Abstract:
A nonimaging optical system for processing a first and second light distribution. The nonimaging optical system includes at least two refractive surfaces, at least one reflective surface nearer to the first light distribution along at least one ray path than the nearer of the two refracting surfaces and the reflective surface and the refractive surfaces cooperating to redirect light edge rays of the first light distribution into the neighborhood of the edge of the second light distribution with a single reflection from the reflecting surface.

Description:
BACKGROUND 
   High efficiency light collection is important in a number of applications, including lighting and illumination, displays, document scanning and machine vision, signalling, aviation and automotive lighting, medical instrumentation, infrared and optical wireless communications, and signal detection. Typically a light collection optical system is needed to convert a first spatial and angular distribution to a second, different spatial and angular distribution. Very commonly the collector couples light from a small, wide-angle source to a larger more collimated beam. It is generally desirable that such light collectors couple the highest possible fraction of light into the desired aperture and angles, with minimum size and cost. 
   Various light collectors are known in the art. Spherical lenses, aspheric lenses, and combinations of parabolic, elliptical, and hyperbolic mirrors have been used for centuries. Most of these systems are “imaging,” meaning that the surfaces are designed to redirect light from a central point or angle in the first distribution to a central point or angle in the second distribution. Light from points or angles near enough to the center point or angle in the first distribution is, by similarity, redirected into the neighborhood of the center point or angle in the second distribution, with the same number of reflections or refractions for almost all the rays of interest. Unlike the central rays, the non-central points and angles are only approximately redirected into each other. Therefore control over the edges of the distributions is typically limited, and one of the light distributions often spreads over larger areas or angles than is desired, with non-uniform beam output and gradual rather than sharp angular cut-off. Control is particularly limited when one of the distributions has very large angles, or when the spatial extent of the smaller distribution is not much smaller than a characteristic length scale of the collector. 
   More recently introduced are “edge-ray” collectors which are designed to redirect the rays at the spatial or angular boundary of the first distribution to a spatial or angular boundary of the second distribution. It can be shown that, when distribution boundaries are so coupled, the rays in the interior of one distribution will then be coupled into the interior of the other distribution. However, different portions of the interior typically have a different number of reflections or refractions from each other or from the edge. In undergoing these different numbers of reflections or refractions, adjacent portions of the first distribution may end up non-adjacent in the second distribution, and therefore these collectors are “non-imaging.” These non-imaging collectors provide much more precise control over the spread of the light distributions, typically maintaining both distributions within their theoretical limits even for large-area or large-angle beams that are poorly handled by imaging collectors. This more precise control is often desirable for the applications described above. Typically for these collectors opposite surfaces are designed to redirect opposite edges of the distribution. 
   Simple imaging collectors are typically very compact: for example, a parabolic mirror with ±90° light collection has a length-to-diameter ratio (“aspect ratio”) of 0.25. By comparison, many non-imaging designs are undesirably U.S. Pat. No. 4,240,692 describes a non-imaging concentrator known as a Compound Parabolic Concentrator (CPC). The CPC is a hollow, funnel-shaped, mirror that redirects rays from a spatial edge at its small end into the angular edge of a beam at its large end. For narrow-angle beams, the CPC is undesirably long: for example, the aspect ratio of a ±10° CPC is over 3. The CPC can be truncated to reduce the length, but then efficiency is reduced or the spread of the light distribution is increased. 
   This aspect ratio has been reduced by a class of collectors using one refractive surface with a funnel-shaped reflective light-pipe. For example, U.S. Pat. No. 4,114,592 shows an alternate edge-ray collector known as a Dielectric Total Internal Reflection Concentrator (DTIRC) that uses a spherical refracting front surface. This improvement reduces the aspect ratio of a ±10° collector to approximately 1.7. U.S. Pat. No. 5,285,318 improves on the DTIRC by using an aspheric instead of a spherical refracting surface, reducing the ±10° aspect ratio to about 1.3. Friedman and Gordon published a further improvement in “Optical designs for ultrahigh-flux infrared and solar energy collection: monolithic dielectric tailored edge-ray concentrators,”  Applied Optics , Vol. 35, No. 34, 1 Dec. 1996, pp. 6684–91. They showed that with a different aspheric refracting surface the ±10° aspect ratio could be reduced to about 1.2, and that this was the theoretical limit with a single refraction at the front surface. Moreover, these designs require very thick dielectric components, which are difficult to mold accurately at low cost. 
