Abstract:
One optical system comprises a first optical surface, a faceted second optical surface, and a faceted third optical surface. The optical system is operative to convert a first bundle of rays that is continuous in phase space outside the first optical surface into a second bundle of rays that is continuous in phase space outside the third optical surface. Between the second and third optical surfaces the rays making up the first and second bundles form discrete sub-bundles each passing from a facet of the second optical surface to a facet of the third optical surface. The sub-bundles do not form a continuous bundle in a phase space that has dimensions representing the position and angle at which rays cross a surface transverse to the bundle of rays.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application claims benefit of U.S. Provisional Patent Application No. 61/274,735, filed Aug. 20, 2009, which is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     Stepped flow-line optics (SFL) were first developed at the turn of the century [Refs. 1-3] and rapidly found applications in the design of backlights [Refs. 4, 5], optics for combining light sources or efficiently distributing light to several locations [Refs. 6-10]. 
     These optics are characterized by having a lower optic (light distributor) which collects the light from a source and distributes it over a given base surface. The bundle of rays coming from the source and redirected by the light distributor generates a field of flow-lines at the base surface. The design process then continues by following a flow-line, then moving across the flow-lines, then following another flow-line, then moving across them, and so on. Each portion of etendue contained between two consecutive flow lines that are followed by this stepped construction is then controlled by a separate (small) optic. This design method is then characterized by “breaking” the incoming light bundle at the base surface in small portions, each one controlled by a separate (small) optic. This process is such that it is possible to later recombine all these portions, rebuilding the continuity of the entire bundle seamlessly. Examples of optics in which this recombination process occurs and does not occur have been proposed [Ref. 3]. For example, this recombination process does not occur in the optics that combine the light from different light sources onto a single exit aperture. In general, the supporting surface may be flat or curved, open or closed (such as a cylinder) [Refs. 2, 3]. 
     In certain of the configurations disclosed here, the seamless recombination of the bundle always occurs. One component of these devices is then the light distributor (lower optic) which distributes the light from the source on the base surface. The other component is made of many small optics constituting an upper optic (microstructure). Each one of these small optics is a microstructure element. 
     The optical surfaces of each microstructure element may be close together or far apart, creating different types of configurations. In the first case, the microstructure is very thin compared with the overall thickness of the optic. In the second case, the distance between the surfaces of each microstructure element is much larger than their size, one set of surfaces following the base surface and another set of surfaces following another surface, such as the entrance aperture. 
     It is the object of embodiments of optical devices proposed in the present specification to enable the design process to introduce many discontinuities in the light bundle, and then to eliminate those discontinuities further down the optic. By contrast, today&#39;s aspheric design methods only allow a single discontinuity to be introduced in the surfaces generated [Ref 11]. 
     SUMMARY OF THE INVENTION 
     One aspect of the invention provides an optical system comprising, in order: a first optical surface; a faceted second optical surface; and a faceted third optical surface; wherein the optical system is operative to convert a first bundle of rays that is continuous in phase space outside the first optical surface into a second bundle of rays that is continuous in phase space outside the third optical surface; wherein between the second and third optical surfaces the rays making up the first and second bundles form discrete sub-bundles each passing from a facet element of the second optical surface to a facet element of the third optical surface, and the sub-bundles do not form a continuous bundle in phase space; wherein the phase space has dimensions representing the position and angle at which rays cross a surface transverse to the bundle of rays. 
     As will be seen from the more specific embodiments described below, many embodiments are substantially reversible. Most of the described embodiments act as concentrators in one direction and as collimators in the other direction. In many of these embodiments, when acting as a collimator the first optical surface acts as a distributing surface, supplying light to the second surface, which then forms a splitting facet structure or microstructure, and the third surface then forms a combining facet structure or microstructure. However, when the same optical system is used as concentrator, the functions of the splitting and combining structures are interchanged, and the “distributing surface” actually acts as a gathering surface. In general, therefore, terminology used in this specification that relates to light flowing in a specific direction is to be understood broadly as including the converse function for light flowing in the opposite direction. 
     Another aspect of the invention provides an optical system comprising, in order: a first optical surface and a faceted second optical surface; wherein the optical system is operative to convert a first bundle of rays that is continuous in phase space outside the first optical surface into a second bundle of rays that is continuous in phase space outside the second optical surface; wherein between the first and second optical surfaces the rays making up the first and second bundles form discrete sub-bundles passing from a facet of the second optical surface to the first optical surface, and the sub-bundles do not form a continuous bundle in phase space. 
     Another aspect of the invention provides an optical system comprising a faceted first optical surface and a second optical surface; wherein the optical system is operative to convert a first bundle of rays that is continuous in phase space outside the first optical surface into a second bundle of rays that is continuous in phase space outside the second optical surface; and wherein the faceted first optical surface is so configured that light entering the system from a defined light source fully flashes the exit aperture of the system. 
     Another aspect of the invention provides an optical system comprising a source or receiver, a faceted light-splitting optical surface, a distributing optical surface directing light between the source or receiver and a faceted light-splitting optical surface, and an exit aperture on the side of the light-splitting optical surface optically remote from the source or receiver, wherein light rays from the source or receiver directed by the distributing and light-splitting optical surfaces fully flash the exit aperture, and form at the exit aperture a ray bundle with edge rays from two wavefronts. 
     Embodiments of that aspect further comprise a faceted light-combining optical structure, wherein the faceted light-splitting and light-combining optical surfaces cooperate such that light forms discrete bundles between the faceted light-splitting and light-combining optical surfaces and forms continuous bundles outside those surfaces. 
