Abstract:
The present embodiments provide methods and systems to homogenize illumination on a target. Some embodiments provide rotational symmetric dual-reflector solar concentrators that include a concave primary reflector with an aim-direction directed toward the sun to receive optical radiation in a far-field angle within an angle of acceptance and redirect radiation upward and centrally generating flux concentration, a secondary reflector positioned coaxial with said primary reflector to receive said redirected radiation and redirect radiation downward and centrally generating flux concentration solar rays, and a central target zone receiving said concentrated solar rays, where cross sections of said primary and secondary reflectors both further comprise a multiplicity of segments that establish a correspondence between pairs of segments, each of said segments of said primary reflector such as to image said angle of acceptance onto said corresponding segment of said secondary reflector to image onto said target zone.

Description:
PRIORITY CLAIM 
       [0001]    This application is a continuation of International Application No. PCT/US2007/063522, filed Mar. 7, 2007 and entitled “MULTI-JUNCTION SOLAR CELLS WITH A HOMOGENIZER SYSTEM AND COPULED NON-IMAGING LIGHT CONCENTRATOR”, which claims the benefit of U.S. Provisional Application No. 60/780,520, filed Mar. 8, 2006 and entitled “MULTI-JUNCTION SOLAR CELLS WITH A HOMOGENIZER SYSTEM AND COPULED NON-IMAGING LIGHT CONCENTRATOR”, each of which is incorporated herein by reference in their entirety; and 
         [0002]    this application is a continuation-in-part of U.S. patent application Ser. No. 11/997,142, filed Jan. 28, 2008 and entitled “FREE-FORM LENTICULAR OPTICAL ELEMENTS AND THEIR APPLICATION TO CONDENSERS AND HEADLAMPS”, which is the National Stage of International Application No. PCT/US2006/029464, filed Jul. 28, 2006 and entitled “FREE-FORM LENTICULAR OPTICAL ELEMENTS AND THEIR APPLICATION TO CONDENSERS AND HEADLAMPS”, which claims the benefit of both U.S. Provisional Application No. 60/776,596, filed Feb. 24, 2006 and entitled “FREE-FORM LENTICULAR OPTICAL ELEMENTS”, and U.S. Provisional Application No. 60/703,667, filed Jul. 28, 2005 and entitled “FREE-FORM LENTICULAR OPTICAL ELEMENTS AND THEIR APPLICATION TO CONDENSERS AND HEADLAMPS”, each of which is hereby incorporated by reference in their entirety. 
     
