Classifications

• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B3/00—Simple or compound lenses
  • G02B3/02—Simple or compound lenses with non-spherical faces
  • G02B3/08—Simple or compound lenses with non-spherical faces with discontinuous faces, e.g. Fresnel lens

Definitions

• optical lenses have primarily been formed by grinding and polishing, their surfaces are figures of revolution, such as spheres, tori, and cylinders. In general, figures of revolution are not suitable for forming illumination patterns that are not circularly symmetric.
• the present invention embodies a different method of lens design than that of optical imaging lenses. It utilizes shapes that are not figures of revolution, but which can be manufactured by molding of plastic or glass. They are especially suitable for use with light-emitting diodes, the tiny sizes of which allow such lenses to be small and easier to injection mold.
• the most important lighting prescriptions addressed by the present invention are for vehicular lamps, by the Society of Automotive Engineers, and for ships, by the United States Coast Guard. Particular embodiments of the present invention address these prescriptions. These are far-field prescriptions for an angular distribution of light, whereas illumination prescriptions are for some nearby surface, such as the walls or ceiling of a room.
• the current art of luminaire design utilizes the method of computerized searching through a number of design variations, with ray tracing used to evaluate the closeness of a candidate luminaire' s output to the desired light distribution. This technique is not completely satisfactory because the vastness of the design space precludes an exact match of luminaire output to prescribed output, given that the design starting point is only a guess.
• An example of traditional design is the lenslet array utilized in automotive signal lamps.
• Numerous small lens elements usually spherical, cylindrical, or toric, transform the collimated beam from a reflector into a wide-angle beam shaped to fulfill government standards.
• Such combinations of reflector and lenslet arrays typically have poor values of efficiency, such as one third.
• the reflector can be blamed for much of this inefficiency, also at fault is the restriction of lenslet shapes to spheres, cylinders, and torics (formed by rotating cutting elements), which greatly limits the designer's ability to match the shape of the output beam to the prescribed pattern.
• Such a match maximizes efficiency, since every point of the specification can be met with a minimum amount of light.
• the general design of rotationally symmetric luminaires uses the method of matching the cumulative distribution of source intensity with that of the desired output. Cumulative intensity runs from 0 to 100 % , starting at the optical axis and going outwards to the edge of the desired output pattern. Another cumulative distribution is calculated for the intensity of the light source, over the angular range to be redirected by the luminaire. Then, any angle of a ray from the source, having a particular percentage of cumulative source intensity, is redirected into an output angle having the same percentage of cumulative output intensity. From these two angles is calculated the angle the luminaire surface must have to perform the redirection. Then the actual luminaire surface is derived by radial integration outwards from an initial starting point. The resultant shape has the slope necessary to redirect the light from a rotationally symmetric source into a prescribed rotationally symmetric output pattern.
• optical lens design the conceptually closest design method is that of anamorphic lenses. These, however, are designed for a prescribed distortion pattern, a quite different matter than fulfilling a prescribed variation in luminous intensity.
• the present invention concerns a general class of illumination lenses that can accurately match a source with a particular desired output, when either or both of these are not figures of revolution. No trial and error processes are required for their design.
• the mathematical discipline of differential geometry is the basis for the generation of the shapes of particular lenses. As with the above-mentioned method of rotational symmetry, there are two basic stages in the design process:
• the lens surface operates in our everyday three-dimensional space, so that extrinsic differential geometry is used to design it.
• extrinsic differential geometry For example, a polyhedron, such as a cube, has a three-dimensional shape studied by extrinsic differential geometry; but, it also has such intrinsic properties as those revealed by drawing triangles on it that enclose a corner. These triangles will violate the laws of plane trigonometry (i.e., their interior angles do not add to 180°), so that this surface's cubic nature is an intrinsic aspect, independent of it being in three-dimensional space.
• extrinsic differential geometry for the present invention is in surface synthesis, whereby the lens surface is integrated from the specification of its tilt at a large number of points.
• the surface tilt is calculated according to the laws of optics from knowledge of how the light from a source must be redirected in order to fulfill a particular prescription.
