Give the spectral reflectance on the other side of the lens, such as the inner surface. In some instances, It may be a neutral density filter, such as a gray glass with a transmittance of about 40%. For example, this combination can achieve a light transmittance of about 20%, a peak transmittance of about 40%, and a light reflectance on one side of the lens of about 8% (i.e., (Approximately 50% light transmittance). In a further example, It may be a neutral density filter consisting of two absorption filters (for example, a brown glass and a blue glass, the combination of which produces a neutral transmission of about 40%) in which the two are colored. . These colors may be selected to affect the color of the reflected light on the outer surface of the lens (eg, for good looking). Neutral density and colored absorbers can also be formed from organic dyes and incorporated into a polymer substrate, and / or applied as a coating (for example by spin coating or dip coating) to one or more surfaces of the lens . Preferably, it can be used with Select the absorber to form a narrow band with complementary spectral transmission Therefore, a higher ratio of the peak transmittance to the average transmittance of the composite filter (for example, higher than the possible ratio when using neutral density absorption) is achieved. For example, narrow-band organic dyes Exciton P491 and Exciton ABS584, which absorb at about 491 nm and about 584 nm, respectively, can be used to form this complementary absorption suitable for use with red-green discrimination enhancement filters as disclosed herein body. Alternatively, certain rare-earth elements such as neodymium, praseodymium, and 'have narrow-band absorption in the visible spectrum, and can 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. In addition, the incorporation of a narrow band absorber (and an interference filter) can improve the quality of the filter design incorporating a color stability constraint on the white point, as previously described in conjunction with Figures 20A and 20B. In other words, the narrow band absorber is improved by the color discrimination provided by the filter at an incident angle of more than 20 degrees off the normal axis. Alternatively or in addition, 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 the front side reflection. A lens incorporated into a circular polarizer can achieve a peak transmittance of about 40%, a light transmittance of about 20%, and a light reflectance of about 2% on one or both sides of the lens. A circular polarizer having a spherical curve of 6 diopters or more can be manufactured, for example, by thermoforming and incorporated into a lens by, for example, lamination. In addition, these circular polarizers can be formed using linear polarizers that achieve only a partial polarization (e.g., a polarization efficiency of about 70%), thereby increasing light reflectivity while damaging one or both of the lenses Achieve a higher peak transmittance. An example configuration of a lens incorporating a circular polarizer is depicted in FIGS. 24A and 24B, where the layers (front to back) are vertically oriented linear polarizers 2401, quarter-wave retarders 2402, An optically transparent substrate 2403, a multilayer interference coating 2404 deposited on the surface of the substrate, a quarter-wave retarder 2405, and (for example, a vertically oriented) polarizer 2406. In FIG. 24B, light incident to the outside of the compound lens is shown along an arrow 2413. The incident light passes through a polarization filter, then through a quarter-wave retarder (hence becoming circularly polarized), and is then divided by an interference filter into a transmission component that is finally received by the eye 2409 and absorbed by the retina 2412. And a reflection component 2414 that travels in the opposite direction to the light source but is absorbed before it can be emitted from the compound lens. The reflected component 2414 is circularly polarized, however, the reflection at the interference filter 2404 causes its handedness to flip from right to left, for example, as it travels in reverse through the circular polarizer 2402, it appears to be circular Horizontally polarized and absorbed by linear polarizer 2401. Still referring to FIG. 24B, a similar procedure for reflection-absorption can occur with 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 made from a metal attenuating coating using physical vapor deposition. Preferably, such absorption filters and an interference filter can be manufactured by physical vapor deposition (i.e., in the same procedure), so the attenuation layer can surround the dielectric layer and / or the dielectric layer Several of them are staggered or partially staggered. Due to the nature of the metal layer when incorporated into an interference filter, these attenuating coatings can provide better reflection attenuation than the equivalent bulk dielectric neutral density absorber. For example, these designs can achieve a peak transmittance of about 35%, a light transmittance of about 20%, and a light reflectance of about 2% on one side of the lens. Alternatively, these designs can achieve a peak transmittance of about 35%, a light transmittance of about 20%, and a light reflectance of about 4% on both sides of the lens. Alternatively, these designs can achieve a peak transmittance of about 50%, a light transmittance of about 20%, and a light reflectance of about 4% on one side of the lens. Alternatively, these designs can achieve a peak transmittance of about 60%, a light transmittance of about 20%, and a light reflectance of about 8% on one side of the lens. An additional feature of these designs is that they have all functional layers (such as interference coatings and (several) attenuation coatings) of a filter positioned on one side of an optical substrate. In such designs, the opposite side of the substrate may 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 reflectance of no more than 0.5%, because the lower-quality anti-reflective coating (for example, has a light reflectance of about 1% or more) ) Visibility can be reduced under general outdoor conditions (specifically, when viewing unusually bright spots (such as sunlight reflections) reflected from a metal surface in a typical outdoor scene) but does not completely eliminate internal reflection artifacts . An example configuration of a lens incorporating an attenuation coating is depicted in FIGS. 28A and 28B, where the layers (front to back) are anti-reflective coating 2801, optical substrate (e.g., glass) 2802, first attenuation coating The layer 2803, the multilayer interference coating 2804, and the second attenuation coating 2805. In FIG. 28B, light incident to the outside of the lens is shown along an arrow 2811. The incident light passes through the anti-reflection coating and the optical substrate, then passes through the first attenuation coating, and is then divided by an interference filter into a lens component that is finally 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 reflected components 2812 is substantially absorbed during the second pass through the first attenuation coating. Still referring to FIG. 28B, a similar procedure for reflection-absorption can occur with stray light entering the lens' rear side (as shown along beam 2806) to cause reflected light 2810 to be absorbed before it reaches the eye. In some examples, the dielectric layers of the attenuating coating and the interference coating are staggered or partially staggered. In some examples, the attenuating coating is only on the backside, ie, does not include the first attenuating coating 2815. Next, along with detailed descriptions of FIGS. 31A-42E, 45A-45E, 48A-53E, and 55A-57E, several implementations including an exemplary multi-band filter for incorporation into glasses are disclosed. example. These figures all conform to a general format that is easily understood by their common layout. First, 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 the respective embodiments will be described in further discussion with reference to specific figures and elements in the figures. In the graph of FIG. 31A, the curve shows the transmittance constraint, which includes the minimum transmittance as a function of wavelength at the solid curve 3101 and the maximum transmittance as a function of wavelength at the dashed curve 3102, and a further curve display The cost function (which is a dimensionless quantity) is a function of wavelength at the dashed curve 3103 on the same graph. Transmittance constraints and additional color appearance constraints (not shown by the graph) and cost functions form inputs to a linear equation solver, where the inputs are processed as previously described in the present invention, which involves such constraints And the cost function is transformed into a standard linear program. In the graph of FIG. 31B, the curve shows the spectral transmittance of a component of one filter f designed to affect color vision in a desired manner, where the design is based on the constraint and guidance cost functions as described in conjunction with FIG. 31A Filter. As explained above, by Specify the "ideal" filter as produced by the linear programming method. The solid curve 3104 defines the weighted combination of the basic filter 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. The dashed curve 3105 shows (optionally) a smoothed (optionally) biased linear program solution q '. The spectral transmittances of the filter elements are listed in lines 5 to 8 (respectively q ', q, p, and f) in FIG. 59B. The second, third, and fourth lines shown in FIG. 59B are used to generate filter objects (respectively , , ) One of the manufacturing specifications of 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 functions used in filter design. The wavelengths corresponding to the columns of the table are listed in line 1 in steps of 5 nanometers, which provide the appropriate spectral resolution to reproduce any of the embodiments disclosed herein. The graph of FIG. 31C includes three curves, of which the solid line curve 3107 is the design target for manufacturing the filter. (Solved with a linear program that is biased and smoothed as appropriate Replace ), The dashed curve 3108 is a minimum transmittance limit, and the dashed 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 tolerance 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 symbol Represents the kernel function k and the filter Frequency domain maneuver between, and Is the bias coefficient as previously described. The core function k is generally characterized by having a half-peak 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 Within a certain range. Also, in the definition and , The proportionality coefficients (0.97 and 1.03) provide a relative transmittance tolerance of approximately +/- 3%, and the addition coefficient (0.03) provides an additional absolute tolerance of approximately + 3%, and the expression and Provides a wavelength shift tolerance of about +/- 2 nm (equivalent to about +/- 0.5% of 400 nm). These tolerances are selected empirically 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 value suitable for these parameters and the resulting tolerances can also be used. In FIG. 31D, the solid line curve 3110 and the dashed line curve 3111 show the function of the incident angle θ as compared to a best-adaptive wideband reference filter. The percentage increase in the relative color gamut area of the filter (PGAI), where the solid curve shows the calculated relative to the Farnsworth D-15 sample , And the dashed curve shows the calculated relative to the natural sample (NWS) . The weighted weighted percentage of increase in relative color gamut area can be calculated from any of these data by calculating a weighted average PGAI based on the eye models previously described in conjunction with Figures 29A to 30B and assuming a standard deviation of eye orientation of 10 degrees (E.g ). FIG. 31E shows a solid line curve diagram of the white point displacement of the filter as a function of the angle of incidence 3112, where the white point corresponds to the illuminant viewed by a transparent filter relative to a CIE 1931 2-degree standard observer The CIELUV (u ', v') chromaticity coordinates of D65, and the white point displacement as a function of the number of incident angles are defined as the white point chromaticity coordinates at 0-degree incident angle (that is, normal incidence) and deviation from normal The distance between the chromaticity coordinates of the white point at the angle of incidence. This calculation is performed assuming that the filter element q ′ is an interference filter having an effective refractive index of about 1.85 and the element p is an absorption filter. In addition, the table in FIG. 59A lists Various additional performance criteria evaluated, where the performance criteria include criteria previously defined in the detailed description of the present invention and selected metrics defined by the industry standard ANSI Z80.3-2010. In particular, for some embodiments, it is labeled " The "" column can be used to evaluate one of the robust estimates of the general quality of color enhancement provided by filters. This increase in quantity is associated with an improved score based on the Farnsworth D-15 lid configuration test and is also generally associated with one of the visual experiences that can be described as color enhancement. Hereinafter, the linearly stylized descriptions described herein are described with reference to FIGS. 31A to 42E, 45A to 45E, 48A to 53E and 55A to 57E, and the corresponding tables presented in FIGS. 59A to 80B. Some additional embodiments of method-designed filters. In these figures, the detailed description of the elements indicated by reference numerals xx01 to xx12 (where xx is a drawing number, for example, 31 in FIGS. 31A to 31E) corresponds to those given above with respect to FIGS. 31A to 31E A detailed description of the components, and further details are provided as appropriate for each individual case. In an embodiment, the graphs shown in FIGS. 31A to 31E and the design criteria of the multi-band filter with enhanced red-green discrimination and green band, the spectral transmittance of the component, the component, Manufacturing specifications and performance evaluation. Lines shown in graph 3107 in FIG. 31C and lines in FIG. 59B The filter manufacturing targets listed in the table have a first passband center at about 450 nm and a half-peak bandwidth of about 40 nm, a second passband center at about 530 nm and about 35 nm. It has 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. Filter manufacturing specifications can be used to produce filters. The 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 linearly stylized method as disclosed herein, where the basic filter is a group of approximately 60 rectangular passband filters, each of which has a single passband width of 10 nanometers and Has a center wavelength in 5 nanometer increments (the same is true for all embodiments described below). To improve manufacturability so that a low-order stacked dielectric material (eg, less than about 50 material layers) can be used to fabricate interference filter components, a Gaussian core (k) having a half-peak width of about 20 nm has been used. To smooth the filter design (q '). It should be further noted that the resulting filter (f) meets the minimum transmittance limit as shown at 3101 in FIG. 31A. The filter design criteria used to produce this embodiment have been configured such that the light transmittance of daylight is about 18%, which is suitable for use of the filter in sunglasses with a medium color. Further embodiments disclosed herein may use the same or nearly the same light transmittance. However, the methods disclosed herein are suitable for manufacturing with any moderate 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, the filter is greater than 40%). In addition, the filter provides a white point that will be considered to be substantially neutral, as shown in the table of Figure 59A (D65 chromaticity coordinates). A filter with a neutral configuration of white point can better balance the overall visual comfort and one of all colors. However, other configurations of white point can be used, but white with strong chromaticity should also be avoided This is because these filters generally do not provide adequate brightness in one of the entire color gamuts. Regarding the white point of this embodiment as viewed within a range of incident angles, as demonstrated by the white point displacement figure 3112 as a function of the number of incident angles in FIG. 31E, the white point moves considerably (for example, at 35 degrees The movement is greater than 0.03 units), so when this filter is incorporated into the glasses (where the filter can be viewed through a range of corners), a clear color shift towards the periphery of the lens can be observed. In addition, as shown in the graphs 3110 and 3111 in FIG. 31D, the color enhancement of the filter is lower than zero at about 20 degrees. Therefore, the filter only provides a relatively narrow field of view in which However, the desired color enhancement function is effective, for example, green (such as leaves) in nature may tend to have a brown appearance when the incident angle approaches or exceeds 20 degrees. A further embodiment of FIGS. 32A to 32E related to the previous embodiment shown in FIGS. 31A to 31E is characterized by a correspondence table in FIGS. 60A and 60B. This embodiment discloses that a filter designed with respect to the same conditions as previously described, except that the cost function shown at 3203 in FIG. 32A has been modified to further improve the color discrimination. The resulting filter design is characterized as an alternative to a passband location that provides a better performance. Currently, this configuration is considered to give the choice of the passband position only for the best possible performance of any three-pass band filter relative to the PGAI metric (however, as shown in further discussion, this metric may not be suitable for e.g. glasses Of practical applications of these filters). The line shown in the graph 3207 in FIG. 32C and the line in FIG. 60B The filter manufacturing targets listed in the table have: a first passband at about 440 nm, which has a half-peak bandwidth of about 30 nm; a second passband at about 535 nm, which has A half-peak bandwidth of about 35 nanometers; and a third passband at about 650 nanometers, which has a half-peak bandwidth of about 80 nanometers. The improved color enhancement effect of this embodiment is partly due to a wider gap between the first frequency band and the third frequency band. 