    
     BACKGROUND OF THE INVENTION 
       [0003]    The present invention is concerned with a multi-junction solar cell that employs an optical system to provide extremely high solar flux, resulting in a system that produces very efficient electrical output. More particularly, the invention is directed to a solar energy system that combines a non-imaging light concentrator, or flux booster, with a Kohler homogenizer primary and secondary mirror subsystem, wherein the non-imaging concentrator is efficiently coupled to the mirrors such that uniform irradiance is achieved for high intensity light concentration onto the multi-junction solar cell. 
         [0004]    Solar cells for electrical energy production are very well known but have limited utility due to the very high Kwh cost of production. While substantial research has been ongoing for many years, the cost per Kwh still is about ten times that of conventional electric power production. In order to even compete with wind power or other alternative energy sources, the efficiency of production of electricity from solar cells must be drastically improved. 
         [0005]    Related prior art is described in (Winston, Gordon, Optics Letters, 2005), which considers a two mirror aplanatic system (which produce sharp imaging of normal-incidence rays on the cell center while satisfying the Abe sine condition) and which may be combined with a non-imaging concentrator.  FIG. 1  shows such a two-mirror aplanatic system without the non-imaging concentrator. Primary mirror  10  concentrates the light onto the secondary mirror  11 , which illuminates the solar cell  12 . This system has a clear limitation in that the illumination on the solar cell it can achieve is highly non-uniform, which reduces the cell efficiency and system reliability. This is because the optics is imaging the plane at infinity onto the plane of the target, where the cell is placed, and thus the sun is imaged on the cell. The angular acceptance of this two-mirror aplanatic concentrator is several times (for example 3) greater than the angular size of the sun to allow for tolerances. The imaging mapping makes the acceptance angle to sun angle ratio the same as the cell diameter to sun image diameter ratio. Therefore, the area of the round target would be 3 2  times greater than that of the solar image. If the average concentration of the prior art design is 500 suns, the local concentration can reach as much as 3 2 ×500=4,500 suns. This concentration value cannot be tolerated by present high-efficiency multifunction cells, which show an abrupt drop in efficiency if they operate above 2,000-3,000 suns. 
         [0006]    Other related prior art is disclosed in a paper by L. W. James, “Use of imaging refractive secondaries in photovoltaic concentrators”, SAND89-7029, Alburquerque, N. Mex., 1989. In that paper, a Kohler integrator system is used as a photovoltaic concentrator ( FIG. 2 ). The Kohler integrator consists of two imaging optical elements (primary and secondary) with positive focal length (that is, producing a real image of an object at infinity). The secondary is placed at the focal plane of the primary, and the secondary images the primary onto the cell. In James&#39; paper, the photovoltaic Kohler concentrator is composed of a Fresnel lens  20  as the primary, and a single-surface imaging lens  21  as the secondary, which encapsulates the cell  22 , as illustrated in  FIG. 2 . The primary images the sun onto secondary aperture  23 . As the primary is uniformly illuminated by the sun, the irradiance distribution on the cell is also uniform, and it will remain unchanged when the sun moves within the acceptance angle (equivalently when the sun image  24  moves within the secondary aperture). The concentration-acceptance angle product that can be attained with this configuration is very limited, because the numerical aperture on the cell is small. Additionally, the system cannot be compact because the optic is refractive and uses a single Kohler integration element. 
       SUMMARY OF THE INVENTION 
       [0007]    A two mirror Kohler homogenizer optical design produces an ultra-compact solar concentrator with moderate irradiance non-uniformity. The Kohler optics are combined with a multi-junction solar cell system to create a system that produces electrical output with very high efficiency. In alternative embodiments a plurality of conventional solar cells can be used in place of a multi-junction cell. 
         [0008]    A variety of Kohler homogenizer and planar optical systems, formed by two mirrors, can provide the necessary components to deliver light to a multi-junction solar cell. In the Kohler homogenizer, radially symmetric mirror segments on both primary and secondary mirrors are pair-wise correlated so that each segment on the primary images the field of view onto the corresponding secondary segment, while the secondary segment in turn, images the primary segment onto the target. In one embodiment a secondary mirror is co-planar with the entrance aperture, and the exit aperture is co-planar with the vertex of the primary mirror. In a preferred embodiment the inter-mirror space is filled with a dielectric with index of refraction n, such that the numerical aperture (“NA”) is increased by a factor of n. A non-imaging light concentrator can be disposed at the exit aperture of the primary mirror wherein the non-imaging concentrator is a θ 1 /θ 2  concentrator, with θ 1  chosen to match the NA of the two-mirror system (sin θ 1 =NA/n) while θ 2  is chosen to satisfy a subsidiary condition, such as maintaining total internal reflection (“TIR”) or limiting the angle of irradiance on the multi-junction solar cell. 
         [0009]    Objectives and advantages of the invention will become apparent from the following detailed description and drawings described herein below. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]      FIG. 1  illustrates the solid-dielectric aplanatic two mirror design disclosed in prior art; 
           [0011]      FIG. 2  illustrates the photovoltaic Kohler concentrator disclosed in prior art; 
           [0012]      FIG. 3  illustrates a solid dielectric two-mirror Kohler radial homogenizer optical system; 
           [0013]      FIG. 4  illustrates a 3D view of the two-mirror Kohler radial homogenizer optical system of  FIG. 3 ; 
           [0014]      FIG. 5  illustrates the operation of the two-mirror Kohler radial homogenizer optical system when the sun is off-center but still within the design acceptance angle; 
           [0015]      FIG. 6  illustrates a non-imaging concentrator added to the two-mirror Kohler radial homogenizer optical system to increase the concentration ratio of the acceptance angle; 