• design methods of the prior art are deficient, as discussed above.
• the present invention utilizes computer calculations to numerically specify a lens surface given the intensity distributions of the source and the desired output.
• the arena of expressing this distribution is the surface of a sphere of unit radius, known mathematically as the Gaussian sphere, measured in steradians, with 4 ⁇ being the solid angle of the entire Gaussian sphere.
• An intensity pattern can be graphically presented with either a two-dimensional map of contours of constant intensity or a three-dimensional map with height representing intensity.
• an intensity function a grid, or mesh, on the Gaussian sphere, with cells of varying size.
• the cell sizes are inversely proportional to intensity, so that each cell has the same amount of luminous flux.
• the particular grid pattern chosen is called a tessellation, or tiling, or the sphere.
• An example is the latitude and longitude grid of geography, and another is the triangulation based on the icosahedron.
• the entire sphere need not be tiled, since ordinarily neither light sources nor illumination prescriptions cover all directions. Therefore, there is more freedom to adopt tilings, for particular designs, that would form what are mathematically known as incomplete atlases.
• a further object is to provide a lens, as referred to, and having overall size relative to the size of the light source, and obtained by selection of the distance from an initial starting point of lens surface generated from the light source, that keeps blurring of the output beam below a level defined by the angular resolution of the object pattern prescription.
• Yet another object concerns a lens shape generation method that includes the steps:
• the method also may include the step of performing successive integrations of adjacent characteristic strips in such a way as to fulfill the integrability condition dictating equality of the crossed second derivatives of the surface of the lens, thereby to ensure that the surface of the lens possesses the surface normals necessary for it to transform the light from the source into an output beam substantially fulfilling the prescription.
• the first lines may define a series of increasingly larger rectangles extending about said source, certain of said second lines intersecting corners of the rectangles.
• the first lines may define circular latitude lines, and said second lines define longitudinal lines.
• a yet further object is to provide a grid that is generally spherical, and defines an axis, said latitude lines extending about said axis, the spacing between successive latitude lines increasing in directions extending along said longitudinal lines.
• An additional object is to provide a grid that is generally spherical and defines an axis, said latitude lines extending about said axis, the spacing between successive latitude lines being equal, in direction along said longitudinal lines.
• Another object is to provide a light projecting surface in the form of a butterfly. That surface may define curved flutes diverging from a dished zone.
• Such a butterfly shaped lens may have a conical base to receive or couple to a light source.
• a yet additional object is to provide a conical lens having a base and diverging from the base toward a light projecting surface, and a light pipe coupled to said base.
• the light projecting surface typically has a center region, and ridges diverging away from said center region; and the surface typically has concavely dished zones located between said ridges.
• Such lenses are well adapted to project or transmit light of uniform or selected areal intensity over selected non-uniform areas such as rectangular surfaces to be uniformly illuminated.
• Fig. 1 depicts a grid on the Gaussian sphere of prescribed intensity output
• Fig. 2 depicts a side view of a corresponding grid on the Gaussian sphere of light-source intensity
• Fig. 3 depicts a top view of the Fig. 2 grid
• Fig. 4 depicts a top view of a lens derived from these grids
• Fig. 5 depicts a side view of the lens
• Fig. 6 is a schematic diagram of grids and a generated lens, and light outputs
• Fig. 7 is a cross section through a lens generated in accordance with the invention
• Fig. 8 is a top plan view of a lens generated in accordance with the invention.