     In certain embodiments, as shown by way of example in  FIGS. 1 ,  13 A, and  13 B, the rays of said ray bundle at each point of the exit aperture form a triangle in two dimensions or a cone in three dimensions, having edge rays from said two distinct wavefronts. 
     In certain embodiments, especially in an embodiment where the optical system is a solar photovoltaic collector, and the receiver is a photovoltaic device, the cones of rays for all points of the exit aperture may have parallel axes and equal cone angles. The size of the cone angle is then chosen to accommodate the angular size of the sun (cone half angle approximately ¼ degree as seen from Earth) plus an appropriate tolerance for errors in aiming the concentrator at the sun. A similar optical configuration in a collimator can produce a narrow beam from a light source. In other embodiments, the cone angle and/or the direction of the cone axis may vary over the exit aperture to produce a different light emission or acceptance pattern. 
     In an embodiment, the criterion for sub-bundles that do not form a continuous bundle in phase space is that it is not possible to move from one such sub-bundle to another such sub-bundle by continuously varying the phase-space coordinates without passing through a region in phase-space that does not belong to any sub-bundle. The corresponding criterion for a continuous bundle in phase space is that it is possible to move throughout such a continuous bundle by continuously varying the phase-space coordinates without passing through a region in phase-space that does not belong to the bundle. It is desirable, but not essential and in many practical embodiments not achievable, for the phase space representation of the recombined bundle to be free from holes. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other aspects, features and advantages of the present invention will be apparent from the following more particular description thereof, presented in conjunction with the following drawings wherein: 
         FIG. 1  shows an upper optic for a stepped flow-line concentrator. 
         FIG. 2  shows a stepped flow-line concentrator (or collimator) resulting from combining several upper optics with one lower optic. 
         FIG. 3  shows the mold for extruding the upper optics of the concentrator in  FIG. 2 . 
         FIG. 4  shows a stepped flow-line concentrator (or collimator) composed of two optics united by a layer of low refractive index material. 
         FIG. 5  shows a similar optic to the one in  FIG. 4 , but now with a constant thickness for the whole optic. 
         FIG. 5A  shows an optic such as the one in  FIG. 5  but with a horizontal receiver. 
         FIG. 5B  shows a variation in the configuration of the  FIG. 5  optic. 
         FIG. 6  shows a 3D view of an optic with V shaped surfaces along the flow lines of the lower optic, extraction steps and corresponding “lenses” on the upper optic that collimate the reflected light at the steps. 
         FIG. 7  shows the optic of  FIG. 6  with the upper optic fully covered with “lenses”, one for each step on the lower optic. 
         FIG. 8  shows an array of elements, forming the complete lower optic. 
         FIG. 9  shows an optic similar to the one in  FIG. 6 , but for a tighter collimation. 
         FIG. 10  shows another possible design for the lower optic, with surfaces following the flow lines and steps crossing them and extracting the light. The complete lower optic is composed of an array of similar elements. 
         FIG. 11  shows part of the lower optic of  FIG. 10  with the corresponding “lenses” covering the upper optic. 
         FIG. 12  shows a diagrammatic view of a compact concentrator. 
         FIG. 13A  is a close-up view of a pair of upper optic elements. 
         FIG. 13B  shows another view of the optic of  FIG. 13A  with different output wavefronts. 
         FIG. 13C  shows a complete upper optic combined with a lower optic. 
         FIGS. 14-21  show variations of the assembly of  FIG. 13C . 
         FIG. 22  shows a mirror generating a given light distribution on a given line for the case of a point source. 
         FIG. 23  is a diagram similar to  FIG. 22  for a case of an extended source. 
         FIG. 24  shows a concentrator utilizing those reflecting elements. 
         FIG. 24A  shows an axial section through a concentrator with circular symmetry. 
         FIG. 25  shows a similar optic for imaging applications. 
         FIG. 26  shows a similar optic, but with integrator elements. 
         FIG. 27  shows a compact optic with different ray trajectories. 
         FIG. 28A  shows a single piece compact optic. 
         FIG. 28B  shows to a larger scale part of an optic similar to that of  FIG. 28A . 
         FIG. 29  shows a single piece compact optic with a central converging lens. 
         FIG. 30  is a diagram illustrating a further method of designing an optic. 
         FIG. 31A  shows an axial cross section through an optic according to the design method of  FIG. 30 . 
         FIG. 31B  shows a further axial cross section through the optic of  FIG. 31A . 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     A better understanding of various features and advantages of the present invention will be obtained by reference to the following detailed description of the invention and accompanying drawings, which set forth illustrative embodiments in which certain principles of the invention are utilized. 
       FIG. 1  shows the geometrical definition of an upper optic of a first embodiment. The insert on the right shows a detail of the mid section of the optic and the paths of some light rays. Cartesian oval  101  concentrates to point  102  the parallel rays  103  perpendicular to flat wavefront  104 . Wall  105 , starting at one edge of Cartesian oval  101 , concentrates to point  102  a first portion of light rays emitted from point  106 , at one edge of bundle of parallel rays  103 , and propagated through Cartesian oval  101 , as shown by exemplary ray  107 . Wall  108 , continuing on from wall  105 , reflects a second portion of light rays emitted from point  106  and propagated through  101 , so that those rays proceed in a direction perpendicular to flat wavefront  109 . This is the case, for example, of ray  110 . These rays then reflect on wall  111  towards the top surface  112  where ray  110  is refracted in a direction perpendicular to flat wavefront  113 . Wall  114 , continuing from wall  111 , concentrates light rays perpendicular to flat wavefront  116 , after refraction at the top surface  112 , to point  115  (propagating in the opposite direction from the rays previously discussed). This is the case, for example, of ray  117 . Wall  118 , continuing from point  115 , reflects to point  102  a further portion of the light rays perpendicular to wavefront  116 . This is the case of exemplary ray  119 . Between point  120 , at the end of Cartesian oval  101  further from wall  105 , and point  102  there is no optical wall, so that section of wall may be defined using some other criteria (as long as this wall is above the straight line connecting points  120  and  102 ). 