           [0016]      FIG. 7  illustrates a two-mirror Kohler radial homogenizer optical system that may be comprised of volumes of different refractive indices; 
           [0017]      FIG. 8  illustrates a Kohler homogenizer optical system that may be comprised of volumes of different refractive indices and the Kohler homogenization is done between the two surfaces of the front top dielectric cover; 
           [0018]      FIG. 9  illustrates a Kohler radial homogenizer optical system that may be comprised of volumes of different refractive indices and the Kohler radial homogenization is done between the entry surface and the primary mirror; 
           [0019]      FIG. 10  illustrates a Kohler radial homogenizer optical system that may be comprised of volumes of different refractive indices and the Kohler radial homogenization is done between the entry surface and the secondary mirror; 
           [0020]      FIG. 11  illustrates a Kohler radial homogenizer optical system that may be comprised of volumes of different refractive indices and the Kohler radial homogenization is done between the entry surface and the exit surface; 
           [0021]      FIG. 12  illustrates a Kohler radial homogenizer optical system that may be comprised of volumes of different refractive indices and the Kohler radial homogenization is done between the inner surface of the top cover and the primary mirror; 
           [0022]      FIG. 13  illustrates a Kohler radial homogenizer optical system that may be comprised of volumes of different refractive indices and the Kohler radial homogenization is done between the inner surface of the top cover and the secondary mirror; 
           [0023]      FIG. 14  illustrates a Kohler radial homogenizer optical system that may be comprised of volumes of different refractive indices and the Kohler radial homogenization is done between the inner surface of the top cover and the exit surface; 
           [0024]      FIG. 15  illustrates a Kohler radial homogenizer optical system that may be comprised of volumes of different refractive indices and the Kohler radial homogenization is done between the primary mirror and the exit surface; 
           [0025]      FIG. 16  illustrates a Kohler radial homogenizer optical system that may be comprised of volumes of different refractive indices and the Kohler radial homogenization is done between the secondary mirror and the exit surface; and 
           [0026]      FIG. 17  illustrates the shaping of the exit surface to improve the uniformity of the system when the sun is on axis 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0027]    This invention makes use of the invention, including embodiments and design methods, described in U.S. Provisional Application No. 60/703,667 titled “Free-Form Lenticular Optical Elements and their Application to Condensers and Headlamps”, filed Jul. 28, 2005 by some of the present inventors, which is incorporated herein by reference in its entirety. 
         [0028]    An optical system constructed in accordance with one embodiment of the invention is shown in  FIG. 3  as a most preferred embodiment. The entrance aperture  30  and the exit aperture  36  can be flat. Segmented secondary mirror  32  is substantially co-planar with the entrance aperture  30  of a primary mirror  31 . The segments on the primary  1   a ,  2   a , etc. are essentially parabolic, each with a focus at the associated mirror segment  1   b ,  2   b , etc. on the secondary and along the vertical axis (not shown). The secondary mirror segments  1   b ,  2   b , etc. are essentially elliptical with foci at the locations of the associated primary mirror segment and the target. There is continuity in profile but discontinuity in slope in both secondary and primary. The target plane of the combination of the primary mirror  31  and the secondary mirror  32  resides at the cell  33 . 
         [0029]    In this embodiment the edges of a given segment of the secondary mirror  32  are designed so that their images at infinity through the associated primary segment match the design acceptance angle. On the other hand, the edges of a given segment of the primary are designed so that their images on the target through the associated secondary segment match the cell-size. Since the segments on the primary are uniformly illuminated, the illumination on the cell is also uniform in two dimensions. 
         [0030]    The mirror segments can also be configured to optimize global performance. For example, the parabola or ellipses focus position and parabola axis could be considered a parameter and a multiparameter optimization program can optimize the acceptance angle of the whole system. Alternatively, the parabola axis could be chosen to coincide with one of the edges of the acceptance angle and its focus placed at one of the edges of the associated secondary mirror, and also the ellipses can have their foci coinciding with the edges of the cell and of the associated primary mirrors. 
         [0031]    The actual three-dimensional device is preferably rotationally symmetric, as shown in  FIG. 4 , so that the segments of primary and secondary mirrors form rings. Since the Kohler integration is only done in the meridional cross-section, no uniformity is gained in the sagittal direction. This means that if the acceptance angle is 3 times the solar disk, the local concentration is only 3 times the average. Therefore, for a 500-sun average concentration the maximum local concentration on the cell is 1,500 (which is acceptable). 
         [0032]    Regarding the local concentration produced on the secondary mirror, when the sun is centered on axis, the irradiance pattern on each annular segment of the secondary mirror is a thin ring centered on the segment with about 100-150 suns concentration, which is also acceptable for mirror durability. 
         [0033]    If the sun is off-center, but still within the design acceptance angle, the thin irradiance ring on each annular segment of the secondary is displaced; but it is still inside the segment. In the meridional cross-section, the solar images are thus displaced as shown in  FIG. 5 . The maximum irradiance levels on the secondary and on the cell remain unchanged. 
         [0034]    Dispersion due to the variation of the refractive index of the dielectric material used (i.e. glass or acrylic) significantly limits the solar flux concentration with reasonable acceptance angle (&gt;15 mrad half angle) by a well-designed flat Fresnel lens to ≈150 suns. The angular dispersion due to a single refraction is: 
         [0000]    
       