• Fig. 9 is a perspective view of a lens unit generated in accordance with the invention, and a reflector;
• Fig. 9a is a section taken through the Fig. 9 lens and reflector
• Fig. 10 is a perspective view of a lens unit array
• Fig. 11 is a video or television unit having a screen incorporating the Fig. 10 lens unit array;
• Fig. 12 is a circuit diagram to control LEDs at each of the lens units in the Fig. 10 array
• Fig. 13 is a diagrammatic view of an audience viewing zone or area in relation to a large video screen incorporating the Fig. 10 array; and showing relative angling of lens units or cells;
• Fig. 14 is a plan view of a vessel carrying light sources as will be referred to;
• Fig. 15 is a top plan view of the Fig. 4 lens;
• Fig. 16 is a rectangular grid representation;
• Fig. 17 is a polar grid representation, on a generally spherical surface
• Fig. 18 is a modification of a polar grid
• Fig. 19 is a representation of a target grid over a polar grid
• Fig. 20 is a representation of a stair step, to be illuminated by a line in accordance with the invention
• Fig. 20a is a section taken through the Fig. 20 stair step, to illustrate lens location
• Fig. 21 is a vector representation, on a polar grid; and Figs. 22-24 are perspective views of modified lenses.
• Fig. 23a is an enlarged view showing a light source fitted in a lens base.
• a regular tessellation where all cells are the same size, can be warped to fit the prescription. With a large number of cells, such a warping can accurately match the prescription.
• This warping is accomplished by a coordinate shrinkage of the regular grid.
• the prescription has a large ratio I(x i ,y 0 )/I(x i ,y t ), from grid center to grid top y t ,at x and a much smaller one at grid edge x e .
• This will cause a much larger number of cells to be generated at x e than at x 0 .
• the x warping is redone at each y i? so that the grid is not orthogonal and the grid lines are curved.
• a polar grid can be used, that is, the polar section of a latitude-longitude grid, with the pole at the source maximum.
• the warping can be by making the latitude circles into ovals or by making the longitude lines at uneven intervals, or both, so that an orthogonal grid would result.
• a non-orthogonal grid could be constructed by bending the longitude lines.
• a regular tessellation with a very large number of cells can be condensed by grouping these small cells into larger ones of varying size, so that each group of cells has the same total luminous flux.
• the grid cells are indexed to express position within the grid, with either a single number or a pair of numbers, analogous to latitude and longitude in geography.
• the key to the design method of the present invention is the construction of two such grids: the first (see Fig. 1) on the Gaussian sphere of output intensity and the second (see Fig. 2) on the Gaussian sphere of source intensity.
• the source grid can be thought of having a miniaturized version of the source at its center.
• the prescription grid can be thought of having a miniaturized version of the present invention at its center. Both express the far-field behavior of light.
• Both grids have the same number of cells and the same indexing pattern, so that a one-to-one correspondence is established between them.
• This correspondence requires that both grids have the same topology, so that if one is triangular, for example, the other cannot be rectangular, or polar.
• Another grid topology is elliptical-parabolic.
• the warping method of grid generation would be preferable, since it could better accommodate the differences between the source and output distributions of intensity.
• the output grid is constructed first because the fulfillment of the prescription is the purpose of the lens, and typically, the prescription will have more irregularities or idiosyncrasies than the source output.
• Fig. 1 depicts one typical grid 100 on the Gaussian sphere of directions, extending horizontally for a span of 112.5° and vertically 25° above and below the horizontal plane.
• cells 110 are half the size of remaining cells 120.
• This grid expresses the U.S. Coast Guard specification for navigation lights, that full intensity be maintained within 5° of the horizontal and half intensity to within 25° of the horizontal.
• each cell contains the same amount of light flux.
• the grid is centered on axis 130.
• Fig. 2 depicts a side view and Fig. 3 a top view of corresponding light source grid 200, also with 22 rows of 46 cells.
• This grid is on the Gaussian sphere of directions of light coming from a Lambertian source, which has intensity that falls off with the cosine of angle 210 with axis 220.
• Cells 230 nearest axis 220 are the smallest, while those further away are larger, with corner cell 240 the largest.
• Horizontal angle 250 is analogous to longitude, and vertical angle 210 to latitude.
• Fig. 4 depicts a top view of a lens 400, a particular embodiment of the invention, generated from the correspondence between the grids of Fig. 1 and Fig. 2.
• the optically active top surface 410 is mathematically generated from the surface normals derived from the corresponding grids 100 and 200.
• conical support base 420 Below the top surface is conical support base 420.