       FIG. 2  shows a combination of optics like the one in  FIG. 1  into a stepped flow-line concentrator. The top portion of the side surfaces  114  and  118 , closest to top surface  112 , has little optical effect, so part of them was removed so that several of these optics can be combined into a single piece. This resulting single piece is upper optic  201 . It is combined with lower optic  202 , which is a parabolic mirror. The receiver is at flat surface  203 , extending from the pole to the focus of the parabolic mirror. Surfaces  204  on the upper optic, corresponding to the section between points  102  and  120  in  FIG. 1 , are non-optical. Parabolic mirror  202  has focus  205  and axis parallel to parallel rays  206 , corresponding to rays  103  in  FIG. 1 . The optics are aligned so that ray  103  or  206  from the upper end  120  of Cartesian oval  101  of one optic just passes the lower end of Cartesian oval  101  of the next optic. Cartesian ovals  101  of  FIG. 1  are combined in  FIG. 2  to form a discontinuous faceted surface. Top surfaces  112  of  FIG. 1  are combined in  FIG. 2  to form a faceted surface. A larger number of optics can be combined in the upper optic. In that case, the lower optic and receiver must be scaled accordingly (their shape does not change, only their size changes). 
       FIG. 3  shows an example of a mold  301  for extruding the upper optic  201  of  FIG. 2 . The upper optic  201  is then uniform and of indefinite length perpendicular to the plane of  FIG. 2 . The light rays shown in  FIG. 1  may then be projections onto the plane of  FIG. 1  of rays that are oblique to that plane. The number of linked cavities in the mold of  FIG. 3  may be varied in order to vary the number of linked optics in the upper optic  201  of  FIG. 2 . 
       FIG. 4  shows a collimator for a source  401 . The collimator is composed of two parts: a lower optic  402  and an upper optic  403 , separated by a layer of low refraction index material  404  (which may be air). The lower optic is a piece of solid, transparent material (dielectric) bounded by the low refractive index material  404  at the top and by a stepped flow-line at the bottom. This stepped flow-line is composed of lines  406  that follow the flow lines and ejectors  407  that cross the flow lines. Light enters the lower optic confined to an angular aperture  405  and travels inside it confined by total internal reflection (TIR) between the bottom surface lines  406  and the low refraction index layer  404 . As it travels, this light encounters mirrors  407 , which cross the flow lines, and reflect light upwards towards the upper optic. This reflected light can cross the low refraction index layer  404  because the angle of incidence it forms with the low refraction index layer  404  is not enough for TIR. This reflected light is then collimated by lenses  408 , exiting the optic with collimation in the vertical direction. Mirrors  407  and lenses  408  may also be designed simultaneously using, for example, the SMS design method. In general the mirrors  407  will be curved. 
     When designing with the SMS method for 2 surfaces, two input and two output bundles of rays have to be prescribed. The SMS method provides the profile of the two optical surfaces that couple the input bundles to the output bundles. In this case, the two surfaces to design are the lenses  408  and the mirrors  407 . The two input bundles can be selected as the two edge ray bundles coming from the source, i.e., the two bundles travelling inside the lower optic  402  with the maximum angles with respect to the flow lines  404 ,  406 . The two output bundles are the two edge ray bundles defining the collimation after refraction at the lenses  408 . In general, lenses  408  are different from each other, and mirrors  407  are different from each other. 
     The SMS is not the only possible design method. Another possibility is, for instance, to design lenses  408  to form a good image of the edges of mirrors  407 , and to design the mirrors  407  to cast the light inside their corresponding lenses. This design is of interest for those applications needing a sharp cut-off of the illumination pattern, such as automotive applications. 
     As in all other cases,  FIG. 4  can also be used as a light concentrator, in particular for photovoltaic applications, replacing the source  401  by a solar cell and facing the vertical direction towards the sun. 
       FIG. 5  shows a similar optic to the one in  FIG. 4 , but in which all mirrors  506  of the lower optic are now at the same level, with the flow line surfaces sloping down from the top edge of each mirror  506  to the bottom of the next mirror. Lenses  505  are all also at the same level, and therefore at the same distance from their respective mirrors  506 . The lenses  505  all have the same focal distance. This allows the use of the same lens and the same mirror design for the whole array. The upper and lower optics are separated by low refraction index layer  504 , which is parallel to the flow lines of collimated light and sloping relative to the levels of lenses  505  and mirrors  506 . Light comes from a source  502 , enters the optic confined to an angular aperture  503  and leaves the optic collimated around the vertical direction. 
     In this and similar embodiments, the reflective surface formed by low refraction index layer  504  and the discontinuous reflective surface  507  together form a first optical surface (distributor surface if  502  is a source, collector surface if  502  is a receiver). Facets  506  form a discontinuous, faceted second optical surface, and facets  505  together form a faceted third optical surface with a discontinuous first derivative (cusped or kinked). 