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 (which has a wavelength shorter than about 450 nm) can be A filter with a third passband (which has a center wavelength longer than 610 nm) is preferred. However, 440 nm and 650 nm are approximately the maximum outer limits of the frequency band positions in filters with this desired effect, because frequency band positions that exceed these limits can tend to render blue and red as unacceptable Dark color. In addition, this embodiment benefits by locating the midpass band at a wavelength longer than 530 nanometers. The configuration of the middle passband at a wavelength less than 530 nm can provide a filter that causes green to appear unacceptably dark. The configuration of the passband at the precise 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 colors and this filter can tend to lead to nature. The green is unnatural green. The natural coloration of chlorophyll (as described previously) is more accurately regarded as a yellow-green color. The configuration of the midpass band at about 540 nanometers tends to maximize the PGAI performance relative to natural samples. The configuration of the middle passband at about 545 nm or longer tends to provide a filter that gives one enhancement of blue-yellow discrimination and a corresponding one of weakened enhancement of red-green discrimination, and if still chooses a longer The wavelength is then tilted towards blue-yellow (discussed in more detail in a further embodiment). Therefore, a configuration with a passband in the center wavelength of about 535 nanometers can achieve one of the best performance balances between artificial color samples and natural color samples, and has one of the center wavelengths of about 545 nanometers. The selection of the mid-band can achieve the best performance balance with respect to one of the red-green axis and the blue-yellow axis of the color space. Further embodiments of the filter for enhancing red-green discrimination disclosed below are consistent with the choice of center between about 535 nm and about 545 nm (if not otherwise specified), however, the examples shown are not It is intended to limit the scope of the present invention because the choice of mid-band position can be usefully varied between about 530 nm and about 545 nm of these filters for improved color discrimination. Returning to the discussion of FIGS. 32A to 32E, the performance of the filter (shown at 3210 and 3211 in Figure 32D, respectively) relative to the filter based on the PGAI measurement of the Farnsworth D-15 sample and the natural sample is shown compared to the previous embodiment One is significantly improved. In particular, for incident angles up to about 30 degrees, the PGAI is greater than zero, so the filter, when incorporated into the glasses, provides a wider field of view that gives one of the desired color enhancements. In addition, the PGAI at the normal incidence is significantly larger than in the previous embodiment. However, in comparison, this embodiment exhibits significantly worse performance with respect to the stability of white points within multiple incident angles. As shown at 3212 in FIG. 32E, the white point displacement at 35 degrees is about 0.05 unit. Due to the wide bandwidth of the long wavelength band, the white point tends to shift rapidly toward a red tone. Using available manufacturing methods, these layers can be partially relieved of unwanted white point displacement by depositing interference filters with a solid thickness that intentionally varies within the area of the lens (where the expected viewing angle is off-normal), however, These methods are too costly. For example, as opposed to a manufacturing method by physical vapor deposition, achieving a desired thickness gradient requires a highly precise processing configuration that would prevent mass production. In addition, even if a lens has a proper physical distribution of an interference coating, one of the filters that is so sensitive to the angle of incidence is difficult to reliably align in the frame of an eyeglass, making the eyeglasses' performance relative to the frame style and head size And similar geometric factors. A further embodiment of FIGS. 33A to 33E related to the embodiment previously shown in FIGS. 31A to 31E and the embodiment of FIGS. 32A to 32E has a correspondence table in FIGS. 61A and 61B. This embodiment discloses an optical filter designed with respect to the same conditions as previously described. However, the design criteria further include a color appearance constraint such that the white point appears to be substantially unchanged over a wide angle range, and the cost function is additionally adjusted to maximize the filter in the widest possible angle range. efficacy. The resulting filter design is characterized by a further alternative to the passband position, which provides good performance relative to the PGAI metric, but additionally ensures a consistent appearance of the color throughout the field of view to thereby incorporate in the filter Achieve robust performance and improved visual comfort when in glasses. In particular, the middle pass band remains at about 535 nanometers, but the upper and lower pass bands are configured between the positions of the embodiment of FIGS. 31A to 31E and the embodiment of FIGS. 32A to 32E. position. Figure 32C is shown at 3207 and Figure 60B. The filter manufacturing targets listed in the table have: a first pass band at about 445 nm, which has a half-peak bandwidth of about 25 nm; a second pass band at about 535 nm, which has A half-peak bandwidth of about 30 nanometers; and a third passband at about 630 nanometers, which has a half-peak bandwidth of about 40 nanometers. Relative to the efficiency of the filter, it can be observed in FIG. 33D that for incident angles up to about 25 degrees, the PGAI is greater than zero. Therefore, the filter, when incorporated into the glasses, provides a reasonably wide field of view that gives the desired color enhancement. Compared to the previous embodiment, the performance of the filter with respect to the stability of white points within multiple incident angles is significantly improved. As shown at 3312 in FIG. 33E, the white point displacement between 0 degrees and 35 degrees is less than about 0.01 units. In a further embodiment, it has been demonstrated that the white point displacement can be extended to an angle of up to 45 degrees while maintaining the same margin. In all of the embodiments disclosed below, a white point stabilization constraint in some form (if not otherwise specified) is used because these constraints are generally considered to be beneficial to any including an interference filter assembly Manufacturing of this filter. In fact, these filters, which incorporate a white point stability constraint, have been subjectively observed to provide a comfortable field of view in the absence of noticeable color distortion in peripheral vision, regardless of the fact that the lens can be incorporated to give relative One of the spectral transmittances, a dielectric interference filter, which varies significantly at the angle of incidence. In general, the methods disclosed herein can be used to discover red-green enhanced multi-band filters with three passbands configured to provide a stabilized white point, where the filters have a position at about 440 nm A first passband between about 450nm and about 450nm, a second passband between about 530nm and about 545nm and a third pass between about 610nm and about 635nm band. The preferred embodiment of the red-green enhancement filter is the following embodiment: it 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 the adjacent passband and resistance The maximum possible contrast ratio between the average transmission of the bands. However, all of these configurations can be adjusted by appropriate constraints to ensure the effectiveness of the filter, for example, when incorporated in glasses. The embodiments of the optical filters disclosed herein (for example, the embodiments disclosed in FIGS. 36A to 36E, 37A to 37E, 38A to 38E, 39A to 39E, and related embodiments) are provided with Proper maximization of the relevant guidance to obey these restrictions of the actual concerns intended to be applied. In a further embodiment related to the embodiment of FIGS. 33A to 33E, a blue-yellow enhancement filter is characterized by corresponding tables in FIGS. 34A to 34E and FIGS. 62A and 62B. This embodiment reveals that an optical 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 discrimination. These filters can be used for individuals with a third type of color weakness, which is one of the types of color vision defects where it is difficult to distinguish between blue and yellow. These filters can also be preferably used in spectacles suitable for certain environments (e.g. golf green grass courts) where the green is the main background (where green appearance is expected to be suppressed to some extent), or better In an optical aid for positioning a camouflaged object in a jungle (where suppression of changes between greens can reveal previously unseen features). The line shown in graph 3407 of FIG. 34C and the line of FIG. 62B The filter manufacturing target listed in the above has a first passband at about 455 nm, the first passband has a half-peak width of about 45 nm, and the second passband is at about 560 nm and It has a half-peak width of about 50 nanometers, and the third pass band is located at about 675 nm and has a half-peak width of about 60 nanometers. The efficiency analysis of the filter relative to the PAGI metric is shown in FIG. 34D. It can be observed that for incident angles up to about 20 degrees, PGAI is mainly negative. In addition, the white point displacement (as shown in FIG. 34E) exhibits excellent stability with a total displacement of less than about 0.01 units of incidence for angles of incidence up to 45 degrees from normal incidence. In addition, as mentioned in the table of FIG. 62A, the filter complies with the chromaticity limit of a traffic signal as defined by ANSI Z80.3-2010. In particular, compared 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. Compared to the filter of the present invention, which maximizes the blue-yellow discrimination and maintains compliance, the chromaticity coordinates of the green traffic signal are essentially located on or near the boundary of the compliance area, so that the green traffic signal appears as permitted by the standard Unsaturated (ie, white). In another embodiment also related to the embodiments of FIGS. 33A to 33E and FIGS. 34A to 34E, a color enhancement filter is characterized by the correspondence tables in FIGS. 35A to 35E and FIGS. 63A and 63B. The filter is further configured to substantially suppress transmission of short-wavelength light, such as light between about 380 nanometers and about 450 nanometers. These filters generally provide a balance improvement of color discrimination along both the red-green axis and the blue-yellow axis. In addition, the suppression of short-wavelength light can improve sharp focus and reduce the total energy of photons received by the eye, whose energy increases inversely with respect to wavelength. This embodiment is difficult to manufacture using a low-order interference filter because the design is preferably characterized by a rapid start point between reflection and transmission at about 450 nanometers. Therefore, a core having a half-peak width of about 10 nanometers is used to smooth the interference filter assembly (q '). To achieve the blue light blocking function, the cost function can be configured with an increasing slope as shown at 3503 in FIG. 35A. The white point of the filter can be oriented toward a yellow configuration, subject to the restriction that the white point is not considered to be "strongly colored" according to ANSI Z80.3-2010. The curve shown in FIG. 35C and the line shown in FIG. 63B The filter manufacturing targets are listed in the assumption that the filter incorporates a neutral density absorption filter (p) having a transmittance of about 50%. The filter manufacturing target has: a first pass band located at about 455 nm, which has a half-peak width of about 15 nm; a second pass band located at about 550 nm, which has about 45 nm One half-peak width; and a third passband located at about 645 nm and having a half-peak width of about 70 nm. The filter has a light transmittance of about 35% (corresponding to a light-colored sunglasses), but the hue can be made deeper by increasing the intensity of the absorption filter element. As shown in Figure 35D, this filter provides a moderately positive value for PGAI within an incident angle of up to 30 degrees. Relative to the color stability performance, the white point displacement is limited to 0.01 units between 0 and 35 degrees of incidence, as demonstrated in Figure 35E. In addition, as indicated in the table of FIG. 63A, the solar blue light transmittance (about 15%) is less than one and a half of the light transmittance. Therefore, the filter can be described as providing an improved blue light blocking function while maintaining the color appearance One of good quality. In a further series of three embodiments discussed below, red-green discrimination enhanced multi-band filters are disclosed, where the filters are configured for use by observers with weak green, which is difficult to distinguish green Crowd with red color vision deficiency. Compared to the previously disclosed embodiments of the red-green enhancement filter herein, these embodiments provide substantially more enhancement of color discrimination along the red-green axis. The manufacturing specifications disclosed in these embodiments provide a filter to be produced as a combination of a neutral density filter and an interference filter, wherein the neutral density filter has about 40% to about 55% One of the transmittance. In addition, interference filters are generally designated as high-order coating stacks because steep transitions between adjacent passbands and stopbands are generally better for maximizing color discrimination enhancement. These filters with steep frequency band transitions can provide an unstable color appearance for certain narrow-band light sources such as light emitting diodes and some types of gas discharge lamps, which include sodium vapor lamps and some fluorescent lamps. To alleviate these instabilities, these filters incorporate a minimum transmittance constraint with respect to a wavelength between about 450 nanometers and about 650 nanometers, which is usually specified to be equal to the light transmission of the filter The lower limit of about one fifth of the rate. Accordingly, the stop band of these embodiments is limited by this minimum transmittance. These filters also preferably conform to ANSI Z80.3-2010 related to the chromaticity coordinates of the traffic signals provided by the filters, and in particular, these filters minimize red and green discrimination enhancement Some embodiments of the device may provide a chromaticity coordinate of a yellow traffic signal at a restricted position relative to its compliant boundary, where the restricted position provides an appearance of the light that is red or almost red (if allowed). An additional difficulty associated with the design of these filters is that the color matching function of the weak green observer is not entirely characterized by the CIE standard observer model. Therefore, constraints related to white point stability can be better calculated relative to a modified observer model. The details of the calculations are well documented and available to the average technician. However, the white point displacement analysis in this article uses the CIE 2 degree standard observer. Therefore, the calculated white point displacement characteristic of the number of incident angles in these designs is a wider tolerance (for example, 0 degrees to 35 degrees). Between about 0.02 units). The white point displacement functions of these designs usually exhibit a local minimum at an angle between about 20 degrees and about 40, where the white point displacement measured at the local minimum is usually at most about 0.01 units. A first embodiment of a filter for a weak green observer is disclosed together with the correspondence tables of FIGS. 36A to 36E and 64A and 64B. The line shown in FIG. 36C and the line shown in FIG. 64B The filter manufacturing targets listed in the table have: a first passband located at about 450 nm, which has a half-peak width of about 25 nm; a second passband located at about 535 nm, which Has a half-peak width of about 35 nanometers; and a third passband, which is located at about 635 nanometers and has a half-peak width of about 35 nanometers. The manufacturing specifications of the filter incorporating a neutral density absorber of about 45% transmittance are given. For incident angles up to about 27 degrees, the PGAI provided by the filter is greater than zero, as shown in Figure 36D. As mentioned in the table of FIG. 64A, the importance weighted PGAI relative to the Farnsworth D-15 color is at least about 30%, which can be better used for an observer with mild green weakness. The white point of the filter, which is essentially neutral in color, is stabilized relative to a weak green observer model, and is characterized by a local minimum in a white point displacement curve of less than 0.01 units at about 32 degrees As shown at 3612 in FIG. 36E. A second embodiment of a filter for a weak green observer is disclosed together with the correspondence tables of FIGS. 37A to 37E and FIGS. 65A and 65B. Figure 37C is shown in graph 3707 and line 65B The filter manufacturing targets listed in the table have: a first passband at about 445 nm, which has a half-peak width of about 25 nm; a second passband at about 535 nm, which Has a half-peak width of about 35 nanometers; and a third passband, which is located at about 635 nanometers and has a half-peak width of about 40 nanometers. The manufacturing specifications of the filter incorporating a neutral density absorber of about 50% transmittance are given. For incident angles up to about 25 degrees, the PGAI provided by the filter is greater than zero, as shown in Figure 37D. As mentioned in the table of FIG. 65A, the importance weighted PGAI relative to the Farnsworth D-15 color is at least about 35%, which can be preferably used for an observer with moderate green weakness. The white point of the filter, which is essentially neutral in color, is stabilized relative to a weak green observer model, and is characterized by a local minimum in a white point displacement curve of less than 0.01 units at about 40 degrees As shown at 3712 in Figure 37E. A third embodiment of a filter for a weak green observer 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 so that the minimum spectral transmittance limit (equal to one-fifth of the light transmittance) is only at the yellow light wavelength to the red light wavelength (e.g., from about 580 nm to about 650 nm M) is mandatory, as shown at 3801 in Figure 38A. Therefore, the resulting filter design can be described as having a third passband with a "shoulder" on the short wavelength side of the frequency band. The curve shown in Figure 38C and the row shown in Figure 65B The filter manufacturing targets listed in the table have: a first passband located at about 445 nm, which has a half-peak width of about 20 nm; a second passband located at about 535 nm, which It has a half-peak width of about 30 nm; and a third passband, which is located at about 635 nm and has a half-peak width of about 30 nm. The manufacturing specifications of the filter incorporating a neutral density absorber of about 55% transmittance are given. For incident angles up to about 25 degrees, the PGAI provided by the filter is greater than zero, as shown in Figure 38D. As mentioned in the table of FIG. 66A, the weighted PGAI relative to the importance of the Farnsworth D-15 color is at least about 40%, which can be better used for an observer with severe green weakness. The white point of the filter, which is essentially neutral in color, is stabilized relative to a weak green observer model, and is characterized by a local minimum in a 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 in conjunction with the correspondence tables of FIGS. 39A to 39E and FIGS. 67A and 67B. This embodiment provides a filter for red-green discrimination enhancement to a weak red observer. Compared to previous examples of red-green enhancement filters, these filters, when designed for weak red viewers, generally prefer a shorter wavelength configuration of one of the second pass band and the third pass band. This is based on the orientation of the third type of color blindness obfuscation line, and the fact that the weak red color is associated with one of the blue shifts of the spectral absorption of the retinal photopigment in long-wavelength cones. Due to the shorter wavelength configuration of the second and third pass bands, the total spectral width of these filters must be relatively reduced so that the red color appears moderately bright. Figure 39C is shown in graph 3907 and line 67B The filter manufacturing targets listed in the table have: a first passband at about 440 nm, which has a half-peak width of about 20 nm; a second passband at about 530 nm, which Has a half-peak width of about 25 nanometers; and a third passband, which is located at about 615 nanometers and has a half-peak width of about 25 nanometers. The manufacturing specifications of the filter incorporating a neutral density absorber of about 55% transmittance are given. For incident angles up to about 20 degrees, the PGAI provided by the filter is greater than zero, as shown in Figure 39D. The white point stability of these filters may be additionally considered in the design, however, analysis of the white point stability according to a standard observer model may be inherently unsuitable for the intended use of the filter (e.g. for a weak red Observer use). In another