   Minano and co-workers have published several designs that combine one refractive surface and one or more reflective surfaces. These designs reduce the aspect ratio to approximately 0.25; but in all these designs the small aperture is placed in front of a large back-reflecting mirror, so that the small aperture obstructs the large aperture. When the apertures are very different in size, as for narrow-angle collimators, the area ratio is low; and the obstruction can be small, but for larger angles the obstruction is unacceptable. Moreover, these collectors are often undesirable when a source or detector at the small aperture needs to be supported by a substrate including a circuit board or heat sink, as is common with high power LED light sources, for example. Minano and co-workers have also published designs with two refracting surfaces and no reflecting surfaces, but the largest collection angle at the small aperture is limited. 
   The current invention uses an aspheric dielectric lens with two refracting surfaces at the large aperture of a hollow, funnel-shaped reflector. The back surface of the dielectric (the surface facing the reflector) has higher curvature than the front surface, making the structure more compact. This approach achieves performance comparable to a non-truncated CPC, with much better compactness. Aspect ratios range from 0.4–0.75. Moreover, the dielectric lens has acceptably low thickness for cost-effective molding. Unlike the Minano designs, the small aperture of the funnel is advantageously positioned behind the optic, so that a source or detector can be supported by a much larger circuit board or heat sink without shadowing. Winston and co-workers have published designs with a spherical lens and funnel-shaped reflector, including U.S. Pat. No. 5,243,459, but these designs are not nearly as compact as the current invention. 

   DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
   One embodiment of an optical system shown generally at  10  in  FIG. 1  with operation is the collector mode. The figure shows a cross-section with a large aperture  12  on the right coinciding with a front-surface distribution  14  having an angular range ±θ, where the rays at +θ and −θ are angular edge-rays.  FIG. 1  also shows a small aperture on the left  16  coinciding with a back-surface distribution  18  having a bottom edge  20  and a top edge  22 . The spatial extent of the back-surface distribution  18  can be smaller than or equal to the extent of the small aperture  16 . In one embodiment, the optical system  10  is a surface of revolution of the cross-section shown, so that the input and output apertures  16  and  12  are circular. In a second embodiment, it can be a trough-shaped element continuing this cross-section perpendicular to the plane of the page. In a third embodiment, the optical system  10  has four or six similar sides connecting to form square or hexagonal input and output apertures. 
   The optical system  10  cross-section shown is designed to transform a large ±15° beam  14  into a smaller ±90° beam  18 . The rays  24  shown are edge rays, entering the lens  26  at −15°, the boundary of the desired front surface distribution  14 . The front surface  28  of the lens  26  is flat. The back surface  30  of the lens  26  is sloped and curved. In  FIG. 1 , the cross-section shows the back surface  30  having a bottom arm  32  and a top arm  34  on opposite sides of the centerline  33 . The back side bottom arm  32  is shaped and angled to redirect the edge rays  24  striking that one side approximately to the top edge  22  of the back-surface distribution. It will be appreciated that opposite edge-rays at +15° (not shown) striking the back surface top arm  34 , by symmetry, would be redirected approximately to the bottom edge  20  of the back-surface distribution. Therefore, necessarily, the −15° edge-rays  24  striking the back surface top arm  34  cannot also be redirected to the back-surface distribution edge  20  by refraction alone. The reflector surface  36  fills this function. The reflector top arm  38 , as shown, is shaped to redirect the −15° edge-rays  24  that strike it to the bottom edge  20  of the back-surface distribution. By symmetry, the +15° edge-rays (not shown) that strike the bottom arm of the reflector  40  would be redirected to the top edge  22  of the back-surface distribution. Thus the lens  26  and reflector  36  act cooperatively to redirect substantially all the angular edge-rays  24  into the neighborhood of the edges  20  and  22  of the back-surface distribution  18 . The collector  10  is etendue-preserving: i.e., the first and second beam distributions  14  and  18  approximately satisfy the equation
 
n 1 D 1  sin θ 1 =n 2 D 2  sin θ 2   (1)
 
In  FIG. 1 , for example, θ 1  is the front surface angle=θ=15° and θ 2  is the maximum back-surface angle=90°.
 
   The refractive surfaces can have a variety of shapes. In  FIG. 1 , the lens front surface  28  is flat and the back surface  30  is a single hyperbola. In another embodiment, the back surface is a compound hyperbola: the bottom and top arms  32  and  34  are opposing, oppositely tilted off-axis hyperbolas. When the front surface  28  is flat, as in  FIG. 1 , the off-axis hyperbola  32  has an axis parallel to the segments  35  of the edge-rays  24  interior to the lens  26 , so that the bottom arm  32  redirects the ray segments  35  to focus substantially near the edge  22  of the back surface distribution. 
   The hyperbola  32  has eccentricity=n=the index of the lens material (1.49 for PMMA plastic in  FIG. 1 ). The focus of the hyperbola is the edge  22  of the back-surface distribution. 