       FIG. 5A  shows the same optic as  FIG. 5 , but now also shown is a revolution axis  5 A 01 . Revolving the optic around this axis results in a device with circular symmetry. “Black hole” optic  5 A 03  collects the light coming in radially from all sides and concentrates it onto receiver  5 A 02 . 
       FIG. 5B  (not to scale) shows an optic similar to the one in  FIG. 5 , but with curved elements in the lower optic  5 B 01 . Now there is no air gap between source  5 B 06  and the optic. Upper optic  5 B 02  is covered by an array of lenses  5 B 03 . These two optics are separated by a layer of low refractive index material  5 B 04  shaped as a parabola with focus  5 B 05  at the edge of the source  5 B 06  and axis parallel to the flat flow-lines  5 B 07 . As it travels inside the lower optic, light is confined (by TIR) between layer  5 B 04  and flow lines  5 B 07  and extracted by steps  5 B 08  (crossing the flow lines) towards the lenses  5 B 03  on the upper optic, which lenses collimate this light as it exits the device. Portion  5 B 09  of the top surface of the lower optic is part of the same parabola as  5 B 04  and needs to be mirrored since TIR will not occur at this surface close to the source  5 B 06 . The lower optic is completed with circular arc  5 B 10  centered at edge  5 B 05  of the source  5 B 06 . This geometry with a parabolic separation between upper and lower optics minimizes the number of reflections inside the lower optic (and has flat flow lines  5 B 07 ). This has practical implications, since reflections always produce some scattering of the light. Minimizing the number of reflections therefore increases the efficiency of the system. Each one of the steps  5 B 08  and corresponding lens  5 B 03  can be designed using the SMS method. 
     Typical concentrators are designed by imposing constant optical path length between the input wavefronts of the edge rays and the edges of the receiver. That is the case, for example, of the (unstepped) RXI concentrator. Stepped flow-line optics (SFL), however, do not fulfill this condition. The result is that light entering at points further away from the receiver will travel a longer optical path length (and distance) than the corresponding light inside an RXI. Also, light entering at points closer to the receiver will travel a shorter distance inside the SFL concentrator than the corresponding distance inside an RXI. In two-dimensional geometry this is not an issue and both the RXI and the SFL are ideal concentrators. 
     Let us now consider the case in which these optics are given circular symmetry. Consider also a pinhole on the entrance aperture of each one of these concentrators. In the case of the RXI, two rays contained on the sagittal plane through the pinhole will travel inside the optic and end up (approximately) at the edges of the receiver. That is true, independent of the radial distance of the pinhole. In the case of the SFL optic, however, light entering a pinhole further away from the center will travel a longer distance than it would in the comparator unstepped RXI and, therefore, illuminate a spot with a larger radius, increasing the size of the receiver and reducing concentration. On the other hand, light entering a pinhole closer to the center will travel a shorter distance than it would in the RXI and, therefore, illuminate a spot with a smaller radius, generating a hotspot in the center. The result is that the SFL optic with circular symmetry needs a larger receiver and will illuminate it non-uniformly, creating a hotspot in the center. Note that the concentration at the center of the SFL receiver cannot be higher than the comparator RXI generates, since the RXI is assumed to be fully optimized and (almost) reaches the maximum limit of concentration. 
     An SFL concentrator with circular symmetry can be obtained, for example, by giving the optic in  FIG. 5B  circular symmetry around axis  5 B 11 . Choosing a revolution axis further to the left (away from the optic) will result in a concentrator with a receiver shaped as a hollow (annular) disk, or a collimator with a source shaped as a hollow disk. 
       FIG. 6  shows a collimator that accepts light confined to cone  601  and emits collimated light  602 . The collimator is composed of two dielectric parts, the lower optic  603  and the upper optic  604 , separated by a low refraction index material  605  (which may be air). Light inside part  603  is confined by stepped flow-surface  606  at the bottom and the low refraction index layer at the top, which together form a first or distributor surface. As light travels inside lower optic  603 , it encounters tilted mirrors  607  (which cross the flow lines) and is reflected upwards. Mirrors  607  together form a discontinuous, faceted second optical surface. The flow-surfaces that arrive at the bottom edges of mirrors  607 , continue backwards from the top edges of mirrors  607 . Light reflected by these mirrors in the lower optic is collected and collimated by lenses  608  on the upper optic. In  FIG. 6 , only one of these lenses is shown so that the interior of the collimator can also be seen. In a real optic, however, there is one of these lenses  608  for each mirror  607 . An array of lenses  608  completely covers the top surface  609  of the upper optic and forms a faceted third optical surface. Lenses  608  and mirrors  607  may be free-form, designed using, for example, the SMS-3D design method. 
       FIG. 7  shows a lower optic  701  and an upper optic  702  separated by a low refraction index layer  703 . The upper optic is covered with lenses  704 , one for each mirror  705  in the lower optic. 
       FIG. 8  shows a detail of a lower optic light guide similar to the lower optics of  FIGS. 6 and 7 . The lower optic of  FIG. 8  results from tiling several parts, such as  801  side by side. Of course, a commercial embodiment of the lower optic may be made in a single piece or in larger tiles, depending on its size. However, recognizing that the upper and lower optics are each formed from a repeating pattern of smaller elements is still useful. The result is a stepped flow-surface in which each step results from introducing mirrors  802  that cross the flow lines of the radiation traveling inside the guide. 