embodiment, together with the corresponding tables of FIGS. 40A to 40E and 68A and 68B, it is disclosed that a normal observer is provided with color enhancement and an improved electronic visual display (such as a liquid crystal display with a light-emitting diode backlight). It is a filter for the light contrast of the primary color light. This filter is intended for use with electronic displays that typically use the following three primary colors: a red primary color having a peak wavelength between about 610 nm and about 630 nm and having about 20 nm to about 50 nm A half-height full width of one meter; a green primary color having a peak wavelength of about 530 nanometers to about 535 nanometers and a half-height full width of about 20 nanometers to about 50 nanometers; and a blue primary color having about 450 nanometers A peak wavelength between about 460 nm and a full width at half maximum of about 20 nm. The filter provides a light transmittance of one of the primary colors of light that is approximately equal to the primary colors of red, green, and blue (hence the white point of the display). In addition, the light transmittance is at least about 15% greater than the light transmittance of daylight provided by the filter. Therefore, the filter can provide an improved contrast ratio for such displays when viewed under outdoor conditions, for example. The line shown in graph 4007 of FIG. 40C and the line of FIG. 68B The filter manufacturing targets listed in this table are characterized by four passbands that provide a stabilized white point at an incident angle of up to 45 degrees. The filter achieves color stability of the white point that provides a white point displacement of 0.01 units less than about 0 degrees to about 45 degrees, as demonstrated by curve 4012 in FIG. 40E. In addition, the filter provides one modest enhancement in color discrimination, as mentioned in Table 68A, with a weighted percentage of importance relative to the color gamut area of Farnsworth D-15 greater than about 20%. It is also possible to design a filter that performs in a similar manner with three pass bands, where the range of the stabilization angle extends to about 35 degrees. A change in one of the three-pass band filter and another change in the four-pass band filter are shown at 2105 and 2106 in FIG. 21B, each of which achieves this optical contrast gain. The filter 2105 has three passbands, of which one of the first passbands has a half-peak width of about 15nm and one of the second passbands has about one-half of 20nm at about 535nm. The peak width, and one of the third pass bands at about 620 nm has a half-peak width of about 25 nm. The filter 2106 in FIG. 21B has four pass bands, of which one of the first pass bands at about 455 nm has a half-peak width of about 15 nm and one of the second pass bands at about 540 nm has about 20 A half-peak width of one nanometer, a third passband at about 610 nanometers has a half-peak width of about 20 nanometers, and a fourth passband at about 650 nanometers has a full-width half-height of about 20 nanometers. Compared to the simple three-band filter 2105, the filter 2106 provides improved color stability with respect to changes in the angle of incidence. Figure 21A shows the spectral radiant flux 2103 of daylight and the spectral radiant flux 2101 of blue primary color light, the spectral radiant flux 2102 of green primary color light, and the spectral radiant flux 2104 of red primary color light, 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 the light contrast gain of these displays. In another embodiment, a multi-band filter for a normal observer is designed to provide substantially normal color discrimination and a blocking band between about 530 nm and about 560 nm. This blocking band protects the eyes from laser radiation at 532 nanometers, such as emitted by a doubled Nd: YAG laser. These lasers have many applications, including their use in various medical procedures. Conventionally designed filters that block visible laser emission, for example at about 532 nanometers, often also result in poor quality color discrimination when used in glasses. For example, filters made of absorbing materials cannot achieve sufficient blocking and do not absorb a wide spectral band. Interference filters (such as Rugate filters) that include a single stopband can provide sufficient protection for the eye, but cause a significant change in color appearance and exhibit a significant shift of the white point from the normal incident angle. In contrast, a multi-band interference filter can provide sufficient protection against a visible laser, and a multi-band interference filter designed using the method of filter generation as previously disclosed can also maintain a normal Color appearance, maintaining color stability at multiple angles, and protecting eyes from visible lasers in a wide angle range. An example of a 532 nm blocking filter is disclosed in the correspondence tables of FIGS. 41A to 41E and FIGS. 69A and 69B. The line shown in graph 4107 of FIG. 41C and the line of FIG. 69B The filter manufacturing targets listed in the table are characterized by four passbands separated by three stopbands, of which the middle stopband is the laser blocking band. The first passband is located at about 440nm and has a half-peak width of about 30nm, the second passband is at about 510nm and has a half-peak width of about 30nm, and the third passband is at about 570nm Meters and has a half-peak width of about 20 nanometers, and the fourth pass band is located at about 630 nanometers and has a half-peak width of about 30 nanometers. In general, similar filters with frequency bands and various frequency band widths can be found within +/- 10 nanometers of a given location, but all of these filters are characterized by at least four passbands. For industrial or medical applications, the barrier passband (between about 530 nm and about 560 nm) can provide a protection level rated at OD6 or higher (OD6 indicates an optical density of 6, which causes attenuation of transmitted light 10 ^-6 Times). For interference level protection (e.g., against a green laser indicator with a 532 nm output), the protection level can be smaller, such as 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. In addition, as shown in FIG. 41E, these four passband filters can provide good stability of white points of less than 0.01 units with an incident angle of up to 35 degrees. As shown in Figure 41D, these filters can also provide a color appearance that is inherently normal over a wide range of angles, as evidenced by the fact that for incident angles up to about 25 degrees, PGAI is almost zero. These filters can be incorporated into safety glasses used in industrial or medical applications. In particular, in some applications of lasers in medical procedures, it can be beneficial for users to accurately perceive the color of biological tissue during surgery and the correct chromaticity appearance of certain colored light, so that the operator can correctly Interpret the lights on your computer display and / or device. It should be useful to note that these filters are not compatible with illumination sources with narrow-band spectral output, such as some fluorescent lamps or RGB light-emitting diode arrays. Corresponding tables of FIGS. 42A to 42E and FIGS. 70A and 70B disclose another embodiment related to the embodiment shown in FIGS. 41A to 41E. The line shown in graph 4207 of FIG. 42C and the line of FIG. 70B The filter manufacturing targets listed in the table are characterized by four passbands separated by three stopbands, of which the long-wavelength stopband is one of the blocking bands that provides protection against a 589nm sodium emission line. Eye protection from this wavelength may have industrial applications in certain procedures, such as glass manufacturing or working with lasers with output power at or near the short wavelength side of the blocking band. The filter design specifications incorporate this blocking band as a spectral transmittance constraint, as shown by the maximum transmittance constraint 2301 in FIG. 23A. This embodiment can provide similar quality color appearance and white point stability, as demonstrated by the previous related embodiments. The variations of this embodiment may include only three passbands, however, these variations tend to provide a substantial reduction relative to one of the PGAI metrics and are therefore somewhat unsuitable for use in applications where normal color discrimination is desired. The correspondence tables of FIGS. 45A to 45E and FIGS. 71A and 71B disclose another embodiment related to the embodiment shown in FIGS. 35A to 35E. 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 dark luminaire conditions, and especially at night, where sodium vapor lamp lighting is expected (such as is common in street lamps). Filter design guidelines are incorporated to ensure that 589 nm light is constrained by one of the minimum transmittances transmitted by the filter, as shown at 4501 in Figure 45A. Then, for example, the filter and a photochromic element can be manufactured, so that the filter incorporated in the glasses can be used in a range of an illumination level. This embodiment provides a substantially normal color appearance, as shown in FIG. 45D, where PGAI is not significantly different from zero within an incident angle of up to 45 degrees. In addition, as shown in the graph of FIG. 43A, the filter meets the spectral minimum transmittance constraint and the spectral maximum transmittance constraint shown at the solid curve 4302 and the dotted curve 4301, respectively. The maximum spectral transmittance constraint stipulates that the designed filter does not transmit light with a wavelength below 450 nm. The minimum spectral transmittance constraint stipulates that: the designed filter passes at least 15% of the transmission between 450 nm and 650 nm through all the stop bands; in addition, the designed filter passes The largest possible portion of light with a wavelength between 610 nm passes through. The designed filter shown at the solid line curve 4303 of FIG. 43B (which is the same as the solid line curve shown in FIGS. 45A to 45D) complies with the spectral transmittance constraint of FIG. 43A, and the smoothness shown at the dotted curve 4304. The filter fully meets the constraints of the intended application; specifically, the filter provides a high-luminance artificial light based on sodium vapor excitation that gathers energy at about 589 nanometers, such as low-pressure sodium lamps and high-pressure sodium lamps commonly used in street lamps. . Short-wavelength blue light (for example, having a near-ultraviolet wavelength between about 380 nanometers and about 450 nanometers) is associated with a series of visual phenomena commonly referred to as glare, and its contributing factor may include fluorescence (specifically, , The fluorescence of organic materials in the eye that partially responds to UV light and near-UV light), scattered scattering of light passing through the eye medium (specifically, this is because the retinal physiology is degraded due to age-related effects) and Eyepiece chromatic aberration (specifically, short-wavelength light cannot be accurately focused on the retina). Therefore, one of the filters that selectively suppress the transmission of the short-wavelength blue light may have the effect of reducing glare and improving visual sensitivity. A standard blue light blocking filter (also known as a cut-off filter) can be generated by incorporating a short-wavelength absorber into a lens, as shown by the transmittance curve at the dashed curve 1904 in FIG. 19B . However, the multi-band blue light blocking filter can provide improved color discrimination (e.g., by the solid line curve 1902 (providing about 35% light transmittance), the dotted line curve 1903 (providing about 60% light transmittance) in FIG. 19B) (Transmittance curve shown) and the filter design shown in Figures 45A and 43B. The color discrimination provided by such filters is shown in further detail in FIGS. 44A to 44C. The spectral transmittance of a conventional blue light blocking filter is shown at 4405 in FIG. 44C, and the spectral transmittance of a blue light blocking multi-band filter is shown at 4404 in FIG. 44C. The chromaticity diagram of FIG. 44A shows the color appearance of selected Munsell colors provided by the filters, including the color appearance provided by the cut-off filter at 4401 and the solid appearance provided by the cut-off filter at 4402. The color appearance provided by this multi-band filter. The color appearance provided by the cut-off filter is essentially dichroic along the red-green axis, that is, the contours are collapsed so that the apparently different blue-yellow axis has a length of zero. In contrast, the color appearance provided by the multi-band filter is trichromatic (without collapse). An exemplary configuration of a lens incorporating an attenuation coating and an absorbing optical substrate is depicted in FIGS. 46A and 46B, where the layers (from front to back) are antireflection coatings 4601, absorbing optical substrates (e.g. Neodymium glass) 4602, multilayer interference coating 4604 and attenuation coating 4605. In FIG. 46B, light incident to the outside of the lens is shown along arrow 4611. The incident light passes through the anti-reflection coating and the absorbing optical substrate, and is then divided by an interference filter into a transmission component that is finally received by the eye 4607 and absorbed by the retina 4609 and travels in the opposite direction toward the light source but passes through the first A reflection component 4612 is further absorbed during an attenuation coating. Still referring to FIG. 46B, a similar procedure for reflection-absorption can occur with 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 dielectric layers of the attenuating coating and the interference coating are staggered or partially staggered. It is known that neodymium-containing glass lenses provide a slightly enhanced color discrimination. For example, the solid line curve 4705 in FIG. 47C shows the spectral transmittance of a 1.5 mm thick ACE modified lens (manufactured by Barberini GmbH). The color discrimination properties of the filter can be analyzed by comparison with Munsell 7.5B 8/4, a best-fit reference filter given by the spectral transmittance curve 4704 in FIG. 47C. 47A shows the appearance of the selected Munsell color provided by the ACE modified lens along the solid line outline 4702 in the chromaticity diagram, and shows the appearance of the selected Munsell color of the reference filter along the dotted outline 4701. The neodymium-containing filter produces an increase in one of the color gamut areas enclosed by these contours. However, the increase was mainly clustered around red samples that were not balanced by one of the apparent purity of the green samples. More preferably, a lens including neodymium can be used as an optical substrate for depositing an interference filter and / or an attenuation coating, such as described in FIGS. 46A and 46B. Then, the obtained composite filter can provide a passband and a stopband by configuring an interference filter and a narrow band absorption filter to be operated. These composite filters can be designed using a linearly stylized method 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 used by PGAI or PGAI _IW Measurements provide better average performance and are generally less sensitive to changes in incident angle. Several embodiments of a filter design incorporating a neodymium-containing absorption element are disclosed below in conjunction with a detailed description of FIGS. 48A-53E and additionally in FIGS. 57A-57E. All of these embodiments represent variations based on the previously disclosed embodiments, and therefore do not require extensive additional detailed discussion. A general observation related to these changes is that a multiband filter containing neodymium can provide a slightly improved angular width in one of the fields of view in which color enhancement is provided. For example, for one embodiment that includes only absorption filters of the neutral density type (where PGAI is greater than zero at up to about 25 degrees), the variation based on such a filter additionally including neodymium can be up to about 30 degrees Provides a PGAI greater than zero. However, these changes tend to cause compromises in other areas, for example, in some changes, the ophthalmic lens incorporating this filter may have a greater light reflectivity on the side of the lens facing the eye. The corresponding tables of FIGS. 48A to 48E and 72A and 72B disclose a first embodiment of a filter incorporating a neodymium absorbing element, which is a change based on the design shown in FIGS. 33A to 33E. . This filter provides enhanced observers with red-green discrimination. This variation provides a wider field of view up to about 5 degrees to which color enhancement is effective. However, the importance weighted percentage of the increase in color gamut area is substantially the same between this change and its related embodiments. A further embodiment of a filter incorporating a neodymium absorbing element is disclosed in the correspondence tables of FIGS. 49A to 49E and FIGS. 73A and 73B, which is a modification based on the design shown in FIGS. 34A to 34E. This filter provides enhanced blue-yellow discrimination to normal observers. This variation provides a wider field of view up to about 5 degrees to which color enhancement is effective. However, the importance weighted percentage of the increase in color gamut area is substantially the same between this change and its related embodiments. A further embodiment of a filter incorporating a neodymium absorbing element is disclosed in the correspondence tables of FIGS. 50A to 50E and FIGS. 74A and 74B, which is a modification based on the design shown in FIGS. 36A to 36E. This filter provides enhanced red-green discrimination for observers with mild green weakness. This variation provides a wider field of view up to about 5 degrees to which color enhancement is effective. However, the importance weighted percentage of the increase in color gamut area is substantially the same between this change and its related embodiments. A further embodiment of a filter incorporating a neodymium absorbing element is disclosed in the correspondence tables of FIGS. 51A to 51E and FIGS. 75A and 75B, which is a modification based on the design shown in FIGS. 37A to 37E. This filter provides enhanced red-green discrimination for observers with moderate green weakness. This variation provides a wider field of view up to about 5 degrees to which color enhancement is effective. However, the importance weighted percentage of the increase in color gamut area is substantially the same between this change and its related embodiments. A further embodiment of a filter incorporating a neodymium absorbing element is disclosed in the correspondence tables of FIGS. 52A to 52E and FIGS. 76A and 76B, which is a modification based on the design shown in FIGS. 38A to 38E. This filter provides enhanced red-green discrimination for observers with severe green weakness. This variation provides a wider field of view up to about 5 degrees to which color enhancement is effective. However, the importance weighted percentage of the increase in color gamut area is substantially the same between this change and its related embodiments. A further embodiment of a filter incorporating a neodymium absorbing element is disclosed in the correspondence tables of FIGS. 53A to 53E and FIGS. 77A and 77B, which is a change based on the design shown in FIGS. 39A to 39E. This filter provides enhanced red-green discrimination for viewers with weak red. This change provides a substantially improved color discrimination function, which is attributed to the optimal positioning of the main absorption band that provides favorable conditions relative to displacement stability constraints, whereby the long wavelength passband can effectively redshift up to about 10 Nanometers thus widen the spectral aperture without compromising other design criteria. One of the further applications of multi-band filters is to consider their effectiveness in increasing the blue and cyan light absorbed by the eyes. In particular, the reception of light between about 450 nanometers and about 490 nanometers can stimulate retinal ganglion cells. These cells do not involve color vision, but rather the suppression of melatonin and the synchronization of circadian rhythm and daylight phase. This light reception may have therapeutic effects, for example, in the treatment of seasonal affective disorders, sleep disorders, and other health problems. The estimated spectral absorption of one of the retinal ganglion cells is shown at 5401 in Figure 54A, where the absorption profile is obtained by shifting a retinal photochrome template to a peak wavelength of about 480 nm. To better understand the effect of filters on high-energy stimulation of 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--a modest range of light transmission for a filter (e.g., between about 20% to about 100) %), The enlargement or reduction of the pupil ensures that the amount of light reaching the retina (ie, the number of photons per second) is approximately constant (for example, the area ratio between an enlarged pupil and a reduced pupil is about 5: 1). For example, as shown at 5403, a broadband blue filter has an average transmittance between about 460 nm and about 490 nm, which is greater than the light transmittance of the filter. The luminosity of light (ie, daylight) affects pupil dilation, and the light sensitivity is greatest at about 555 nanometers, and the retinal ganglion cell absorption rate is greatest between about 460 nanometers and about 490 nanometers. A filter with a transmittance at about 555 nanometers and substantially more light transmitting at about 480 nanometers can cause pupil dilation and increase the number of photons absorbed by ganglion cells. However, wideband filters, such as the blue example shown in the figure, do not provide a substantial gain. These blue filters can improve ganglion cell stimulation by about 30%. However, this increase can be substantially enhanced by a multi-band filter, such as shown at 5402. This filter can improve ganglion cell stimulation by up to about 80%. A first embodiment for improving ganglion cell stimulation is shown in the correspondence tables of FIGS. 55A to 55E and FIGS. 78A and 78B. This embodiment provides an increase of about 80% of ganglion cell stimulation, that is, the ratio of the average transmittance between 460 nm to 490 nm and the light transmittance of the filter is about 1. 