• At the bottom of the lens is an indentation or recess 430 to receive a circuit board 440, upon which are mounted two rows of light-emitting diodes 450, embedded in a protective, transparent, epoxy mass 460.
• Lens 400 is in optical contact with transparent mass 460, so that there is no air gap.
• This lens will efficiently transform the Lambertian output, represented by grid 200, of absorbing-substrate LEDs 450 into radiation conforming to the Coast Guard Standard, represented by grid 100.
• This view shows how maximum horizontal source angle 470 is 77°, within which is emitted 95% of the output of a Lambertian source. This illustrates how the weak fringes of a source's output may not be worth collecting.
• the generated, curved, surface lines 421 correspond to generated, curved, grid lines 230 in Fig. 3; and generated, curved, grid lines 422 in Fig. 4 (orthogonal to lines 421) correspond to generated, curved, grid lines 231 in Fig. 2.
• FIG. 4 Vertical lines 423 in Fig. 4 represent a side view of the tilted side of 420.
• the Fig. 4, Fig. 5 lens is generally dome-shaped and has overall length L, in the directions indicated by arrows 424 in Fig. 4 that is greater than its overall width Wj in the direction indicated by arrows 427 in Fig. 5 normal to 424 and normal to the page of Fig. 4.
• the lens is upwardly convex along its different lengthwise surface indicated at 426, and upwardly convex along its uppermost widthwise surface 428.
• Fig. 5 depicts a side view of the lens 400, with light-emitting diodes
• Maximum vertical angle 480 is 60°, the maximum that can be refracted into the 25° limit of the grid 100.
• the overall height of a working model of lens 400 is only about half an inch, far smaller than equivalent light output incandescent lamps of the prior art.
• Initial point 500 at the lens crest is the starting point for striating lens surface 410.
• Initial strip 510 extends horizontally from 500. Characteristic strips
• 520 extend orthogonally from 510.
• the boundary is located at 530.
• the geometry of the source grid is sufficiently different from " "' «• ii ..'- ' if if ; ⁇ : IF"» irir > ⁇ • • ,. a
• the source grid can be overloaded so that some of the output grids will have more light than that prescribed.
• the overall light utilization can be maximized, and the extra light will result in the prescribed intensity being exceeded.
• the prescription is only for a minimum intensity, so this would be permissible.
• the source grid and the output grid specifies the redirection function that the lens must perform in order to transform the light from the source into the desired output beam.
• the grid cells must be sufficiently small so that the intensity is nearly constant within a cell. They also must be sufficiently numerous that the redirection function changes slowly from cell to adjacent cell. This enables a smooth construction of the lens surface.
• Fig. 6 shows a lens 80 in cross sectional elevation, and which has been constructed in the manner described.
• the lens surface is shown at 81.
• the first grid 82 is shown as a section through the expanded Gaussian sphere of directions of the light output beam exiting from the surface 81 of the lens. See for example beam vector V ! exiting the lens surface, and corresponding to desired beam vector V, 1 exiting the surface of the grid 82; and beam vector V 2 exiting the lens surface, and corresponding to the desired beam vector V 2 * exiting the surface of the grid.
• the second grid 83 is shown as a section through the reduced Gaussian sphere of direction of light output from the LED source at 84. See light output vector V 3 .
• deflection of source ray to output ray that must be carried out by the lens.
• This deflection can be produced by refraction, reflection by a thin-film metal coating, total internal reflection, or a combination of these, if the deflection is carried out in stages. Large deflection angles may require such staging, as in the case of a wide-angle source and a narrow output beam.
• n sin i n' sin i' for incidence angles i and i' , in the plane of incidence.
• Rays of light are represented by three-dimensional, unit-length vectors pointing in the direction of propagation.
• the boundary surface between the two media is represented by a unit-length vector perpendicular to it, the surface normal vector.
• the refracted ray R can be calculated from the vector form of Snell's law , via the sine vector S and the cosine vector C:
• the source is in optical contact with the lens, so that the surface normal values N(i,j) are determined by the case of n > n'.