       FIG. 9  shows an optic similar to that in  FIG. 6 , but now with the tilted mirrors  901  much smaller relative to their spacing on the bottom surface of the lower optic. This results in lenses  902  that are much larger than the tilted mirrors and, therefore, in an optic that emits light  904  much more collimated than the incoming light  903 , or a concentrator with a high concentration factor. The mirrors  901  collectively still form a discontinuous faceted surface, even though the discontinuities are now large compared with the facets. 
       FIG. 10  shows another possible geometry for the stepped flow-surface forming the bottom of the lower optic. Now light is confined by horizontal walls  1001  and vertical walls  1002  and extracted by mirrors  1003 . The bottom surface of the lower optic is in this case obtained by a rectangular tiling of several pieces  1004 . 
       FIG. 11  shows a tiling similar to that in  FIG. 10 , but with the corresponding lenses  1101  on top of the extraction mirrors  1102 . Pieces  1103  with extraction mirrors  1102  and corresponding lenses  1101  are tiled side by side. 
       FIG. 12  shows an embodiment for a compact concentrator. It is composed of an upper optic  1201  and a two surface lower optic. In this example the lower optic is composed of two mirrors  1202  and  1203 . We denote each reflection by an X and call this lower optic an XX. The optic has a receiver  1204 . 
     A vertical ray  1205  is deflected by the upper optic  1201  towards the first mirror  1202  of the lower optic and from there towards the second mirror  1203  of the lower optic and finally towards the receiver  1204 . Although in this example the receiver  1204  is shown well above the lower tip  1207  of mirror  1202 , they can be much closer together and receiver  1204  may even be below tip  1207  of mirror  1202 . Also, mirror  1202  may be truncated close to the optical axis  1206  (since it is shaded by mirror  1203 ), exposing receiver  1204  to the outside environment (for electrical connection, cooling, and mechanical support) even if receiver  1204  is above mirror  1202 . 
     In the limiting case in which the acceptance angle of the optic goes to zero (aplanatic limit), the path of the rays fulfills x=m sin(α) where m is a constant, x is the horizontal coordinate at which the ray enters the optic and α is the angle with which the ray hits the receiver  1204 . This condition guarantees that, in this limit case, the meridional acceptance of the concentrator equals its sagittal acceptance when the optic has circular symmetry about vertical axis  1206  through receiver  1204  and tip  1207 , which is then the pole of the circular mirror  1202  (although the optic may also have linear symmetry). In that case, the mirrors  1203 ,  1202  in the lower optic are designed so that, if traced backwards (as if light were being emitted from the receiver  1204 ), the light rays would hit the upper optic  1201  at an angle given by a function ψ(x). This function is a parameter of the design. For different functions ψ(x), different upper and lower optics result. 
     The upper optic may in this case be designed as a Fresnel lens closer to the optical axis  1206  and as a TIR lens further away, just like in the case of a regular TIR lens. 
     In the case of a finite acceptance angle the incoming light has an angular aperture  20  and it exits the upper optic with an angular aperture β(x) that fulfills θ=arcsin(sin ψ(x)sin β(x)) [See Ref. 3]. In that case, the optical surfaces in the upper optic are designed with the SMS design method [See Ref 3]. The two optical surfaces (two mirrors in this example) of the lower optic are also designed with the SMS design method. 
     This configuration thus makes it possible to shape the lower optic mirrors  1202 ,  1203  so that each point of the faceted lens  1201  has the same acceptance angle 2θ (for a concentrator) or emission beam angle (for a collimator) for rays to and from the receiver or source  1204  without needing an explicit second faceted surface. Alternatively, as explained below with reference to  FIGS. 13A to 13C , two distinct faceted surfaces can be integrated into a single faceted optical element. The edge rays of the acceptance cone of angle 2θ in  FIG. 12  correspond to the rays of two extreme wavefronts, as shown at  113  and  116  in  FIG. 1 . 
       FIG. 13A  shows two elements of an upper optic, each one composed of a top refractive surface  13 A 01 , a reflective surface  13 A 02  and another refractive surface  13 A 03 . It is, therefore an RXR optic (where R stands for refraction and X for reflection). This example shows the particular case of the upper optic in  FIG. 12  in which β=ψ, although the SMS design method can be used the same way in designs for other parameter values of these angles. As may be seen from the rays shown in  FIG. 13A , the refractive surfaces  13 A 01  of all the elements together form a faceted optical surface with a discontinuous first derivative (cusped or kinked) and the reflective surfaces  13 A 02  of all the elements together form a faceted optical surface with a discontinuous surface. 
     In this particular example, the edge rays perpendicular to wavefront  13 A 04  are concentrated onto point  13 A 06  at the lower tip of the next optic to the left of the one under consideration, while the edge rays perpendicular to wavefront  13 A 05  exit the optic in a direction perpendicular to wavefront  13 A 07 . 
     Also in this example, second refractive surface  13 A 03  was prescribed and surfaces  13 A 02  and  13 A 01  calculated using the SMS design method. Other options include prescribing the shape of  13 A 01  and calculating  13 A 02  and  13 A 03  or prescribing surface  13 A 02  and calculating surfaces  13 A 01  and  13 A 03 . An option with special practical interest is when top surface  13 A 01  is chosen as flat and horizontal since this results in an upper optic with a flat top surface. 