8. However, this embodiment is not characterized by a stable white point. As shown by the graph 5512 of FIG. 55E, the appearance of the white point quickly shifts toward blue as the incident angle increases. A further embodiment for improving ganglion cell stimulation is disclosed in the correspondence tables of FIGS. 56A to 56E and FIGS. 79A and 79B. This example provides about a 50% increase in ganglion cell stimulation. This embodiment is also characterized by a stable white point, as shown by the graph 5612 of FIG. 56E. For incident angles up to about 30 degrees, the white point displacement is less than about 0. 01 units. In addition, as shown in FIG. 56D, for incident angles up to about 30 degrees, PGAI is essentially zero, thereby demonstrating that the filter provides a substantially normal color appearance. However, the filter design with four passbands is relatively complicated and the improvement of ganglion cell stimulation is not significant. A further embodiment for improving ganglion cell stimulation is disclosed in the correspondence tables of FIGS. 57A to 57E and FIGS. 80A and 80B. This embodiment provides an increase in ganglion cell stimulation of about 65% and a stable white spot. The design of the filter incorporating a neodymium absorbing element promotes improved performance under these conditions. As shown by the graph 5712 of FIG. 57E, for incident angles up to about 30 degrees, the white point displacement is less than about 0. 01 units. In addition, as shown in FIG. 57D, for incident angles up to about 30 degrees, PGAI is essentially zero, thereby demonstrating that the filter provides a substantially normal color appearance. In a further embodiment, a filter may be designed to be incorporated into a lamp assembly, wherein the filter manufactured as, for example, a multilayer dielectric coating provides a beam splitting function by which Function, the transmission component and reflection component of the light emitted by a light source in the lamp are configured to have the same white point. Matching the reflective white point with the transmitted white point allows two beam components to be used for illumination, so no energy is wasted by filtering. In addition, 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 one of the enhanced qualities of light (see additional discussion below with respect to FIG. 27B). An opposite effect on the appearance of the color can be observed in reflected light, where it can be reduced in an opposite effect as compared to an increase in the relative color gamut area as presented by the transillumination body as presented by the reflected illumination body The relative color gamut area, that is, the average color gamut area of the recombined beam is consistent. A lamp assembly containing such a filter preferably includes a wide-band illuminator. In one embodiment, a light emitting diode may be used for illumination. If a white LED including an LED-driven phosphor cannot provide sufficient wideband emission alone for good color appearance, it is usually possible to combine a white LED with a red LED, for example, at a ratio of about 4: 1 to produce a color temperature and spectrum that is approximately the same as sunlight A wide band lighting body. 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 are shown in FIG. 25A. These luminaires 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 including an LED to stimulate daylight may include a white LED, a red LED, and a blue (or cyan) LED having a ratio of, for example, about 4: 1: 2 to produce a light having a temperature of about 5000 K to about 7000. A wide band illuminator with a color temperature between K and a CRI between about 90 and about 100. One of the filters with a spectral transmittance of 2504 (as shown in Figure 25B) can perform the spectral splitting described. These filters are also called dichroic filters or dichroic reflectors. The design criteria of this filter may, for example, include: a cost vector configured to maximize the relative color gamut area; an LED mixture as described above as an illuminant; and a reference filter, which is The neutral filter makes the white point of the illuminating body under the filter the same as the white point of the illuminating body and the reflection filter under the neutral filter. In addition, the white point constraint may better specify a white point at a deviation from the normal incident angle up to about 20 degrees. This adaptation is potentially difficult when perfectly collimating incident light. A 20-degree beam width can be achieved with a small footprint collimating lens. In addition, a filter with a minimum spectral transmittance of about 10% across the visible wavelength may preferably be specified, which may be used to adjust the increase in color gamut area to reduce the color appearance when the split beams are spatially recombined. The uneven appearance in the mixed regions of these split beams. The spectral transmittance 2605 of the illuminant beam splitter filter and the spectral transmittance 2606 of its inverse (reflection) are shown again in FIG. 26C. The spectral radiant flux 2604 of the mixture of LED luminaires is again shown in FIG. 26B. The chromaticity coordinates of the white points of the filter and the inverse filter are shown at point 2603 of the chromaticity diagram of FIG. 26A. 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 color gamut area can be easily seen in these contours, whereby the illuminator transmitted through the filter increases the color gamut area and the illuminator reflected through the filter responds to decrease the gamut area. small. One possible arrangement of components for forming a lamp assembly including such a beam splitter is shown in FIGS. 27A and 27B. Here, the assembly can be configured as a stack, which 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 multilayer interference coating (which can be deposited Onto the surface of an optically transparent substrate, such as glass). Referring now specifically to FIG. 27B, in an exemplary configuration, a beam of light emitted by LED 2702 is collimated up to a beam width of about 20 degrees by optics (such as a light guide) 2703, and then incident on an interference filter 2704 on. Thereafter, the transmitted component of light appears in the central portion of the output beam 2708, and the reflective portion is redirected by the light guide (e.g., by internal reflection along the boundary indicated by 2709), and then emitted along the annular portion of the output beam 2707 . As shown in the figure, this configuration enables the lamp assembly to incorporate a color enhancement filter without compromising luminous efficiency, because the light that is not transmitted by the filter is radiated back to an environment that can still be used for general lighting. While an absorption filter will reduce the efficiency of the lamp, the interference filter has an almost uniform efficiency. These illuminants can be advantageously employed indoors to provide improved color discrimination for weak green observers and weak red observers. In these configurations, the illuminator can also be used with a filter (as previously disclosed) incorporated into the glasses. For the spectral transmittance of any filter disclosed above in this specification as a function of wavelength, one method for calculating the center position and width of the passband and stopband includes: applying a Gaussian smooth core application To the spectral transmittance curve (e.g., by the convolution of the core and the transmission data sequence), where the width of the core is wide enough to essentially eliminate any useless changes to the curve (for example, such as not being valued by the filter of interest Transient, ripple, noise, or other artifacts); then normalize the curve so that the maximum transmission is equal to 100%; and then round each transmission value to 0% or 100% so that each adjacent spectral region ( The rounded value of 0% corresponds to the band boundary of a stopband, and each adjacent spectral region (where the rounded value is 100%) corresponds to the band boundary of a passband. As for the band boundary calculated according to this method, the average transmittance in each pass band and each stop band can be calculated relative to the original curve. The width of a passband or stopband is equal to the distance between the lower band boundary and the upper band boundary, and the center of a passband or stopband is equal to the midpoint between the lower band boundary and the upper band boundary. Preferably, for any such calculated set of passband boundaries and stopband boundaries, for each interleaved stopband, the average transmittance of the stopband is at most half of the average transmittance of an adjacent passband. If this condition is not applicable, the change between the passband and the stopband may be essentially useless. In this case, the width of the smoothing core may be increased and calculations may be repeatedly performed until a suitable smoothing width is determined. For most filters of interest in the present invention, a smooth core with a half-peak width of about 20 nanometers is suitable for the purpose of this calculation. For most of the filters described in the present invention, the specified values related to the band boundary position, band center position, and band width can be given in units of wavelengths rounded to the nearest 5 nm. The teachings herein are sufficient to specify filters with greater spectral resolution. However, a larger spectral resolution is not necessarily required to practice the invention. The above section of this specification discloses a method for generating a multi-band optical filter that affects color perception in a desired manner, including: a method of designing a filter specification that meets one of the constraints associated with the intended use of the filter; Method for evaluating the performance of filter specifications and adjusting the design to further improve the performance of the filter specifications relative to the desired effect to achieve the specifications of one of the preferred embodiments of such a filter; fabricating filters and / or providing A method suitable for a machine specification having a filter manufactured by another method; and incorporating the filter into an ophthalmic lens or a lamp assembly to produce one of a device that provides a desired effect on color perception Method of the preferred embodiment. The scope of the effect on color perception achieved by the present invention includes: maintaining normal color discrimination (which is also referred to as providing "good color discrimination" in the present invention); enhanced color discrimination (also sometimes referred to as """Enhanced" or "improved" color discrimination), can unconditionally assume that the improvement of color discrimination between red and green is equivalent to the improvement of color discrimination between blue and yellow; enhanced red and green discrimination, where the desired effect brings red and green between Maximize discrimination improvement; and enhance blue-yellow discrimination, where the desired effect maximizes discrimination improvement between blue and yellow. It is generally expected that filters that also provide additional functions, 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 cause a filter to provide poor quality color discrimination. For example, conventional notch filters or cut-off filters that act as one of the interference filters can cause significant changes in the chromaticity appearance of certain colors, and / or can be incorporated into the glasses when the filter is incorporated One way to cause the appearance of some colors to change relative to a variable viewing angle is to make the viewer uncomfortable. In a further example, the average absorption that affects the spectral transmittance can cause the filter to have a low light transmittance and / or a strong color rendering white point, because the aggregation of the absorbing material required to achieve the spectral transmittance limitation can be Significantly affects transmittance in a wide area of the visible spectrum. The methods disclosed herein enable the design, specification, and manufacture of filters that maintain normal color discrimination over a wide range of viewing angles and provide useful limits with respect to spectral transmittance. Specific variations of these filters and products incorporating these filters disclosed herein include: filters that block blue light between about 380 nanometers and about 450 nanometers; blocks about 380 nanometers to about Filters for blue light between 450 nm and at the same time ensuring high spectral transmittance of light at a wide viewing angle range of about 589 nm; filters that block green light at a wide viewing angle range of about 532 nm An optical filter; and a filter that provides a high average transmittance of light between about 460 nm and about 490 nm with respect to the light transmittance of the light. The filters in the group of this embodiment all include three pass bands interleaved with two stop bands. 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 limit. Based on further changes in the methods disclosed herein, the design, specifications, and manufacture of filters that enhance color discrimination over a wide range of viewing angles are realized. These filters include: filters that enhance red-green discrimination; blue-yellow Identify enhanced filters; or both. These filters can be configured to enhance color discrimination for observers with normal color vision, or can be configured to target color vision defects (which include green weak color vision defects, red weak color vision defects, and third Observation of color weakness and color vision defects) enhances the color discrimination of the observer. The configuration of a filter that is intended for use by a particular observer may provide a preferred embodiment of a filter that affects color perception 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 weak green observers and weak red observers. These color vision-deficient people are characterized by a sensitivity to changes between red and green, which is lower than that of normal observers. Filters that enhance red-green discrimination can also be used in other applications that include: general-purpose glasses (such as sunglasses) for normal observers; and activity-specific glasses such as those used in certain sports including golf . Filters that enhance blue-yellow discrimination can be used for Type III color-weak observers, and also have other applications that include enhancing light contrast, stimulating red-green perception defects, and detecting camouflaged objects. A balanced-enhancement filter that provides one of the color discrimination between red and green and between blue and yellow can be better used by observers with normal color vision, where these filters are incorporated into glasses Provides general improvements in visual quality. The filters in these embodiment groups all include three pass bands interleaved with two stop bands. However, some of these filters may include four passbands interleaved with three stopbands. Generally, the fourth passband has a center at a location greater than about 660 nanometers and is configured such that the filter maintains a substantially constant white point at an extreme angle of incidence. Filters configured to enhance color discrimination can be classified according to the center position of the second passband. For a center position between about 520 nanometers and about 540 nanometers, the filter mainly focuses on providing a discrimination improvement between red and green. For a center position between about 545 nanometers and about 550 nanometers, the filter provides a discrimination improvement that is approximately the same between red and green and between blue and yellow. For a center position between about 555 nanometers and about 580 nanometers, the filter focuses on providing an improvement in discrimination between one of blue and yellow. For one of the filters configured to enhance the blue-yellow discrimination, the preferred center position of the second passband is about 580 nanometers, which corresponds to a monochromatic wavelength that is considered only yellow by most observers. However, it may be impractical to have a filter at the center of a second passband at 580 nanometers because it can cause the appearance of color to be dichroic and correspondingly lose all between red and green. Identify. Therefore, it is useful to constrain these filters, for example, by ensuring that the chromaticity coordinates of a green traffic signal are within a defined boundary giving one of its acceptable limits. Thus, an optimal filter with a second passband position less than or equal to about 560 nanometers can be found, which maximizes the discrimination between blue and yellow without compromising the color discrimination between red and green. . For one of the filters configured to enhance the discrimination between red and green, the optimal center position of the second passband varies according to the color group of interest. Compared to Munsell color samples and / or Farnsworth D-15 colors, the best choice for the center position is about 530 nm. However, the better location is about 540 nm compared to the natural sample. Therefore, the choice of 535 nanometers can give the best average selection of such a filter for use in a mixed environment. In contrast to one of the filters configured to enhance a green weak observer to red-green discrimination, the preferred embodiment may depend on a sub-category of this type of observer. For a mildly green weak observer, one modest contrast ratio between the passband average transmission and the stopband average transmission may be suitable, for example, about 4: 1. For a moderately weak green observer, a ratio of at least about 6: 1 may be preferred. For a severely green weak observer, a ratio of at least one of 8: 1 may be