   The parameter l is chosen such that the curve intersects the desired outer edge position  42  of the lens aperture  44 , giving the lens  26  the desired aperture diameter and placing it at the desired distance from the back-surface distribution  18 . In  FIG. 1 , the back surface  30  is a single conic with parameters chosen to best-fit the off-axis hyperbolas. As will be apparent to one skilled in the art, the surface shapes  28  and  30  can be varied slightly as long as the overall slope changes are sufficiently small that the surface  32  continues to redirect the angular edge-rays  24  approximately to the edge  22  of the back-surface distribution as shown. 
   The reflector  36  in  FIG. 1  can likewise have a variety of shapes, so long as it redirects the angular edge-rays  24  approximately to the bottom edge  20  of the back-surface distribution as shown. The shape may be calculated once the lens shape is determined. This shape could be designed to focus the edge-rays exactly, by solving numerically for the slope and position at each point (i.e., by solving the appropriate differential equation), or by solving an equal-optical-path-length equation. Alternatively, the reflector  36  can focus the edge-rays  24  only approximately at the bottom edge  20  of the back-surface distribution, either by solving a slightly different differential equation or path length equation, or by iteratively optimizing a polynomial or conic section. The reflector  36  in  FIG. 1  is an off-axis conic section. 
     FIG. 2  shows another embodiment of the optical system  10 , in which the front-surface angular edge-rays  24  at −θ 1  are redirected to the extreme angles of the back-surface distribution  18  +θ 2  (shown at  46 ) and −θ 2  (shown at  48 ), rather than to a spatial edge of the back-surface distribution  18  as in  FIG. 1 . In this case θ 1  and θ 2 , along with the associated spatial diameters, approximately satisfy equation (1). The reflector  36  can also be a compound reflector, in which a front portion of the reflector  36  focuses the edge-rays  24  to the bottom  20  of the back-surface distribution as in  FIG. 1 , and a back portion focuses the edge-rays  24  to a maximum angle  46  as in  FIG. 2 . 
     FIG. 3  shows another embodiment (for simplicity the reflector is not shown). In this embodiment each back surface arm  32  and  34  is a combination of off-axis hyperbola and logarithmic spiral. The inner portion  46  of each arm (closest to the centerline) is a hyperbola as described above. The outer portion  48  is a logarithmic spiral, with the equation in the same coordinate system described above:
   r (φ)= r   0   e   (φ−φ     0     )tan θ     imax     (2) 
   Since the logarithmic spiral is the outer section, the parameters r 0  and φ 0  are chosen to provide the desired diameter and position. The parameter θ imax  is the angle of incidence made by the edge-rays  24  with the lens surface  48  in the medium (usually air) between the lens  26  and the reflector. The designer may limit this angle to minimize Fresnel reflections. The inner section  46  of each arm is an off-axis hyperbola as described above, but now the parameter l is chosen to provide a continuous surface with the outer logarithmic spiral section  48 . 
   In the embodiment of  FIG. 3  the front surface  28  of the lens  26  is likewise two sections. The outer portion  50  is designed to cooperate with the log spiral portion  48  of the back surface to refract the angular edge-rays  24  to the edge  20  of the back-surface distribution as described previously. This portion  50  could be designed by solving numerically for the slope and position at each point, by solving an equal-optical-path-length equation, or by iteratively optimizing a polynomial or conic section. The inner portion  52  of the front surface is flat. The edge rays  24  striking this flat inner portion  52  are redirected to the inner, off-axis hyperbola portion  46  of the back surface. 
   In  FIG. 3 , θ imax =70° and is held constant; but θ imax  could also be varied across the surface without changing the essential focusing of the angular edge-rays  24  onto the back-surface distribution edge  20 . The compound back surface  34  can also include a flat central section, to simplify the optics by avoiding having a cusp at the center  54 , and increase manufacturability. 
   The refractive component  26  can be made of a variety of materials. In  FIG. 1  the lens material has index 1.49, as for PMMA (also known as acrylic) that is commonly used for molded optical parts. Other materials such as glass and polycarbonate can also be used, as long as the material is substantially transparent to the wavelengths of interest. Higher-index materials increase the overall compactness, and can also affect the cost, reliability, manufacturability, or mechanical properties of the device. The lens  26  shown in  FIG. 3  uses polycarbonate with index approximately 1.59. The small-aperture-to-lens distance is accordingly smaller than would be obtained with PMMA. The material can be formed to the desired shape by one or more processes of molding, machining, or casting. 