       FIG. 13B  shows a similar optic to the one in  FIG. 13A , but now in the more general case in which angle β is different from angle ψ. This optic is bound by optical surfaces  13 B 01 ,  13 B 02  and  13 B 03 . Edge rays perpendicular to input wavefront  13 B 04  are either concentrated to point  13 B 07  (at the lower tip of the optic to the left—not shown) or exit the optic in a direction perpendicular to wavefront  13 B 06 . Edge rays perpendicular to wavefront  13 B 05  exit the optic in a direction perpendicular to wavefront  13 B 08 . 
       FIG. 13C  shows an optic similar to the one in  FIG. 12  in which the upper optic  1201  is now made of optical elements similar to the ones in  FIG. 13A  or  FIG. 13B , resulting in upper optic  13 C 01 . In general, the shape and use of the optical surfaces of these optical elements will vary along the upper optic  13 C 01 . Similar optical elements may be used in the devices of  FIGS. 14 to 21 . 
       FIG. 14  shows a special case of an embodiment in the general shape of  FIG. 12 . Its upper optic  1401  is designed as a Fresnel lens while the lower optic is composed of two mirrors,  1402  and  1403 . The optic has a receiver  1404 . Exemplary vertical ray  1405  at radius x is deflected towards the first mirror  1402  where it is reflected towards the second mirror  1403  and then again reflected toward the receiver  1404 . The upper optic may also be designed as a Fresnel lens closer to the optical axis  1406  and as a TIR lens further away, just like in the case of a regular TIR lens. The conditions of design are the same as in  FIG. 12 . 
       FIG. 15  shows another case of an embodiment similar to that in  FIG. 12 . In this example the upper optics  1501  is designed as a Fresnel lens, while the lower optics is a dielectric solid piece with refractive index n&gt;1, with three optically active surfaces,  1502 ,  1503  and  1504 . The embodiment has a receiver  1505 . The incoming vertical ray  1506  is deflected by the Fresnel lens  1501  towards the solid entry aperture  1502 , where it is refracted towards the surface  1503  where is reflected towards surface  1504 . The surface  1504  reflects the ray towards the receiver  1505 . The surfaces  1503  and  1504  can work by total internal reflection, or can be metalized in areas where the condition of TIR is not accomplished. As in the case of  FIG. 14  the upper optic can be designed also as a Fresnel lens closer to the optical axis and as a TIR lens further away. 
       FIG. 16  shows a similar concept to that in  FIG. 15 . This example is composed of a single dielectric piece that has three optically active surfaces  1601 ,  1602  and  1603 , and a receiver  1604 . The first optical surface,  1601 , has integrated teeth (that can be either Fresnel or TIR) and it deflects the incoming vertical ray to the first reflective surface  1602  that reflects the ray towards the second reflective surface  1603 , which reflects the ray to the receiver  1604 . The reflective surfaces can work by total internal reflection, or be metalized in areas where the condition of TIR is not accomplished. 
       FIG. 17  shows another special case of an embodiment similar to  FIG. 12 . The first optic of this embodiment consists of a curved TIR lens  1701 , while the lower optics is composed of two mirrors  1702  and  1703 . In this example the condition of flatness of the upper optic is removed, which gives another degree of freedom in the design and allows a better control of the teeth size. The top surface of  1701  is shown as curved (to minimize the thickness of this optical component), but it may also be flat. The teeth are on the underside of the lens  1701 , so that the upper surface is smooth, even if not flat, and is easier to keep clean. The teeth are protected from damage because they are inside the device. 
       FIG. 18  shows a particular case of the embodiment shown in  FIG. 12 . First mirror  1202  of the lower optic is now chosen to be flat, resulting in flat mirror  1801 . For a given acceptance angle and concentration, this condition defines function ψ(x). Upper optic  1802  is either a Fresnel lens or a combination of Fresnel (closer to the receiver  1803 ) and a TIR lens (further away from the receiver). 
     Light is deflected at upper optic  1802 , bounces off mirror  1801  and then off mirror  1804  on its way towards receiver  1803 . 
       FIG. 19  shows a variation on the embodiment in  FIG. 18 . The device is made of two parts: upper optic  1901  and dielectric lower optic  1902 , bounded by flat surfaces  1903  and  1904  (which may be parallel) and mirror  1905 . Mirror  1905  may have to be metalized in the area closer to the receiver  1906 . 
       FIG. 20  shows a particular case of the embodiment in  FIG. 12 . This device is composed of upper optic  2001  (shown diagrammatically) and dielectric lower optic  2002 . 
     Second mirror  1203  of the lower optic in  FIG. 12  is now chosen as flat, resulting in flat surface  2003 . For a given acceptance angle and concentration, this condition defines function ψ(x). Different areas of optic  2001  may be designed either a Fresnel lens or a combination of Fresnel and a TIR lens. 
     Incoming light is first deflected by upper optic. The light then refracts at flat surface  2003  into the lower optic  2002 . The light then bounces off bottom surface  2004  (by TIR), then again off flat surface  2003  (again by TIR) to the receiver  2005 . Surfaces  2003  and/or  2004  may have to be mirrored in the area closer to the receiver  2005 . 
       FIG. 21  shows an optic similar to the one in  FIG. 12 , but in which the second mirror of the lower optic  1203  is replaced by a refractive surface  2103 . The resulting optic is now composed of an upper optic  2101  and a lower optic composed of a mirror  2102  and a refractive surface  2103 . In  FIG. 21 , the space between upper optic  2101 , mirror  2102 , and refractive surface  2103  is air, and the receiver  2104  is in optical contact with a dielectric material bounded by surface  2103 . 