better. For filters with a pass-band to stop-band contrast ratio greater than about 6: 1, the filter specifications may be better limited to provide between about 580 nm to about 620 nm and / or about 560 nm to Minimum spectral transmittance of at least about one fifth of the light transmittance between about 580 nanometers. This can ensure that the filter is suitable for general use, such as operating one of the suitable visibility motors in which certain narrow-band yellow lights (including light-emitting diodes and low-pressure sodium lamps) are required. In these changes, the filters may be better restricted to constrain the chromaticity coordinates of a yellow traffic signal in a specific area, so that these lights cannot be mistaken for orange or red, for example. Compared to a filter configured to make a red weak observer enhance red-green discrimination, a change based on one of the above ranges is applicable to the center position of the second passband. Due to the retinal physiology associated with the abnormality, the preferred wavelengths are all blue-shifted to about 5 nanometers, for example, the choice of 535 nanometers is modified to about 530 nanometers. In addition, it should be noted that the center position of the third passband is preferably at most between about 610 nanometers and about 625 nanometers relative to the configuration of the filter for the weak red viewer. The use of long wavelengths can result in reduced red visibility for these observers. The filters in the family of embodiments described above for enhanced color discrimination all include three passbands interleaved with two stopbands. With regard to the configuration of filters for color vision, these filters generally provide a light transmittance (e.g., at least about 8%) within a moderate range, and also preferably provide a non-powerful display. A white point (ie, the chromaticity coordinate of the average daylight as viewed through a filter). A constrained white point area can be better selected to provide a neutral tone in nature, because a filter with a white point that is moderately or strongly colored cannot provide suitable brightness for some colors. In addition, a restriction may preferably be imposed such that the white point remains within a relatively small area within a range of viewing angles because these filters provide the most comfortable viewing experience when incorporated into glasses and are Tolerance for misalignment and beam divergence when entering into the lamp assembly. The CIELUV (u ', v') chromaticity coordinates can be preferably used for these calculations because, based on this scale, for the range of white points of interest, the ellipse that defines the smallest perceptible difference between colors Approximately round. (U ', v') coordinates can be calculated relative to CIE 1931 2 degree standard observer or CIE 1964 10 degree standard observer, where the former gives a better prediction of the apparent color of an object at a distance, and the latter gives A better prediction of the apparent color of an object in a larger part of the field of view. Relative to a filter configured for use by observers with normal color vision, the white point constrained region may have about 0 on the (u ', v') chromaticity diagram. One radius of 02 units. More preferably, the region may have about 0. A radius of one unit of 01, and also better, the range of incident angles that make the white point of the filter conform to the limit can be expanded from 0 degrees to at least about 25 degrees, and more preferably, from 0 degrees to at least about 35 degrees . Compared to filters that are configured for use by observers with color vision defects, the constrained region may be better defined as an elliptical region, for example, where the major axis of the ellipse corresponds to the type of color vision defect Confusion lines are oriented. Therefore, when analyzing the properties of these filters based on a circular constrained area, the properties of these filters are characterized by a white point that leaves the constrained area within a certain range of the intermediate angle and then starts with a The steeper angle enters the constrained area again, where the steeper angle is usually between about 20 degrees and about 40 degrees. In some embodiments, this may provide a filter that appears to provide one of the white dots with good stability when the white dot is viewed by the intended observer, but an observer with normal color vision cannot perceive the same degree of stability. Relative to mild green weak observers and moderate green weak observers, the white point constrained area may be better limited to about 0. One radius of 01 units. Relative to severe green weak observers, has about 0. An unconstrained area with a radius of one of 02 units may be preferred. Relative to the red weak observer, the angular range within which the constraint is considered can be reduced to, for example, between about 0 degrees and about 20 degrees. One of the first methods for designing a filter that enhances color discrimination includes: selecting a desired center position of the second passband according to a desired effect as described above; selecting a desired light transmittance suitable for the filter The minimum required width of one of the second passbands (note that this preference also implies that the average transmittance of the second passband is as high as possible); and then the appropriate selection of the first and third passbands is appropriate 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, where the center position and width are restricted by restrictions related to the white point of the filter. Where possible, the limitation includes the desired chromaticity coordinates of the white point at normal incidence; and the area within which it will contain the chromaticity coordinates of the white point relative to a range of viewing conditions away from one of the normal incidence angles. Next, the average transmittance in the three pass bands is preferably selected as the maximum possible value (if the filter is designated to incorporate, for example, an absorption filter, the value may be less than 100%), and may be better Ground selects the average transmittance of the staggered stopbands within a range of values, which corresponds to the ratio of the average transmittance between the passband and the stopband between about 2: 1 to about 10: 1 or greater. Higher contrast ratios produce stronger color discrimination enhancements. These high ratios can also be associated with the rare and / or unstable color appearance of certain lamps, such as narrow-band lamps. The above descriptions related to better choices of passband locations and passband to stopband contrast ratios and methods of designing the filters disclosed herein provide appropriate teachings for designing filters (which are members of the identified groups above). For example, to achieve this filter through an exhaustive search process, the center position and width of the second passband, and the passband can be determined, for example, based on the calling range associated with the effect on color vision as described above. Contrast of band and stopband, then enumerate all possible combinations of the center position and width of the first and third pass bands, and then use a computer to evaluate each filter in the enumerated group to select the better member. The preferred member satisfies the desired design constraints to maximize one of the performance measures relative to color discrimination. The enumerated group may include thousands of members, and the resulting calculations may require significant calculation time due to the number of frequency bands in consideration and the calculated spectral resolution. More preferably, the method disclosed in this paper can be used to design these filters by solving a linear program, thereby transforming the design constraints into a well-formed linear program, which will allow feasible filter design. The limitation is defined as a geometric abstraction best described as a generalized multidimensional convex polyhedron. By directing (which uses a cost vector as described in the teachings of the present invention), a linear equation solver can quickly locate the filter component on the boundary of the feasible set to maximize along the cost indicated by the cost vector. Given constraints of direction. As disclosed herein, a linearly stylized method can determine the test filter specifications almost instantaneously, so that the best method for practicing the present invention can interactively guide cost vectors and / or design constraints so that an operator can immediately evaluate a Performance trade-offs associated with specific test filters. The linear programming method also realizes the design of a composite filter including, for example, an interference filter and a narrow-band absorption filter (such as an optical substrate containing neodymium), wherein the linear programming solver determines the interference filter The transmittance specifications of the filter are used together with the absorption filter to produce the desired effect. A feasible filter set considered by the linear program solver may essentially include any spectral transmittance curve that is difficult or impossible to achieve by enumerating frequency bands or iterative local search procedures. Since the linear program solver is not strictly limited to designing a multi-band filter (which is a sequence passband that is interleaved with the stopband), it can be used to design when it is used with another specific filter A filter with a multi-band spectral transmittance that includes a constraint criterion that takes into account the properties of these composite filters within an incident angle range. For any test filter specification (such as produced by the method just described), the further method disclosed herein enables prediction of the effect of the test filter on color discrimination. For example, in one embodiment, a method involves: determining a best-fitting wideband reference filter; and 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, determine a best-adaptive wideband reference filter, then calculate the chromaticity coordinates of a set of reference colors as viewed through the test filter and the reference filter, and then The chromaticity coordinates are projected onto one axis of the color space, and the relative standard deviations of the coordinate groups along the axis are compared. Preferably, the axis may include one or more of a third type of color blind obfuscation line, a green blind obfuscation line, and a red blind obfuscation line, so that the calculated ratio corresponds to the enhancement, reduction or maintenance of color discrimination along the corresponding direction, where The third type of color-blind confused line generally corresponds to the discrimination between blue and yellow, and the green-blind confused line and red-blind confused line generally correspond to the discrimination between red and green. More preferably, these performance analysis calculations are performed with respect to a test filter viewed within a range of deviation from a normal incident angle, such as between about 0 degrees and at least about 25 degrees. The average performance in these angles can be used to estimate the overall performance of a product, such as when incorporated into an ophthalmic lens, making it necessary to consider filter performance over a wide range of viewing angles. Even better, this analysis can take into account 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, these performance evaluations relative to the reference color can be considered in terms of color expression conditions under which the product can be used with, for example, eyeglasses. The reference color should include two samples from nature and artificial colors, For filters configured to be incorporated into an interior light assembly, the reference colors may include only artificial colors. In terms of a preferred test filter specification, the filter can be manufactured, for example, as an interference filter by physical vapor deposition of a stacked dielectric material onto an optical substrate. The test filter specification can be limited by the minimum transmittance curve and the maximum transmittance curve to, for example, provide a processing tolerance specification suitable for enabling the filter to be manufactured by an operator familiar with such production methods. Some embodiments of the filters disclosed herein can be manufactured, for example, as high-order interference filters that include about 100 layers of dielectric material and have a total thickness of about 6 microns. Implementation with respect to some embodiments (specifically, where only a moderate 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) Example), the number of layers and thickness can be significantly reduced to, for example, require up to about 50 layers and / or have a total thickness of about 3 micrometers, where these limitations can be achieved by applying a smooth core to the filter specifications For example, this core preferably has a Gaussian shape and a half-peak of at least about 20 nanometers. The resulting simplified design can then benefit from shorter processing times, compatibility with lower accuracy programs, 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, these composite designs are feasible relative to a red-green enhancement filter with a constrained white point in a corner range, which can be longer than the feasible wavelength when considering the same confinement criteria and no neodymium absorption component The position of the third passband is selected at one wavelength. A longer wavelength center position is preferred, as previously described, which can lead to a composite filter design that further enhances color discrimination. In addition, these composite designs can provide improved stability of color, such as when analyzing performance in a corner range, for angles that are 5 degrees greater than the angle of an equivalent filter design that does not include neodymium, including neodymium A composite design can maintain a color gamut area ratio greater than 1: 1. However, it can be found that the improved angular stability is usually impaired by a slightly lower peak performance caused by one of the undesired secondary absorption bands present in the neodymium-containing filter, the second pass of the resulting filter The band is slightly wider than the best pass band. However, such composite designs, including neodymium, may be preferred as filters that are incorporated into the glasses (where overall visual comfort is a consideration). Alternatively or in addition, other narrow-band absorbers may be used as neodymium, which contains narrow-band organic dyes and other rare-earth elements, such as erbium or ', whereby some of these combinations of narrow-band absorbers can provide including an interference filter One of the composite filters is designed to exhibit improved angular stability and / or reduce light reflectivity. Such combinations can be designed, for example, using a linearly stylized approach as disclosed herein. When any of the disclosed filters are manufactured as interference filters, the high reflectivity of these filters must be considered. When incorporated into spectacles, the ratio of light transmittance to light reflectance on the inner surface of the lens is preferably at most about 2: 1. Compared to a filter in which the interference filter has a high transmittance (for example, more than 60%), the reflectance of the interference filter can be small enough to be ignored. Preferably, these filters can be combined with either a linear polarizer in the form of an absorption filter or a photochromic absorption filter. The absorption filters are combined with an interference filter. The light reflectivity will not be significantly reduced during installation. The management of the reflectance on the inner surface of the lens is a considerable problem compared to a filter in which the interference filter has a light transmittance of less than about 60%. A first method is to apply a neutral density absorber to the rear side of the lens to promote 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 transmittance of the lens, which in turn implies that one of the average transmission contrast ratios between the passband and the stopband is required to be reduced, which may, for example, reduce the effective color provided Identify improvements. In one embodiment, a circular polarizer may be applied to the inner surface and configured such that the linear polarizing element absorbs backside reflections. This construction can achieve a very high contrast ratio. Alternatively, a metal attenuating coating may be incorporated into the interference filter, wherein the interference filter includes, for example, titanium dioxide and silicon dioxide (TiO ₂ And SiO ₂ ), And the metal layer includes pure titanium. Due to the nature 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 the reflectance. In addition, due to the good material compatibility between metals and metal oxides, this configuration can provide a robust product that is also more economical to produce and provides the desired effect on color vision. A further concern related to the reflectivity of interference filters is the placement of the interference filters in the ophthalmic lens assembly, where if these filters are placed on the inner surface, they may exist within the substrate Visible artifacts caused by reflections; these are preferably mitigated by a high-quality anti-reflection coating on the opposite surface of the lens. Regarding the incorporation of a filter configured to enhance color discrimination into a lamp assembly (where the filter may also be referred to as a dichroic reflector), the preferred embodiment of the filter may be considered 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 illuminator may be a broadband source, for example, where the transmission component enhances the discrimination between red and green, and the reflection component enhances the discrimination between blue and yellow. More preferably, the illuminator can be a multi-band source (such as an array of red light emitting diodes, green light emitting diodes, and blue light emitting diodes), so that the transmitted component provides enhanced color discrimination and the reflected component remains normal. Color discrimination. There is a preferred configuration of the lamp assembly in which both the transmitted component and the reflected component of light are used for illumination. For example, a computer with a 2.3 GHz Intel Core i7 processor and 8 GB of RAM can be used to implement the disclosed software software Mathematica® (including its linear program solver) from Wolfram Research. Filter design method. However, those skilled in the art should understand that the methods disclosed herein are not limited to the above embodiments and have nothing to do with the computer / system architecture. Accordingly, these methods can be implemented equivalently on other computing platforms, using other computing software (commercially available software for filter design methods or specific coded computing software), and can also be hardwired into a circuit or other computing component . The invention is illustrative and not restrictive. Those skilled in the art will appreciate further modifications in light 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 that such modifications are in accordance with the invention disclosed herein. In addition, if feasible, several of the steps may be performed simultaneously in a parallel program, and several of the steps may be performed sequentially as described above. An action referred to herein as a method or procedure can also be understood as a "step" in the method or procedure. Therefore, in this regard, there are changes to the invention disclosed herein, which are within the spirit of the invention or equivalent to the invention disclosed herein, and the scope of the invention and its patent application is also intended to cover such changes. The entire disclosure of all publications and patent applications cited in the present invention are incorporated herein by reference as if each individual publication or patent application was specifically and individually filed herein.