   The reflector  36  can be any solid material including plastic, glass, ceramic, or metal, provided that inner surface is given an approximately specular finish and has a high reflectivity for the wavelengths of interest. The material can be formed to the desired shape by one or more processes of molding, machining, or casting. For materials that lack intrinsically high reflectivity, the surface  36  can be coated with high-reflectivity materials, for example aluminum. The inner surface can also have a transparent protective coating to increase the robustness and lifetime of the reflectivity. 
   Compactness is a critical advantage of the current optical system  10 , and there are a number of design modifications that can be introduced to reduce the size. The focus of the edge-rays  24  onto the back-surface distribution edge  20  or  22  can be approximate, as shown in  FIG. 1 , rather than exact as in  FIG. 3 . Likewise, the angles of the angular edge-rays  24  at the large aperture could be varied to reduce the required curvature, particularly at the outer portion where the largest refraction is required. 
     FIG. 4  shows a further embodiment of the optical system  10 , in which the front refractive surface is overlaid with a diffuser layer  54 . The diffuser layer  54  redirects a ray from a single angle θ into a spread of angles θ±Δθ. The diffuser improves the uniformity of the light output distribution.  FIG. 5  shows an example  56  of a light output distribution measured with ( 62 ) and without ( 64 ) a diffuser  54 . In the device used to make this measurement, the back-surface distribution  18  is the light output of an LED array placed at the small aperture. The measurement shows the front-surface output  14  vs. far-field angle. Without the diffuser  54 , the output light has exceptionally sharp cut-offs  58 , but also has noticeable non-uniformities  60 . In the measurement of  FIG. 5  the non-uniformities  60  are especially pronounced because the LED array source is non-uniform. The diffuser  54  removes the non-uniformities  60  and also softens the angular cut-off  66 . In most cases a more uniform beam is advantageous. In general it is desirable to maximize uniformity while maintaining sharp as possible angular cut-off, but in some cases a softer cut-off is advantageous as well. Different diffusers will provide different uniformity vs. cut-off trade-offs. In general a diffuser with larger Δθ will improve the uniformity more, but will also soften the cut-offs more. 
   The exact nature of the diffuser will determine the trade-off, and also other characteristics of the output as well. Other desirable features of a diffuser are high transmission efficiency, and a low degree of scattering into large angles beyond the desired Δθ.  FIG. 5  was measured with a high-quality holographic diffuser. Such diffusers provide high (90% or greater) transmission efficiency, low scattering, and provide an excellent maximum uniformity enhancement for a given angular cut-off. Other types of diffusers known in the art include random rough-surface diffusers, microlens diffusers, and lenticular diffusers. All of these diffusers can be cost-effectively manufactured by embossing or casting a polymer film or sheet with an appropriate surface pattern. For example, holographic diffusers can be made by creating a holographic surface pattern in a metal tool and using the tool to emboss or cast a polymer film. 
   In a further embodiment the diffuser  54  can be an “elliptical diffuser” that redirects light into an asymmetrical distribution. For example, a ray at θ can be redirected into ±Δθ H  in the horizontal direction and ±Δθ V  in the vertical direction. The resulting light output distribution can then be larger in one axis than in the other. For example, a wider horizontal distribution is often desirable for lighting a display arranged on a horizontal surface. 
   An advantage of using a separate polymer film  54 , as in  FIG. 4 , is that multiple beam patterns can be obtained without changing the shape of the optic. For example, multiple patterns can be obtained from a single set of optic molds, enabling the supplier to offer multiple options without incurring the tooling cost associated with multiple mold sets. Another advantage is that the user can buy a single light source with optic and multiple diffusers, and then change the beam pattern in place by substituting different diffusers. 
   However, adding a separate diffuser layer  54  to the assembly also increase per-unit cost and potentially reduces reliability. In a further embodiment, uniformity enhancing features can be added to the reflective or refractive surfaces  36 ,  28 , and  20  of the optical system  10 . These features can include facets, roughness, or a holographic diffuser pattern. In a preferred embodiment, a holographic diffuser pattern is added to the mold surface that forms the front refractive surface  28 . 
   A highly preferred feature of the invention is the presence of an aspheric back refractive surface together with a front refractive surface and at least one funnel-shaped reflective surface, all three surfaces acting cooperatively to redirect edge-rays from a first distribution into edge-rays of a second distribution. An advantageous feature is that the two distributions approximately satisfy the etendue-preservation equation in equation (1). An additional advantageous feature is the higher curvature of the back refractive surface, causing the lens to protrude substantially back into the funnel-shaped reflector to maximize the compactness of the device. Another advantageous feature is the addition of at least one uniformity-enhancing feature, such as a holographic diffuser surface. 
   While preferred embodiments of the invention have been shown and described, it will be clear to those skilled in the art that various changes and modifications can be made without departing from the invention in its broader aspects.