       FIG. 22  shows a mirror  2201  that collects the light from a point source  2202  and distributes it on a line  2203 . Its shape is such that each ray fulfills x(α)=m sin(α) where m is a constant, x is the horizontal coordinate at which the ray hits line  2203  and α is the angle with which the ray leaves the receiver. In general, this mirror can be calculated to obey a different law x(α). 
       FIG. 23  shows a similar situation to that in  FIG. 22 , but now for an extended light source  2302 . Mirror  2301  collects light from extended source  2302  and distributes it on a line  2303 . The shape of mirror  2301  is such that it generates on  2303  a prescribed etendue distribution U(x) and the shape may be calculated by the same method used to calculate luminaires for extended sources. The description of that method in Ref. [3] is incorporated herein by reference. If the path of the trailing edge ray  2307 , reflected at known point  2305 , is known, function U(x) determines the leading edge ray  2306  and a new point  2304  at which ray  2306  is reflected on mirror  2301 . Particularly interesting is a uniform etendue distribution U(x)=Constant. Line  2303  is shown in  FIG. 23  as a straight line, but in the more general case, line  2303  may be curved. 
       FIG. 24  shows an optic composed of an upper optic  2401  and a lower optic  2402 , separated by a low refractive index layer  2403 . The low refractive index layer is calculated according to the method described in  FIG. 22  and  FIG. 23 . 
     The upper optic  2401  has a microstructure on top, composed of many convex surfaces  2404 . The lower optic has another microstructure at its bottom composed of surfaces  2405  and  2406 . This last microstructure follows line  2203  of  FIG. 22  or  2303  of  FIG. 23 . 
     Incoming rays  2407  are deflected at one of the top surfaces  2404  towards one of the bottom surfaces  2405 . From there these rays are deflected towards the low refractive index layer, which reflects them (by TIR) towards the receiver  2408 . The bottom surface of the low refractive index layer  2403  may have to be mirrored on the area closer to the receiver if TIR fails. Vertical light  2409  that hits the intersection between two surfaces  2410  and  2411  may either be refracted by  2410  towards  2412  or by  2411  towards  2413 . However, after reflection of  2412  or  2413 , this light is again reassembled as  2414  in its way towards the receiver. 
     Each pair of surfaces  2405  and corresponding surface  2405  may be designed as aplanats (in the case of an infinitesimal receiver size) and a vertical ray entering the optic at a distance x from the optical axis arrives at the receiver making an angle α, also to the optical axis. These quantities are related by x=m sin(α) where m is a constant. When the receiver is of a finite size, the SMS design method may be used to simultaneously design a surface  2404  and its corresponding  2405 . Lines  2406  are flow-lines of the source or receiver  2408  when reflected off the low refractive index layer  2403 . These guide the light after reflection off surfaces  2405  on its way towards the receiver if the device is used as a concentrator, or away from the source  2408  towards the surfaces  2405  if the device is used as a collimator. 
     Macroscopically (including many surfaces  2404  on top and the corresponding  2405  at the bottom), the etendue distribution across the top surface of the upper optic  2401  is the same as the etendue distribution across the bottom surface of the bottom optic  2402 . 
       FIG. 24A  shows a vertical section through a concentrator similar to the one in  FIG. 24  when given circular symmetry. The axis  24 A 01  in  FIG. 24A  corresponds to the vertical axis through source or receiver  2408  at the left edge of  FIG. 24 . 
       FIG. 25  shows an embodiment similar to that in  FIG. 24  in which surfaces  2406  along the flow lines are replaced by arbitrary shaped surfaces  2501  that do not intersect the light as it travels inside the device. This is usually a better arrangement if these optics are used for imaging applications, because reflections off the flow-lines would redirect light rays from one edge of the image to the other, destroying image formation for the rays reflected off the flow lines. 
       FIG. 26  shows a device similar to the one in  FIG. 25 , but now designed as an integrator. Each one of the optical surfaces  2601  on the upper optic images the light source onto the corresponding surface  2602  on the lower optic. Surface  2602 , in its turn, images surface  2601  onto the receiver  2603  (after reflection in the low index layer corresponding to layer  2403 ). 
       FIG. 27  shows an optical device composed of upper optic  2701  and lower optic  2702 . Surface  2703  on the lower optic is similar to the one in  FIG. 22 , but designed for a given function x(α) in which x(0)=x 0  with x 0 &gt;0, that is, a ray  2704  emitted vertically (α=0) from the receiver  2705  and reflected off surface  2703  hits horizontal line  2706  at a coordinate x 0 . Any given ray  2707 , however, satisfies the condition of aplanatism, that is, it complies with r=m sin(α) where m is a constant and r is the distance from the optical axis to the point the light ray enters the optic. 
     The advantage of this configuration is that light rays hitting surface  2703  at points closer to the optical axis (such as point  2708 ) do so at wider angles, opening the possibility of the whole device working by TIR. However, if necessary, the region from point  2709  to  2710  can be mirrored since the incoming light does not cross it. 
     This design method can also be used in the geometries presented from  FIG. 12  through  FIG. 26 . 
       FIG. 28A  shows an optic with receiver  2801 . The optic is composed of a single piece. There may (or may not) be an air gap between the receiver and the optic. Top surface  2802  may have to partially mirrored if there is no TIR at the central area. To the extent that top surface  2802  works by TIR, the inner part of the bottom face of the optic (shown as flat in  FIG. 28A ) may be made into a concave mirror to collect light entering through the TIR surface  2802 . 
     In general, this configuration can be used as a collimator, a concentrator or an imaging device. If used as a collimator,  2801  would be a light source (such as an LED). 