101‧‧‧lighting body

102‧‧‧optical system

103‧‧‧light reflection

104‧‧‧Reference color

105‧‧‧light transmission

106‧‧‧ Optical Filter

107‧‧‧ light absorption

108‧‧‧ short-wavelength cone cells

109‧‧‧light absorption

110‧‧‧medium wavelength cone cells

111‧‧‧light absorption

112‧‧‧long wavelength cone cells

113‧‧‧ Observer

115‧‧‧Visual Light Transduction Operation

116‧‧‧Chroma

117‧‧‧ Luminosity

118‧‧‧Color appearance model

Graph of spectral absorption rate of photosensitive pigments in short-wavelength cones 201 · ‧‧

Graph of spectral absorption of photosensitive pigments in 202‧‧‧medium wavelength cone cells

203‧‧‧The graph of the spectral absorptivity of photosensitive pigments in long wavelength cone cells

204‧‧‧ Genotype

205‧‧‧Classification

206‧‧‧The wavelength of the maximum absorption rate of light-sensitive pigments in short-wave cone cells

207‧‧‧ the wavelength of the maximum absorption rate of light-sensitive pigments in cone cells

208‧‧‧The wavelength of maximum absorption rate of photosensitive pigment in long-wave cone cells

Neural stimulation of 301‧‧‧long-wave cone cells

302‧‧‧points

303‧‧‧Luminance Response Line

304‧‧‧plane

305‧‧‧ projection

Neural stimulation of 306‧‧‧medium wavelength cone cells

307‧‧‧axis / origin

309‧‧‧ contour / spectral trajectory

310‧‧‧ Neural Excitation of Short Wavelength Cones

401‧‧‧test filter

402‧‧‧lighting 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‧‧‧lighting body

503‧‧‧ Filter

505‧‧‧ Optical Interaction

506‧‧‧Visual Light Transduction

507‧‧‧ Observer

508‧‧‧Color appearance model

509‧‧‧ chromaticity coordinates

510‧‧‧Delaunay triangulation measurement algorithm

512‧‧‧ color gamut area

Spectral reflectance of 601‧‧‧Munsell 5B 5/4

602‧‧‧Spectral reflectance of Munsell 5G 5/4

Spectral reflectance of 603‧‧‧Munsell 5Y 5/4

Spectral reflectance of 604‧‧‧Munsell 5R 5/4

Spectral reflectance of 605‧‧‧Munsell 5P 5/4

606‧‧‧Spectral reflectance of blue flower

607‧‧‧Spectral reflectance of green leaf

608‧‧‧Spectral reflectance of Huanghua

609‧‧‧Spectral reflectance of safflower

610‧‧‧Spectral reflectance of purple flower

701‧‧‧ dotted outline

702‧‧‧ solid line outline

703‧‧‧solid outline

704‧‧‧ points

705‧‧‧ dotted outline

706‧‧‧ points

708‧‧‧line segment

709‧‧‧ Enclosed solid line

710‧‧‧Spectral Radiation Flux of Illuminant D65

711‧‧‧Spectral transmittance of reference filter

712‧‧‧White point of test filter

802‧‧‧ solid line outline

803‧‧‧solid outline

804‧‧‧White dot

807‧‧‧dot / dotted outline

808‧‧‧ dotted line

809‧‧‧Spectral Radiation Flux

810‧‧‧Spectral transmittance of reference filter

Spectral transmittance of 811‧‧‧test filter

901‧‧‧ cost vector

902‧‧‧Spectrum transmittance constraint

903‧‧‧ Filter Generator

904‧‧‧lighting body

905‧‧‧ Linear Program Solver

906‧‧‧ Constrained Projection Boundary / Constrained Projection Boundary 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 Filter

922‧‧‧offset

923‧‧‧offset coefficient

1001‧‧‧ convex polyhedron

1002‧‧‧ convex polyhedron

1003‧‧‧Three-color value

1004‧‧‧ and other bright planes

1005‧‧‧wall surface / cone

1006‧‧‧ Upper Luminance 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 / visual light transduction

1116‧‧‧ Matrix-Vector Product

1117‧‧‧Three-color value

1118‧‧‧ boundary

1119‧‧‧ vector length / norm

1201‧‧‧ cost function

1202‧‧‧ cost function

1203‧‧‧Nature Filter

1204‧‧‧Munsell Color Filter

1301‧‧‧ Filter Design Guidelines / Reference Colors

1302‧‧‧ Filter Design Program / Filter Design and Analysis Program

1303‧‧‧ Filter Generator

1304‧‧‧Reference Filter

1305‧‧‧test filter / test function

1306‧‧‧lighting body

1307‧‧‧Performance Analysis Operation

1308‧‧‧Manufacturing analysis procedures / operations

1309‧‧‧ Additional Information

1311‧‧‧Manufacturing Specifications

1312‧‧‧Manufacturing cost

1313‧‧‧Result 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

Graph of spectral radiant flux of 1407‧‧‧green traffic signal

Graph of 1408‧‧‧Daylight's spectral radiant flux

Curve of spectral radiant flux of 1409‧‧‧yellow traffic signal

1410‧‧‧ Filter / Constrained Filter Transmittance

1411‧‧‧Transmittance of Unconstrained Filter

1501‧‧‧ Graph

1502‧‧‧ Graph

1503‧‧‧ Graph

1504‧‧‧ Filter / Spectral Transmission Graph

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 / dotted curve

2002‧‧‧Solid curve / Dotted curve

2101‧‧‧Spectral radiant flux of blue primary light

2102‧‧‧Spectral radiant flux of green primary light

2103‧‧‧Spectral radiant flux of daylight

2104‧‧‧Spectral Radiant Flux of Red Primary Light

2105‧‧‧Tri-band filter

2106‧‧‧ Filter

2201‧‧‧Maximum transmittance constraint

2301‧‧‧Maximum transmittance constraint

2401‧‧‧ Linear Polarizer

2402‧‧‧ quarter-wave retarder / circular polarizer

2403‧‧‧Optical transparent substrate

2404‧‧‧Multi-layer interference coating / interference filter

2405‧‧‧ quarter-wave retarder

2406‧‧‧Polarizer

2408‧‧‧Beam

2409‧‧‧Eye

2411‧‧‧Reflected light

2412‧‧‧ Retina

2413‧‧‧Arrow

2414‧‧‧Reflected component

2501‧‧‧Spectral Radiation Flux

2502‧‧‧Spectral Radiation Flux of White LED

2503‧‧‧Spectral Radiation Flux of Red LED

2504‧‧‧Spectral transmittance

2601‧‧‧ chromaticity coordinates

2602‧‧‧ Chromaticity Coordinates

2603‧‧‧points

2604‧‧‧Spectral Radiation Flux of a Mixture of LED Illuminations

2605‧‧‧Spectral Transmission

2606‧‧‧Spectral Transmission

2701‧‧‧Conductive substrate

2702‧‧‧light-emitting diode

2703‧‧‧Beam Forming Optical Light Guides / Optics

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‧‧‧Eye

2809‧‧‧ Retina

2810‧‧‧Reflected light

2811‧‧‧arrow

2812‧‧‧Reflected component

2815‧‧‧First attenuation coating

2901‧‧‧ spherical section

2902‧‧‧ spherical segment

2904 ‧ ‧ ‧ hemisphere

2905‧‧‧ Hemisphere

2906‧‧‧ dotted arrow

2909‧‧‧ dotted arrow

3001‧‧‧ contour

3002‧‧‧ contour

3003‧‧‧ contour

3004‧‧‧Edge / 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 map

4301‧‧‧dashed 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‧‧‧ Absorbing Optical Substrate