         
           
             
               
                 
                   
                     δθ 
                     
                       tan 
                        
                       
                           
                       
                        
                       θ 
                     
                   
                   = 
                   
                     - 
                     
                       
                         δ 
                          
                         
                             
                         
                          
                         n 
                       
                       n 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where n is the relative refractive index at the interface and θ is the refracted angle. 
         [0035]    For the concentrator as the invention disclosed in  FIG. 3 , there are two refractive surfaces: the entry surface  30  and the exit surface  36 . In the first one, if the refractive entrance aperture  30  is flat, the incidence angle is limited to the acceptance angle and equation (1) states (approximating the tangent function by its argument) that relative dispersion of the refraction angle equals (in absolute value) to relative dispersion of the refractive index, which is below 1% in most optical dielectrics. In the second refraction, the effect is even smaller since the angular acceptance at that surface is very wide (close to ±90°). It is also smaller because the dispersion of the relative refractive index δn is much smaller (assuming a limited cell illumination angle, up to say ±45°) and because the concentrator dielectric material and the cell encapsulant have a more similar variation with wavelength than that of the dielectric as compared to air of the first refraction). 
         [0036]    Therefore, the preferred dielectric optical system in  FIG. 3  is for practical purposes achromatic. In fact, Equation (1) indicates some flexibility in design. For example, the dielectric/air interface (the entrance aperture  12 ) does not have to be strictly normal to the beam. A modest inclination is allowable, just as long as chromatic effects, as determined by Equation (1) are kept reasonably in bounds. If the entrance surface is not flat, the rays should be traced through them in the design. For example, if the segments of the primary are parabolas when the entrance surface is flat, then when it is non-flat, its shape should be calculated so as to enable the impinging parallel rays, after the refraction on the non-flat aperture, to be focused onto the associated secondary. This calculation is called generalized Cartesian Oval, which in general solves the inverse problem of calculating the optical surface (reflective or refractive) that couples the rays normal to two given wavefronts. The same considerations apply to the change of the exit surface from flat. A hemispherical shape, for instance, could also be prescribed. 
         [0037]    In case an increase in concentration or acceptance angle is desired, it is preferable to add a final-stage nonimaging concentrator, as shown in  FIG. 6 . This concentrator  60  could be a θ 1 /θ 2  non-imaging concentrator where θ 1  is chosen to match the numerical aperture (NA 1 ) at the exit of the two mirror system where sin θ 1 =NA 1 /n. The value of θ 2  is chosen to satisfy a subsidiary condition, such as maintaining total internal reflection (TIR) on the nonimaging concentrator sides or limiting angles of irradiance onto a multi-junction cell. The concentration or flux boost of the terminal stage approaches the fundamental limit of (sin θ 2 /sin θ 1 ) 2 . The overall concentration can approach the etendue limit of (n/sin θ 0 ) 2  where sin θ 0 =n sin θ 1 . In alternative embodiments, the non-imaging concentrator can be a known tailored non-imaging concentrator or a flow line concentrator. 
         [0038]    The planar all-dielectric optical system presented here embodies inexpensive high-performance forms that should be capable of (a) concentrating the solar radiation with acceptable nonuniform irradiance levels, (b) incurring negligible chromatic aberration even at ultra-high concentration, (c) passive cooling of the cell, (d) accommodating liberal optical tolerances, (e) mass production with existing glass and polymeric molding techniques, and (f) high compactness. 
         [0039]      FIG. 7  illustrates a two-mirror Kohler radial homogenizer optical system that may be comprised of volumes  70 ,  71 ,  72  and  73  of different refractive indices. If  72  is air and  70  and  71  are of the same dielectric material (so interface  702  does not exist), the device in  FIG. 7  reduces to that in  FIG. 3 . The optical design of the device in  FIG. 7  is done in substantially the same way as described for the design of  FIG. 3 . 
         [0040]    Another preferred embodiment considers that  71  is air, in which the optical losses due to absorption in that medium are eliminated. In this case, the flat cover  70  prevents dust from accumulating in the system and protects mirrors from the environment. If medium  73  is also air, the cell is not encapsulated, which increases the system optical efficiency since the Fresnel reflection on the interface  705  is eliminated. However, to prevent cell degradation by moisture, it may be preferable to encapsulate the cell within a dielectric dense medium  73 , such as silicone rubber. The prescribed surface  705  of the encapsulating dielectric material will be considered in the design as a prescribed surface through which the rays are traced. Additional surfaces may be included as prescribed in the system, and the application of the same design procedure of the invention is straightforward for one of skill in the art. For instance, the encapsulating lens can be made of glass or transparent plastic, and the cell coupled to it with a gel or a silicon rubber. In this case, an additional interface (without a specific optical function) will appear. 
         [0041]    Instead of establishing a design of the two mirrors, any other two surfaces of the five surfaces  701 ,  702 ,  703 ,  704  and  705  in  FIG. 7  could be designed. Therefore, nine alternative families of devices are illustrated in  FIG. 8  through  FIG. 16 . Other like configurations can be established using combinations and variations by employing the principals of the invention. For all this cases, the design can be generated in 4 steps:
       (1) Three of the five surfaces are prescribed,   (2) The remaining two surfaces are calculated in 2D to make the coupling of two parallel input wavefronts defined by the acceptance angle into the two spherical exit wavefronts defined by the target edges. Alternatively, the target and acceptance angle can be scaled down to converge to zero, and then the resulting two surfaces will be aplanatic (i.e., stigmatic and fulfilling the Abbe sine condition). If the calculated surfaces are not manufacturable, a new selection of the three prescribed surfaces in step (1) is done,   (3) Two of the five surfaces are selected,   (4) The two selected surfaces in (3) are recalculated to contain the Kohler-integrator segments as disclosed above, ray tracing through the prescribed or precalculated surfaces.       
 