• Fig. 7 shows another embodiment in which the lens 700 has an entry surface 710 as well as an exit surface 720, so that there is an intermediate ray 730 inside the lens with vector T(i,j), in the plane defined by incident ray 740 with vector I and exiting ray 750 with vector R and somewhere between them.
• T is chosen so that the two surface normals, entry N, (755) and exit N 2 (756), have the same angles with rays I and R. This can be done numerically with a root-bisection procedure.
• the entry surface may be hemispheric, with no net deflection of light. This would be the case for incandescent lamps, with envelopes having elevated temperatures that require an air gap to intervene between the lamp and the lens.
• the Coast Guard standard for masthead lamps for an anchored ship has a 360-degree pattern, calling for an incandescent lamp with a vertical filament.
• Such filaments come with a vertical supporting post that casts a shadow.
• the current invention can take a teardrop shape to in effect get light around this shadow.
• Fig. 8 shows an overhead view with lamp 800, having transparent envelope 810, vertical oriented cylindrical filament 820, and vertical support post 830.
• Lens 840 has inner surface 850 and teardrop exterior 860. Ray 865 that just clears post 830 is refracted into its shadow, so the 360-degree prescription is fulfilled.
• incandescent lamps usually transmit light into a pattern much bigger than a hemisphere, typically the entire sphere minus a small portion blocked by the filament support means or envelope sealing means.
• the prescribed illumination pattern is relatively narrow (e.g., Society of Automotive Engineers taillight standard with 40° pattern width)
• even refraction by two surfaces would be insufficient to redirect a 300° wide lamp output into such a narrow pattern.
• part of the lens would utilize total internal reflection (TIR) as well as refraction by an entry and an exit surface.
• TIR total internal reflection
• the second strategy amounts to having two independent sub-lenses acting in parallel to additively fulfill the illumination prescription.
• the reflecting surface requires its own exit surface, which must not block significant amounts of light from the source. Therefore, the exit surface should take the form of a conicoid with its apex at the light source.
• a conicoid is a warped cone, a developable surface consisting of lines radiating from its apex.
• lens 900 has central body 910 that is similar to the lens of Fig. 4 & Fig. 5, with light source 920. Surrounding it and extending from its periphery is conicoid surface 930 with its apex at source 920. Reflecting surface 940 extends downward from conicoid 930.
• the light-emitting diode in contrast, typically emits light into only a hemisphere, because of being mounted on larger objects, such as circuit boards. Also, its low operating temperature allows it to be in optical contact with a plastic lens, in the case of a relatively wide illumination prescription, such as the Coast Guard navigation lights. For the narrower-angle automotive lights, an entry surface may be necessary to redirect the light from the edge of the second grid to the edge of the first grid.
• the object of the present invention is to construct one or more lens surfaces.
• the first surface encountered by light from the source is given by
• r is the distance from the source to the lens surface, in the direction of ray vector I.
• Each lens surface must be shaped so that each ray vector encountering it is properly redirected: I into R (single surface) or I into T and T into R ,or T into
• i, j, and k are the Cartesian unit vectors defining the x, y, and z coordinate axes, respectively.
• This constraint can be utilized to check the fit of the generated surface to the array of surface normals.
• Surface curvature is measured by how fast the normal vector rotates, due to motion tangent to the surface. Except for a very few surfaces, such as spheres that have constant curvature, the surface curvature at a point varies with the tangent direction, according to a function known as the shape operator.
• the maximum and minimum values of the surface curvature define the principal curvatures, primary and secondary respectively. They lie in directions perpendicular from each other.
• the two orthogonal tangent vectors aligned to the principal curvatures, along with the surface normal vector, define the principal frame field. This is a triad of vectors that is defined for every surface point. Also known as the Darboux frame, it is very convenient for surface generation.
• the generation of the lens surface would typically begin at some initial point, r(0,0), and proceed outwards, generating an initial strip of surface (using the terminology of partial differential equations).
• the most accurate integration is obtained when the outward direction is chosen to coincide with the primary principal curvature (for example as seen in Fig. 4), so that successive changes of the normal vectors align with the initial strip. Along this principal curvature, the integration is one-dimensional and hence easier to perform.