4604‧‧‧Multi-layer interference coating

4606‧‧‧beam

4607‧‧‧ eyes

4609‧‧‧ Retina

4610‧‧‧Reflected light

4611‧‧‧Arrow

4612‧‧‧Reflected component

4701‧‧‧ dotted outline

4702‧‧‧solid outline

4704‧‧‧Spectral transmittance curve

4705‧‧‧solid curve

5801‧‧‧Round corner frame / entity

5802‧‧‧Solid / square frame

5803‧‧‧Round corner frame / entity

5805‧‧‧square frame

5806‧‧‧Combined operation

5808‧‧‧composite

5811‧‧‧Composite objects

Figure 1: Flowchart depicting the human eye's photosensitive observation and color perception. Figures 2A and 2B: a graph of the spectral absorption rate of retinal photosensitive pigments in a normal person (Figure 2A); and one of the peak variables of the spectral absorption rate of retinal photosensitive pigments corresponding to known genotypes in the population (Figure 2B) ). Figure 3: A three-color diagram showing the three-color values corresponding to a color appearance and their projections into the luminous component and the chromaticity component. Fig. 4: A flow chart of a procedure for calculating the relative color gamut area for comparing the effects of color discrimination between two filters. Figure 5: Flow chart of the calculation of the color gamut area of a reference group, a illuminant, a filter, and an observer relative to a specific group. Figures 6A and 6B: a graph of the spectral reflectance of a selected Munsell color (Figure 6A); and a graph of the spectral reflectance of a selected color from a natural object (Figure 6B). Figures 7A to 7C: Chromaticity diagrams of the color appearance of selected Munsell colors under sunlight (as viewed through a first filter and a second filter) (Figure 7A); spectral radiation of sunlight A graph of flux (Figure 7B); and a graph of spectral transmittance of these filters (Figure 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 (Figure 8B); and a graph of spectral transmittance of these filters (Figure 8C). Figure 9: Flow chart of a program generated by a linearly-programmed filter. Figures 10A and 10B: Three-color diagrams showing the three-color values corresponding to a color appearance and the boundary of a constrained convex polyhedron (Figure 10A); the exploded views of the three-color values and the boundary of the constrained convex polyhedron (Figure 10B) . Figure 11: Constrained projection norms of a specific reference light, a convex chromaticity boundary, a luminosity boundary, a first viewer, a basic filter, a pre-filter and a second viewer, and Process flow chart for calculation of constraint 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 (Figure 12A); and the corresponding design A graph of the spectral transmittance of the two filters as a function of cost (Figure 12B). Figure 13: Flow chart of the iterative filter design process considering design criteria, usage criteria, and manufacturing criteria. 14A to 14C: Chromaticity diagrams of green and yellow traffic signals and the color appearance of daylight viewed through a first filter and a second filter (Figure 14A); green and yellow traffic signals and daylight Graph of spectral radiant flux (Figure 14B); and graph of spectral transmittance of the filter (Figure 14C). 15A to 15B: a graph of two variables of a minimum spectral transmittance constraint (FIG. 15A); and a graph of spectral transmittance of a corresponding color enhancement filter that satisfies the constraint (FIG. 15B). Figures 16A and 16B: Curves of displacement of a percentage of wavelength of an interference filter with a refractive index of 1.85 as a function of the incident angle according to Snell's law (Figure 16A); and a filter providing enhanced red-green discrimination A graph of the spectral transmittance of an optical device and a graph of the spectral transmittance of a filter that additionally provides a stable color appearance to a wavelength shift range (Figure 16B). Figures 17A to 17C: Chromaticity diagrams of the color appearance of selected Munsell colors under sunlight (as viewed through a filter and as viewed by the same filters with wavelength shifts of -2.5% and -5%) (View) (Figure 17A); a graph of the spectral radiant flux of sunlight (Figure 17B); and a curve of the spectral transmittance of the filter and the filter with a wavelength shift of -2.5% and -5% Figure (Figure 17C). Figures 18A to 18C: Chromaticity diagrams of the color appearance of selected Munsell colors under sunlight (as viewed through a filter and as viewed by the same filter with a wavelength shift of -2.5%) (Figures 18A); a graph of the spectral radiant flux of sunlight (Figure 18B); and a graph of the spectral transmittance of the filter and the filter with a wavelength shift of -2.5% (Figure 18C). Figures 19A and 19B: Graphs of the blue light hazard function as a function of wavelength (Figure 19A); and the spectral transmittance of two multi-band filters that provide blue light blocking and one of the conventional cut-off filters that provide blue light blocking Graph (Figure 19B). Figures 20A and 20B: Graphs of the spectral transmission of two narrow-band selective absorption filters (Figure 20A); and the spectral transmission of two multi-band interference filters and absorption filters that provide red-green discrimination enhancement Graph of rate (Figure 20B). FIG. 21A and FIG. 21B: a graph of the spectral radiant flux of daylight and one of the primary colors of a liquid crystal display with a light-emitting diode backlight (FIG. 21A); and an enhancement of one of the display primary colors relative to the luminosity of sunlight A graph of the spectral transmittance of a luminosity filter (Figure 21B). Figure 22A, Figure 22B: Curves that protect the eyes from the spectral transmittance of one of the 532 nm radiation filters that are emitted by a frequency doubling 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 and 23B: Graphs showing the spectral transmittance constraints of a filter that protects the eye from an 589 nm radiation emitted by a sodium illumination torch with an incident angle between 0 degrees and about 30 degrees (Figure 23A ); And a graph of the spectral transmittance of this filter (Figure 23B). Figures 24A and 24B: Schematic diagrams of a composite lens containing an interference filter and a circular polarizer that absorbs light reflected by the interference filter (Figure 24A); and the operation of the composite filter is shown A pattern (Figure 24B). Figures 25A and 25B: Curves of the spectral radiant flux of a 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 spectral transmittance of the filter that provides the color appearance of the object illuminated by the light transmitted by the filter and provides the good color appearance of the object illuminated by the light reflected by the filter (Figure 25B). Figures 26A to 26C: Chromaticity diagrams of the color appearance of selected Munsell colors under the illumination of one of a combination of white LEDs and red LEDs (e.g., when the illuminant is viewed through a filter and transmitted by the illuminant) (Viewed when the filter reflects) (Figure 26A); the spectral radiant flux of the illuminant (Figure 26B); and a graph of the spectral transmittance of these filters (Figure 26C). 27A, 27B: containing a light-emitting diode, an interference filter and providing a composite beam (where the central region of the beam includes light transmitted through the filter and the annular region of the beam includes the filter (A light reflected by the filter) is a schematic diagram of a lamp assembly (FIG. 27A); and a diagram showing the operation of the lamp assembly incorporated in the filter (FIG. 27B). 28A and 28B: a schematic diagram of a composite filter containing an interference filter and an absorption filter (where the absorption filter attenuates light reflected by the interference filter) (FIG. 28A); And a diagram showing the operation of the composite filter incorporated into the glasses (FIG. 28B). Figure 29A, Figure 29B: shows the geometry of a lens in glasses relative to the eye, and two beams of light that pass through the lens at different positions and are imaged on the retina of the eye; a top view (Figure 29A) and Angle view (Figure 29B). Figures 30A and 30B: Contour maps of the effective incidence angle of light passing through a position on the surface of a lens, where the effective incidence angle corresponds to the surface normal of the lens at a position and the position passing through the position The lens is an angle between a beam of light imaged onto the retina (FIG. 30A); and a graph of the relative importance and the component of the relative importance function as a function of the effective angle of incidence (FIG. 30B). Figures 31A to 31E: Curves for designing the transmittance constraint and cost function of a filter that enhances the color discrimination of a normal observer (Figure 31A); curves for the spectral transmittance of the filter components Figure (Figure 31B); a graph of one of the filter's manufacturing specifications (Figure 31C); relative to the Farnsworth D-15 reference color as a function of the number of incident angles and relative to a selected one provided by the filter A graph of the percentage increase in the color gamut area of the natural reference color (Figure 31D); a graph of the white point displacement of the daylight provided by the filter as a function of the number of incident angles (Figure 31E). Figures 32A to 32E: Curves for designing the transmittance constraint and cost function of a filter that enhances the red-green discrimination of a normal observer (Figure 32A); the spectral transmittance of components of the filter Graph (Figure 32B); one of the manufacturing specifications of the filter (Figure 32C); the reference color relative to Farnsworth D-15 as a function of the number of incident angles and the selected color provided by the filter A graph of the percentage increase in the color gamut area of the natural reference color (Figure 32D); a graph of the white point displacement of the daylight provided by the filter as a function of the number of incident angles (Figure 32E). 33A to 33E: graphs showing the transmittance constraint and cost function of a filter designed to enhance the red-green discrimination of a normal observer and provide a stable color appearance within a range of incident angles (FIG. 33A); A graph of the spectral transmittance of the components of the filter (Fig. 33B); a graph of one of the filter's manufacturing specifications (Fig. 33C); relative to the Farnsworth D-15 reference color and Graph showing the percentage increase in the color gamut area of the selected natural reference color provided by the filter (Figure 33D); the white point displacement of the daylight provided by the filter as a function of the number of incident angles Graph (Figure 33E). 34A to 34E: graphs of the transmittance constraint and cost function of a filter used to design a filter that enhances the blue-yellow discrimination of a normal observer and provides a stable color appearance within a range of incidence angles (Figure 34A); A graph of the spectral transmittance of the components of the filter (Fig. 34B); a graph of one of the filter's manufacturing specifications (Fig. 34C); relative to the Farnsworth D-15 reference color and Graph showing the percentage increase in the color gamut area of the selected natural reference color provided by the filter (Figure 34D); the white point displacement of the daylight provided by the filter as a function of the number of incident angles Graph (Figure 34E). Figures 35A to 35E: Curves for the transmittance constraint and cost function of a filter used to design a filter that enhances the red-green discrimination of a normal observer and provides suppression of short-wavelength blue light and a stable color appearance over a range of angles of incidence Figure (Figure 35A); a graph of the spectral transmittance of the components of the filter (Figure 35B); a graph of one of the filter's manufacturing specifications (Figure 35C); relative to Farnsworth as a function of the number of incident angles Graph of D-15 reference color and the percentage increase in color gamut area relative to the selected natural reference color provided by the filter (Figure 35D); the function provided by the filter as a function of the number of incident angles Graph of white point displacement of sunlight (Figure 35E). Figure 36A to Figure 36E: Curves for designing the transmittance constraint and cost function of a filter designed to enhance the red-green discrimination for an observer with mild green weakness and provide a stable color appearance within a range of incidence angles (Figure 36A); a graph of the spectral transmittance of the components of the filter (Figure 36B); a graph of one of the filter's manufacturing specifications (Figure 36C); relative to Farnsworth D as a function of the number of incident angles -15 Reference color and graph of percentage increase in color gamut area relative to the selected natural reference color provided by the filter (Figure 36D); daylight provided by the filter as a function of the number of incident angles Graph of white point displacement (Figure 36E). Figures 37A to 37E: Curves for designing the transmittance constraint and cost function of a filter designed to enhance the red-green discrimination of an observer with a moderately weak green and provide a stable color appearance within a range of incidence angles (Figure 37A); a graph of the spectral transmittance of the components of the filter (Figure 37B); a graph of one of the filter's manufacturing specifications (Figure 37C); relative to Farnsworth D as a function of the number of incident angles -15 Reference color and a graph of the percentage increase in the color gamut area relative to the selected natural reference color provided by the filter (Figure 37D); daylight provided by the filter as a function of the number of incident angles Graph of white point displacement (Figure 37E). Figures 38A to 38E: Curves for designing the transmittance constraint and cost function of a filter designed to enhance the red-green discrimination for an observer with severe green weakness and provide a stable color appearance within a range of incidence angles ( Fig. 38A); a graph of the spectral transmittance of the components of the filter (Fig. 38B); a graph of one of the filter's manufacturing specifications (Fig. 38C); relative to Farnsworth D- 15 A graph of the reference color and the percentage increase in the color gamut area relative to the selected natural reference color provided by the filter (Figure 38D); the amount of daylight provided by the filter as a function of the number of incident angles Graph of white point displacement (Figure 38E). 39A to 39E: graphs for designing the transmittance constraint and cost function of a filter for red-green discrimination enhancement for an observer with a weak red and providing a stable color appearance within a range of incidence angles (Figures 39A); a graph of the spectral transmittance of the components of the filter (Figure 39B); a graph of one of the filter's manufacturing specifications (Figure 39C); relative to Farnsworth D-15 as a function of the number of incident angles A graph of the reference color and the percentage increase in the color gamut area relative to the selected natural reference color provided by the filter (Figure 39D); the whiteness of daylight provided by the filter as a function of the number of incident angles Graph of point displacement (Figure 39E). Figures 40A to 40E: Transmittance constraints and cost of a filter used to design 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 within an angle of incidence range A graph of the function (Figure 40A); a graph of the spectral transmittance of the components of the filter (Figure 40B); a graph of one of the filter's manufacturing specifications (Figure 40C); a function of the number of incident angles A graph of the percentage increase in the color gamut area relative to the Farnsworth D-15 reference color and the selected natural reference color provided by the filter (Figure 40D); the filter is a function of the number of incident angles as a function Curve of white point displacement of daylight provided by the device (Figure 40E). Figure 41A to Figure 41E: Transmittance constraint and cost function of a filter used to design an optical filter that protects the eye from a 532 nm octave Nd: YAG laser and provides a stable color appearance over a range of angles of incidence Graph (Fig. 41A); Graph of spectral transmittance of components of the filter (Fig. 41B); Graph of one of the filter's manufacturing specifications (Fig. 41C); Relative Graph of the reference color at Farnsworth D-15 and the percentage increase in the color gamut area relative to the selected natural reference color provided by the filter (Figure 41D); from the filter as a function of the number of incident angles A plot of the white point displacement of daylight is provided (Figure 41E). 42A to 42E: Plots of the transmittance constraint and cost function of a filter designed to protect the eyes from a 589 nanometer sodium illumination torch and provide a stable color appearance within a range of incidence angles ( Fig. 42A); a graph of the spectral transmittance of the components of the filter (Fig. 42B); a graph of one of the filter's manufacturing specifications (Fig. 42C); relative to Farnsworth D- 15 Reference color and a graph of the percentage increase in the color gamut area relative to the selected natural reference color provided by the filter (Figure 42D); the amount of daylight provided by the filter as a function of the number of incident angles Graph of white point displacement (Figure 42E). Figure 43A and Figure 43B: Curves of the spectral transmittance constraint of a filter that blocks short-wavelength light and passes narrow-band light of 589 nanometers through one filter (Figure 43A); A graph of the filter smoothed by a smooth core (Figure 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 cut-off filter (Figure 44A); spectrum of sunlight Radiation flux (Figure 44B); and a graph of the spectral transmittance of these filters (Figure 44C). Figure 45A to Figure 45E: Curves for designing the transmittance constraint and cost function of a filter that provides suppression of short-wavelength blue light and high light transmittance (Figure 45A); the spectral transmittance of components of the filter Graph (Figure 45B); one of the manufacturing specifications of the filter (Figure 45C); the reference color relative to the Farnsworth D-15 as a function of the number of incident angles and the selected color provided by the filter A graph of the percentage increase in the color gamut area of the natural reference color (Figure 45D); a graph of the white point displacement of the daylight provided by the filter as a function of the number of incident angles (Figure 45E). 46A and 46B: a schematic diagram of a composite filter containing an interference filter and an absorption filter (where the absorption filter attenuates light reflected by the interference filter) (FIG. 46A); And a diagram showing the operation of the composite filter incorporated into the glasses (FIG. 46B). Figure 47A to Figure 47C: Chromaticity diagrams of the color appearance of selected Munsell colors under sunlight, as viewed through a reference filter and a neodymium glass filter (Figure 47A); the spectral radiant flux of sunlight (Figure 47B); and a graph of the spectral transmittance of these filters (Figure 47C). Figures 48A to 48E: Curves for the transmittance constraint and cost function of a neodymium-containing filter designed to enhance the red-green discrimination of a normal observer and provide a stable color appearance within a range of incidence angles (Figure 48A ); A graph of the spectral transmittance of the components of the filter (Figure 48B); a graph of one of the filter's manufacturing specifications (Figure 48C); a reference to Farnsworth D-15 as a function of the number of incident angles Graph of color and percentage increase in color gamut area relative to the selected natural reference color provided by the filter (Figure 48D); white point of daylight provided by the filter as a function of the number of incident angles Graph of displacement (Figure 48E). 49A to 49E: Curves of the transmittance constraint and cost function of a neodymium-containing filter used to design to enhance the blue-yellow discrimination of a normal observer and provide a stable color appearance within a range of incidence angles (Figure 49A ); A graph of the spectral transmittance of the components of the filter (Figure 49B); a graph of one of the filter's manufacturing specifications (Figure 49C); a reference to Farnsworth D-15 as a function of the number of incident angles Graph of color and percentage increase in color gamut area relative to the selected natural reference color provided by the filter (Figure 49D); white point of daylight provided by the filter as a function of the number of incident angles Graph of displacement (Figure 49E). Figures 50A to 50E: Designed for designing a red-green discrimination enhancement for an observer with a mild green weakness and providing a stable color appearance over a range of incidence angles, one of the transmittance constraints and cost function of a neodymium-containing filter Graph (Fig. 50A); graph of the spectral transmittance of the filter components (Fig. 50B); graph of one of the filter's manufacturing specifications (Fig. 50C); relative to the number of incident angles as a function of Graph of Farnsworth D-15 reference color and percentage increase in color gamut area relative to the selected natural reference color provided by the filter (Figure 50D); provided by the filter as a function of the number of incident angles Graph of white point displacement of daylight (Figure 50E). Figure 51A to Figure 51E: Design of a transmittance constraint and cost function for a neodymium-containing filter for designing red-green discrimination enhancement for an observer with a moderate green weakness and providing a stable color appearance within a range of incidence angles Graph (Fig. 51A); graph of spectral transmittance of the filter components (Fig. 51B); graph of one of the filter's manufacturing specifications (Fig. 51C); relative to the number of incident angles as a function of Graph of Farnsworth D-15 reference color and percentage increase in color gamut area relative to the selected natural reference color provided by the filter (Figure 51D); provided by the filter as a function of the number of incident angles Graph of white point displacement of daylight (Figure 51E). 52A to 52E: Curves for designing the transmittance constraint and cost function of a neodymium-containing filter for designing red-green discrimination enhancement for an observer with severe green weakness and providing a stable color appearance within a range of incidence angles Figure (Figure 52A); a graph of the spectral transmittance of the filter's components (Figure 52B); a graph of one of the filter's manufacturing specifications (Figure 52C); relative to Farnsworth as a function of the number of incident angles Graph of D-15 reference color and percentage increase in color gamut area relative to the selected natural reference color provided by the filter (Figure 52D); the function provided by the filter as a function of the number of incident angles Graph of white point displacement of sunlight (Fig. 52E). Figures 53A to 53E: Graphs of the transmittance constraint and cost function of a neodymium-containing filter used to design a red-green discrimination enhancement for an observer with a weak red color and to provide a stable color appearance within a range of incidence angles (Figure 53A); a graph of the spectral transmittance of the components of the filter (Figure 53B); a graph of one of the filter's manufacturing specifications (Figure 53C); relative to Farnsworth D as a function of the number of incident angles -15 graph of reference color and percentage increase in color gamut area relative to the selected natural reference color provided by the filter (Figure 53D); daylight provided by the filter as a function of the number of incident angles Graph of white point displacement (Figure 53E). Figure 54A and Figure 54B: Curves of approximate spectral absorption of retinal ganglion cells (Figure 54A); a blue wideband reference filter and a multi-band filter that maximizes the photons absorbed by retinal ganglion cells Optical device graph (Figure 54B). Figures 55A to 55E: graphs of the transmittance constraint and cost function of a filter designed to enhance the optical power received by retinal ganglion cells (Figure 55A); the spectral transmittance of the filter components Graph (Figure 55B); one of the manufacturing specifications of the filter (Figure 55C); the reference color relative to the Farnsworth D-15 and the warp provided by the filter as a function of the number of incident angles A graph of the percentage increase in the color gamut area of the selected natural reference color (Figure 55D); a graph of the white point displacement of the daylight provided by the filter as a function of the number of incident angles (Figure 55E). 56A to 56E: graphs showing the transmittance constraint and cost function of a filter designed to enhance the optical power absorbed by retinal ganglion cells and provide a stable color appearance within a range of angles of incidence (Figure 56A) ; The graph of the spectral transmittance of the components of the filter (Figure 56B); the graph of one of the filter's manufacturing specifications (Figure 56C); the reference color relative to Farnsworth D-15 as a function of the number of incident angles And a graph of the percentage increase in the color gamut area of the selected natural reference color provided by the filter (Figure 56D); white point displacement of daylight provided by the filter as a function of the number of incident angles Graph (Figure 56E). 57A to 57E: graphs of the transmittance constraint and cost function of a neodymium-containing filter used to design an enhancement of the optical power received by retinal ganglion cells and provide a stable color appearance within a range of incidence angles 57A); a graph of the spectral transmittance of the components of the filter (Figure 57B); a graph of one of the filter's manufacturing specifications (Figure 57C); relative to Farnsworth D-15 as a function of the number of incident angles Graph of reference color and percentage increase in color gamut area relative to the selected natural reference color provided by the filter (Figure 57D); white of daylight provided by the filter as a function of the number of incident angles Graph of point displacement (Figure 57E). FIG. 58: An exemplary program flow diagram for describing and demonstrating the syntax and structure of the program flow diagram (as they are presented in other figures). Figure 59A, Figure 59B: Tables of the evaluated performance criteria of the filters of Figures 31A to 31E for enhancing the color discrimination of a normal observer (Figure 59A); transmittance and cost functions of filter components Table of transmittance constraints and filter manufacturing specifications (Figure 59B). Figures 60A and 60B: Tables of the evaluated performance criteria of the filters of Figures 32A to 32E for enhancing the red-green discrimination of a normal observer (Figure 60A); transmittance and cost of filter components Table of functions, transmittance constraints, and filter manufacturing specifications (Figure 60B). Figure 61A, Figure 61B: Tables of the evaluated performance criteria of the filters of Figures 33A to 33E for enhancing the red-green discrimination of a normal observer and providing a stable color appearance over a range of incident angles (Figure 61A ); A table of the transmittance, cost function, transmittance constraints, and manufacturing specifications of the filter assembly (Figure 61B). Figures 62A, 62B: Tables of the evaluated performance criteria of the filters of Figures 34A to 34E for enhancing the blue-yellow discrimination of a normal observer and providing a stable color appearance within a range of incident angles (Figure 62A ); A table of the transmittance, cost function, transmittance constraints, and manufacturing specifications of the filter assembly (Figure 62B). Figures 63A and 63B: The evaluated effectiveness of the filters of Figures 35A to 35E for enhancing the red-green discrimination of a normal observer and providing suppression of short-wavelength blue light and stable color appearance over a range of angles of incidence Table of criteria (Fig. 63A); table of transmittance, cost function, transmittance constraints, and manufacturing specifications of the filter assembly (Fig. 63B). Figures 64A, 64B: Evaluated performance criteria for the filters of Figures 36A to 36E for red-green discrimination enhancement for an observer with mild green and weak and providing a stable color appearance over a range of incident angles Table (Fig. 64A); a table of the transmittance, cost function, transmittance constraints, and manufacturing specifications of the filter assembly (Fig. 64B). Figures 65A and 65B: Evaluated performance criteria for the filters of Figures 37A to 37E for red-green discrimination enhancement for an observer with moderate green weakness and providing a stable color appearance over a range of incident angles Table (Fig. 65A); a table of the transmittance, cost function, transmittance constraints, and manufacturing specifications of the filter assembly (Fig. 65B). Figure 66A, Figure 66B: Evaluated performance criteria for the filters of Figures 38A to 38E for red-green discrimination enhancement for an observer with severe green weakness and providing a stable color appearance over a range of incident angles Table (Figure 66A); a table of the transmittance, cost function, transmittance constraints, and manufacturing specifications of the filter assembly (Figure 66B). Fig. 67A, Fig. 67B: Tables for the evaluated performance criteria of the filters of Figs. 39A to 39E for enhancing the red-green discrimination of an observer with a weak red and providing a stable color appearance within a range of incidence angles (Fig. 67A); Table of transmittance, cost function, transmittance constraint, and manufacturing specifications of the filter assembly (Fig. 67B). Figures 68A and 68B: Processes of the 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 evaluated performance criteria (Figure 68A); table of transmittance, cost function, transmittance constraints, and manufacturing specifications of the filter assembly (Figure 68B). Figures 69A and 69B: Evaluation of the filters of Figures 41A to 41E used to protect the eyes from a 532 nm multiplier Nd: YAG laser and provide a stable color appearance over a range of incident angles Table of performance criteria (Figure 69A); table of the transmittance, cost function, transmittance constraints, and manufacturing specifications of the filter assembly (Figure 69B). Figures 70A and 70B: Evaluation of the performance criteria of the filters of Figures 42A to 42E for protecting the eyes from a 589 nanometer sodium illumination torch and providing a stable color appearance over a range of incident angles Table (Fig. 70A); a table of the transmittance, cost function, transmittance constraints, and manufacturing specifications of the filter assembly (Fig. 70B). Figure 71A, Figure 71B: Tables of the evaluated performance criteria of the filters of Figures 45A to 45E for providing the suppression of short-wavelength blue light and high light transmittance (Figure 71A); transmittance and cost of filter components Table of functions, transmittance constraints, and filter manufacturing specifications (Figure 71B). Figures 72A and 72B: Tables of the evaluated performance criteria for neodymium-containing filters of Figs. 48A to 48E for enhancing the red-green discrimination of a normal observer and providing a stable color appearance within a range of incidence angles ( Fig. 72A); Table of transmittance, cost function, transmittance constraint, and manufacturing specifications of the filter assembly (Fig. 72B). Figures 73A and 73B: Tables of the evaluated performance criteria for neodymium-containing filters of Figures 49A to 49E for enhancing the blue-yellow discrimination of a normal observer and providing a stable color appearance within a range of incident angles ( Fig. 73A); Table of transmittance, cost function, transmittance constraint, and manufacturing specifications of the filter assembly (Fig. 73B). Figures 74A, 74B: Evaluation of red-green discrimination for an observer with a mild green weakness and providing a stable color appearance over a range of incidence angles. Table of performance criteria (Figure 74A); table of transmittance, cost function, transmittance constraints, and manufacturing specifications of the filter assembly (Figure 74B). Figures 75A and 75B: Evaluations of neodymium-containing filters of Figures 51A to 51E, which are used to enhance the red-green discrimination of an observer with a moderate green weakness and provide a stable color appearance over a range of incident angles Table of performance criteria (Figure 75A); table of transmittance, cost function, transmittance constraints, and filter manufacturing specifications for filter components (Figure 75B). Figure 76A, Figure 76B: Red-green discrimination enhancement for an observer with severe green weakness and providing a stable color appearance within a range of incident angles Figure 52A to Figure 52E The evaluated effectiveness of neodymium-containing filters A table of criteria (Figure 76A); a table of the transmittance, cost function, transmittance constraints, and manufacturing specifications of the filter assembly (Figure 76B). Figure 77A, Figure 77B: Evaluated performance criteria for neodymium-containing filters of Figures 53A to 53E for enhanced red-green discrimination for an observer with a weak red color and providing a stable color appearance over a range of incident angles Table (Fig. 77A); table for the transmittance, cost function, transmittance constraints, and manufacturing specifications of the filter assembly (Fig. 77B). Figure 78A, Figure 78B: Tables of the evaluated performance criteria for the three-pass filter of Figures 55A to 55E for enhancing the optical power received by retinal ganglion cells (Figure 78A); Table of transmittance, cost function, transmittance constraints, and filter manufacturing specifications (Figure 78B). Figure 79A, Figure 79B: Evaluated performance criteria for the four-pass filter of Figures 56A to 56E for enhancing the light power received by retinal ganglion cells and providing a stable color appearance over a range of angles of incidence Table (Figure 79A); a table of the transmittance, cost function, transmittance constraints, and manufacturing specifications of the filter assembly (Figure 79B). Figure 80A, Figure 80B: Evaluated efficacy of neodymium-containing three-pass band filters for enhancing the power of light received by retinal ganglion cells and providing a stable color appearance over a range of angles of incidence Figures 57A to 57E Table of criteria (Figure 80A); table of transmittance, cost function, transmittance constraints, and manufacturing specifications of the filter assembly (Figure 80B).