       FIG. 28B  shows one side of an optic similar to that in  FIG. 28A , but in greater detail. If used as a collimator, it has a source  28 B 02  separated from the optic  28 B 01  by an air gap  28 B 03 . Therefore, as the light from this source enters the optic, it will be confined to the critical angle. This light is reflected at top surface  28 B 04 . The central part of surface  28 B 04  may have to be mirrored, but the outer region will work by TIR. Light then proceeds towards the bottom structure of optic  28 B 01  where it encounters walls  28 B 05  that guide it along the flow lines. Eventually light reaches steps  28 B 06  that reflect it towards the top lenses  28 B 07 . The light finally exits from lenses  28 B 07  as a collimated beam  28 B 08 . The whole optic has circular symmetry around axis  28 B 09 . Depending on the geometry, steps  28 B 06  may or may not have to be mirrored. 
     The optic is made of a single dielectric part and it may be produced by the methods used to produce Compact Disks (CDs) or Digital Video Disks (DVDs). 
       FIG. 29  shows a similar device to that in  FIG. 28 . Also in this case the optic is a single piece, with receiver  2901  separated from the optic by an air gap. Additional central lens  2902  concentrates some light onto the receiver. Lens  2902  may also be used in some other embodiments. 
       FIG. 30  shows a construction method similar to that in  FIG. 22 , but now for the case in which the emitted light appears to come from a virtual point source. A light ray  3001  emitted from a point source  3002  at an angle α to the vertical (optical axis) is reflected by TIR at a low-index surface  3003  towards microstructured bottom surface  3004 , which the ray meets at point  3008 . From here this ray is reflected upwards, passing through low-index layer  3003  towards top surface  3005 , where the ray is refracted, exiting in a direction  3006  making an angle β to the vertical, as if coming from a virtual source  3007 . 
     The shape of low-index reflective surface  3003  can be calculated if, for example, we assume surface  3005  to be flat and that angles α and β are related, for example, by sin β=m sin α where m is a constant. For a given ray emitted from  3002  at an angle α to the vertical, we can calculate angle β and the path of ray  3006  since its extension must intersect virtual point source  3007 . Ray  3006  may then be refracted at surface  3005  and continued to intersect with surface  3004 , giving us point  3008 . Using this method, for each ray emitted from  3002  we can determine to what point  3008  on  3004  it must be reflected and therefore the shape of mirror  3003  can be determined. This is similar to what happens in  FIG. 22 . 
       FIG. 31A  shows an example of a design based on the overall geometry in  FIG. 30 . Optic  3101  creates a virtual image  3102  of the source  3103 . The optic is composed of two parts  3104  and  3105  separated by a low refractive index layer  3106 . 
     In this figure, insert  3107  shows a detail of the optic  3101 . A light ray  3108  emitted from the source  3103  is reflected by TIR at surface  3106 . From there it is redirected towards bottom microstructure. Reflective surface  3109  of the bottom microstructure and corresponding refractive surface  3110  of the top surface are calculated simultaneously so that incoming ray  3108  exits the optic as if coming from virtual source  3102 . The relationship between emission angle α at the actual source and exit angle β (see  FIG. 30 ) is given by sin β=m sin α as stated above. Surfaces  3111  follow the flow lines of the light emitted by the source and reflected at surface  3106 . 
       FIG. 31B  shows another detail of the same optic  3101  shown in  FIG. 31A . Again, the light emitted from source  3103  exits the optic as if coming from virtual source  3102 . The optical surfaces of the top microstructure may form a continuous surface, as is the case at point  3112 , or there may be discontinuities, as is the case at point  3113 . 
     The central portion of surface  3106  (directly above source  3103 ) that cannot achieve TIR, and the associated portion  3114  of the undersurface of the top part of the optic may be calculated simultaneously so that a ray emitted from source  3103  is refracted at surface  3106 , then at surface  3114 , then at (flat) top surface  3116 , exiting the device as if coming from virtual source  3102 . 
     Various changes are possible without departing from the scope of the invention as defined in the claims. 
     Although specific embodiments have been described, the skilled reader will understand how features of different embodiments may be combined. Even where not explicitly stated, the skilled reader will understand how the two-dimensional sections shown in the drawings may be translated perpendicular to the plane of the paper to form an elongated “trough” configuration, rotated to form a circularly symmetric configuration, or otherwise expanded into a three-dimensional device. 
     Various terms of orientation have been used, for ease of reference to the drawings, which are mostly oriented with the collimated beam aimed directly upwards away from the collimator or downwards towards the concentrator. However, those orientations are not limiting, and the various optical devices disclosed may be used in any expedient orientation. For example, a concentrator used in a solar photovoltaic collector will usually be used with the collimated beam aligned on the sun. A collimator used in an automobile headlight will usually be used with the collimated beam aligned approximately horizontally, and the exact alignment chosen to comply with relevant laws and regulations. 
     When analyzing a constructed optical device, the wavefronts used to construct the device can be determined, either notionally or physically, by placing a light source at the source (or receiver) position, placing a pinhole in the exit (or entrance) aperture, and determining the edge rays of the cone of light that emerges through the pinhole. By repeating this process for different pinhole positions, the phase space representation of the wavefronts outside the exit aperture can be reconstructed. 
     The preceding description of the presently contemplated best mode of practicing the invention is not to be taken in a limiting sense, but is made merely for the purpose of describing the general principles of the invention. The full scope of the invention should be determined with reference to the Claims. 
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