• Another initial strip would be generated along the secondary principal curvature (for example as seen in Fig. 5). Then the surface is completed by successively generating characteristic strips parallel to the primary initial strip, beginning on successive sites on the secondary initial strip.
• the primary and secondary initial strips would be formed by integrations from initial point r(0,0) through r(l,0), r(2,0), etc., and from r(0,0) through r(0, l), r(0,2), etc., respectively.
• the prior strip if it is not an initial strip, can be checked point-by-point for fit to both sides, and adjusted according to the integrability constraints. Then, the characteristic strip could be regenerated from this new prior strip. This is known as a relaxation method.
• the surfaces are generated with the innermost surface first, and outwards in succession.
• the initial points for successive surfaces would be chosen so that the iteration does not collide with a prior surface. This may require several trials.
• the initial strip of reflecting surface 840 can be either upper rim 850 or lower rim 860.
• a lens design when a lens design is completed and checked for performance, it may need to be adjusted if its transmittance is anywhere significantly reduced by large angles of refraction. For example, at refractive index 1.5, the largest useable incidence angle from air into the material is 75°, where the transmittance is 75%, rather than the 96% of normal incidence. This is equivalent to a reduction in source intensity.
• the source grid would have its cells enlarged to accommodate this effect, and the lens would be recalculated with the modified grid. Similar adjustments can be made for scattering from surface roughness or from metal-film reflectivity of less than unity.
• the invention contemplates an illumination system with a prescribed output pattern comprising a light source and an optical lens redirecting the light of the source into an output beam, the lens with multiple surfaces, at least one of which has a shape that is not a surface of revolution, the shape generated by the following method:
• lens surfaces are generated from the distributions of normal vectors by the following method:
• the source is typically provided to be in optical contact with the lens, and the redirection is from within the lens material outwards into the environment, by refraction, with the distribution of surface normals determined by the vector form of Snell's law of refraction.
• the lens is provided to have an entry surface admitting light from the source into its interior and an exit surface for light leaving the interior; and the entry surface performs negligible redirection, and substantially the entirety of the redirection is performed by the external surface.
• the entry surface redirects the source light, so that a new system of interior rays is used to generate the surface normal distributions of both of the surfaces, with redirection allocated between the entry and exit surface normals.
• a reflecting surface may be provided, and wherein large redirection angles are implemented with the reflecting surface.
• the reflecting surface typically utilizes total internal reflection, which is preferable to thin film metal coating. The coating would only be necessary when the incidence angle is less than the critical angle arcsin (1/n) for refractive index n.
• An important application of the present invention is in large-scale video displays utilizing groups of individually controlled, light-emitting diodes: red, green, blue, and possibly yellow. Each group would have its own lens, similar to that of Figs. 4 & 5, but possibly somewhat smaller.
• a full video display, as for a sports stadium, would have 525 rows of 800 lenses, each with a group of LEDs. As shown in Fig.
• Lens 1101 and 1102 lie vertically staggered so that they do not obstruct each other's horizontally directed output.
• Lens 1101 is positioned over array 1110 of six LEDs: 2 red, 2 green, 1 blue, and 1 yellow.
• the lens has a horizontal swath of 120° and a vertical swath of 30°.
• An advantage over the prior art of large-scale television is that the curved surfaces of the lens disperse reflections from glare sources such as the sun.
• back surface 1120 would have a low reflectance means, such as a black matte coating.
• Fig. 12 shows multiple LEDs at 850-855, controlled as at their luminous intensities, as by a master control 856. They have different wavelengths, as for example two red-emitting LEDs 850 and 851, two green- emitting LEDs, as at 852 and 853, one blue-emitting LED 854, and one yellow-emitting LED 855.
• Each of the lenses in Fig. 10 typically has a light source consisting of the Fig. 12 LED cluster; and the LEDs are controlled, as to provide a viewable colored picture, changing with time.
• Bus 857 represents control signal path to other LEDs in the array.