Claims (10)

A multi-band optical filter configured to block the transmission of blue light between about 380 nanometers and about 450 nanometers and maintain normal color discrimination. The filter includes: a plurality of passbands that divide the visible spectrum and Stopbands, which include at least first, second, and third passbands interleaved with two or more stopbands; wherein each passband has a center, a width equal to the center minus one-half of the width One lower-band boundary, equal to the center plus one-half the upper-band boundary, and an average transmittance; each stopband has a center, one width, equal to the center minus one-half of the width, and a lower-band boundary equal to The center plus one half of the width of the upper frequency band boundary and an average transmittance; the lower frequency band boundary of each interleaved stopband is the same as the upper frequency band boundary of an adjacent passband; the upper frequency band boundary of each interleaved stopband The lower frequency band boundary is the same as that of an adjacent passband; the center of each passband is between about 450 nanometers and about 700 nanometers, and the width of each passband is between about 10 nanometers and about 110 nanometers; each The stopband center is located at about 410 nm to Between 690 nanometers, and each stopband width is between about 10 nanometers and about 80 nanometers; each of these interleaved stopbands has an average transmission less than one-half of the average transmission of an adjacent passband Rate; the first passband has a center between about 450 nanometers and about 470 nanometers and a width between about 10 nanometers and about 40 nanometers; the second passband has a width of about 545 nanometers To a center between about 575 nanometers and a width between about 30 nanometers to about 60 nanometers; the third passband has a center between about 630 nanometers to about 670 nanometers and about 40 A width between nanometers and about 90 nanometers; each of the staggered stopbands has a width of at least about 20 nanometers and an average of less than about a quarter of the average transmittance of an adjacent passband Transmittance; and the spectral transmittance of the filter between about 380 nanometers and about 440 nanometers is less than about 10%. The multi-band optical filter of claim 1, wherein the first passband is located at a center between about 455 nm and about 465 nm. The multi-band optical filter of claim 1, wherein the spectral transmittance of the filter between about 380 nm and about 450 nm is less than about 10%. The multi-band optical filter of claim 1, wherein the spectral transmission of the filter between about 380 nm and about 460 nm is less than about 10%. The multi-band optical filter of claim 1, wherein the spectral transmission of the filter between about 380 nm and about 440 nm is less than about 1%. The multi-band optical filter of claim 1, wherein the spectral transmission of the filter between about 380 nm and about 450 nm is less than about 1%. The multi-band optical filter of claim 1, wherein the spectral transmission of the filter between about 380 nm and about 460 nm is less than about 1%. The multi-band optical filter of any one of claims 1 to 7, wherein each of the interleaved stop bands has an average transmittance greater than about one sixth of the average transmittance of an adjacent passband. . The multi-band optical filter of claim 1, wherein the first passband has a center located at about 465 nanometers and a width of about 15 nm; the second passband has a wavelength of about 565 nanometers. A center and a width of about 45 nanometers; the third passband has a center at about 660 nanometers and a width of about 70 nanometers; each of the interleaved stopbands has an adjacent passband The average transmittance is about a quarter of the average transmittance; and the spectral transmittance of the filter between about 380 nanometers and about 450 nanometers is less than about 1%. The multi-band optical filter of claim 9, wherein the filter includes an interference filter and an absorption filter and the absorption filter includes a metal attenuation coating.