• the multiple lenses or units indicated at 1120 are in an array, as shown (arranged in rows and columns), and may comprise a video screen for display of television or computer imagery, so that each of the lenses comprises a pixel of the display.
• Fig. 11 showing a video unit, same as a flat TV set 859 having a viewable screen 860 made up of the lens array or raster of Fig. 10.
• Fig. 13 shows the lens array 860 like that of Fig. 10, for example, which is shallowly curved to be effectively aimed at a specific audience location indicated at 861. Lenses at opposite ends of the screen are differentially angled to provide light outputs subtending the audience zone.
• the lenses in the array in Fig. 10 are mounted as on a surface 1150 of low reflectance, to provide the effective
• Fig. 14 shows a vessel 870 in plan view, incorporating lens units as described.
• the light sources shown may include incandescent lamps, at the LED locations described above, with a white light prescription for lenses.
• Lens 871 is a
• the lens has a horizontal cross section with a teardrop shape that eliminates shadowing of the filament of the lamp by support posts of the filament.
• the lamps 872 may have a substantially cylindrical filament in a vertical orientation.
• the prescription is the Coast Guard 135-degree stern navigation light; and the lens utilizes a reflective surface to redirect a portion of the output of the lamp into the prescribed output.
• Fig. 9a shows a luminaire, in accordance with the invention, and characterized by the following: a) a lens body 880 having a forwardly dome-shaped inner portion 880a, and an outer portion 880b extending about and spaced from the inner portion, the portions being light-transmitting and integral; b) the inner portion extending non-circularly about a forwardly extending axis 882; c) there being a reflector 883 on the outer portion, whereby a light source at 884 in rearward alignment with the inner portion provides certain light rays 885 that travel forwardly and are refracted by the dome-shaped inner portion to travel forwardly from the inner portion, and other light rays 886 that travel in the outer portion and are reflected by the reflector to travel forwardly in the outer portion and forwardly from the outer portion.
• the Fig. 9a luminaire may have the configuration of the Fig. 9 lens unit.
• the reflecting surface of reflector 883 is typically generated by the method that includes: a) partitioning the first grid into an inner refraction-only portion and an outer reflection-assisted zone, according to the maximum practical redirection angle of the refractive index of the material of the lens, and effect a co ⁇ esponding partition of the third grid of light interior to the lens, b) su ⁇ ounding the exterior surface of the central refraction-only portion of the lens, establish an outer conicoid portion of the exterior surface of the lens, the conicoid tilted so as to minimize the impingement upon it of rays coming directly from the source, c) via backwards ray tracing of refraction through the tilted surface, transform the outer portion of the first grid into a grid upon the Gaussian sphere of directions of light interior to the lens, d) establish a one-to-one correspondence between the partial grid of backwards-ray-traced light interior to the lens and the outer portion of the third grid, e) by the vector form
• the lens is further characterized as having a) TIR surface, b) mirror surface.
• Fig. 15 shows the generally ellipsoidal (elongated) top plan view outline shape of the Fig. 4 lens.
• N ⁇ 32 concentric rectangular subdivisions 710a, with a square-root size dependence, so that the zone between any pair of successive rectangles has an area equal to that of central rectangle 711.
• N ⁇ 64 radial lines 712 emanating from pole 713 of the grid, and terminating at points 712a with equal spacing
• the total number of defined cells as at 717 is N ⁇ N ⁇ , and in spite of their widely varying shape all have the same area lw/ N ⁇ N ,.
• a polar grid of an irregular shape will have its pole at the shape's centroid, and the instantaneous azimuthal spacing of the radial grid lines, at any point on the shape's perimeter, will be inversely proportional to the closest approach of the perimeter tangent to the pole, in analogy with the conservation of angular momentum in mechanics.
• the non-uniform radial spacing of the sides 714 and ends 715 of successive rectangles of a polar grid is due to the square root factor required for equal areas of the grid cells. This equality can be relaxed, however, when the cells of the source grid are varied in size to match. This is necessary to obtain equally spaced points on the surface of the lens, which is important for manufacturing accuracy.
• the grid is illuminated to produce a lens.
• Fig. 17 shows co ⁇ esponding source grid 720' on unit radius sphere
• first gap 723a between the pole and first colatitude line 722 shown as larger than succeeding concentric gaps 723.
• Changes in source light flux passing cell size co ⁇ espond to varying source intersection.
• Cells 724 are defined by successive circular lines 722 and successive longitudinal lines 725.
• Fig. 18 is like Fig. 17 but shows source grid 730' with uniform spacing ⁇ between successive colatitude lines 731. Successive cells transmit different light flux, i.e. increasing toward the equator.
• Fig. 19 shows the same, but adding corresponding target grid 740' projected onto unit sphere 741, and with projected rectangles 742 on the sphere distributed in size according to the encircle flux of their respective colatitude lines.
• the target grid is projected from a position only 6.5 inches above a 20 inch by 48 inch rectangular step.
• Fig. 20 depicts this step lighting situation for a cement stair 750 and having an overlying carpet 751.
• L-shaped moulding 753 is interrupted or configured to form recess 754 where the step light is located. See also the section of Fig. 20a, showing light uniformly projected at 756 onto the step 757, for step uniform lighting.
• the step light includes a lens defined or determined (generated) by a source grid as in any of Figs. 16-19. Figs. 19 and 20 may be considered prefe ⁇ ed.
• the a ⁇ ay of surface normal vectors required to transform the source grid into the output grid becomes a vector field N[r] when it is placed on the lens surface ⁇ ( ⁇ , ⁇ ), as expressed in spherical coordinates, azimuth ⁇ , and colatitude ⁇ .
• the array of surface normals N corresponding to the grids in Fig. 19 is depicted in Fig. 21 and is in fact i ⁇ otational because of the extreme obliquity of the lighting situation depicted in Fig. 20.
• the generated lens typically has discontinuities in order to express the surface normal vectors.
• Figs. 22 and 23 show views of the butterfly surface scalloped lens 760, with radial stepped or fluted segments 761, extending and diverging as shown from a contiguous central depressed or dished zone 765, and a conical base 763 for location of LED source at 764 in that base in alignment with the central depression 765 formed by the butterfly curved surface lens, and from which curved fluted or stepped segments 761 diverge.
• the steps at 761 are parallel to the light from the source.
• the edges of the flutes form ridges.
• the Fig. 22 lens may also be described as having radially associated segments, each segment having a characteristic light bending profile. The segments are shown to have curved, fluted configuration.
• Steps 761 are defined at boundaries between the curved flutes which extend in a succession of arching configurations. Further, the steps lie in planes containing the light source 764, or central pole.
• Fig. 23a shows a recess 768 in the conical base 763 to receive LED source unit 764, having a domed upper surface 769.
• FIG. 24 Another important application of the invention is fiber-optic lighting, for which a lens is coupled to the end of an illumination fiber in order to shape its circular output into a more useful form, such as a square or rectangle, especially from an oblique situation.
• a conical lens is shown in Fig. 24, with fiber 770, conical lens base 771, and ridged outer surface 772 which forms a square periphery illumination output.
• the outer surface 772 of the lens has four ridges 773 diverging from a center 774 in alignment with 770.
• Surface 772 is dished over each of the four pie-shaped segment surfaces 772a — 772d, as shown.
• This lens configuration changes the circular periphery light beam in 770 into a square periphery beam, from surface 772.
• the dishing of the surface at multiple locations from a modified butterfly surface shape.

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• Physics & Mathematics (AREA)
• General Physics & Mathematics (AREA)
• Optics & Photonics (AREA)
• Lenses (AREA)
• Non-Portable Lighting Devices Or Systems Thereof (AREA)

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• 2000
  • 2000-11-14 AU AU2001230828A patent/AU2001230828A1/en not_active Abandoned
  • 2000-11-14 EP EP00991028A patent/EP1334395A4/de not_active Withdrawn
  • 2000-11-14 JP JP2002542931A patent/JP2004526222A/ja active Pending
  • 2000-11-14 CA CA002428696A patent/CA2428696C/en not_active Expired - Fee Related

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