         [0046]    When the exit surface is to be selected, it is possible to shape it to even improve the uniformity of the Kohler homogenizing device when the sun is on-axis, provided that there is a significant refractive index difference at both sides of the exit surface. FIG.  17  illustrates how this can be accomplished. In order to provide the uniformity improvement, the exit surface profile should have a concavity  171  or a convexity  172  at the center when the cell side  173  has respectively, a higher or lower refractive index These profiles cause rays  174  going to the cell-center to be deflected and strike closer to the cell rim. 
         [0047]      FIG. 8  illustrates a Kohler homogenizer optical system that can be comprised of volumes  80 ,  81 ,  82  and  83  of different refractive indices; and the Kohler homogenization is done between the two surfaces  801  and  802  of the front top dielectric cover  80 . In one embodiment, the medium  82 , is air and the lenses in cover  80  are top-down symmetric. Here the Kohler homogenization can be only in the radial direction. Alternatively, the Kohler homogenization can be done in both the radial and sagittal directions using with rotationally symmetric lens units in the lens array, displaced either in a rectangular or hexagonal pattern. This embodiment would increase further the illumination homogeneity of the lens. 
         [0048]      FIG. 9  illustrates a Kohler radial homogenizer optical system that can be composed of volumes  90 ,  91 ,  92  and  93  of different refractive indices; and the Kohler radial homogenization is done between the entry surface  901  and the primary mirror  903 . In this case, the focal length and pitch of the lens and mirror segment will decrease from the optical axis to the rim, due to the progressively smaller separation of the Kohler integrator pairs. 
         [0049]      FIG. 10  illustrates a Kohler radial homogenizer optical system that is comprised of volumes  100 ,  101 ,  102  and  103  of different refractive indices; and the Kohler radial homogenization is done between the entry surface  1001  and the secondary mirror  1004 . In one embodiment, material  101  is air and dielectric material materials  100  and  102  are identical (so interface  1002  does not exist), so it can be manufactured as a single piece. 
         [0050]      FIG. 11  illustrates a Kohler radial homogenizer optical system that is comprised of volumes  110 ,  111 ,  112  and  113  of different refractive indices and the Kohler radial homogenization is done between the entry surface  1101  and the exit surface  1105 . In one embodiment, the material  112  is air, so the lens segments of exit surface  1105  are concave. In another embodiment, the material  112  is a dielectric and  113  is air, so the lens segments of exit surface  1105  are convex. 
         [0051]      FIG. 12  illustrates a Kohler radial homogenizer optical system that is comprised of volumes  120 ,  121 ,  122  and  123  of different refractive indices; and the Kohler radial homogenization is done between the inner surface  1202  of the top cover and the primary mirror  1203 . Also in this case, the focal length and pitch of the lens and mirror segment will decrease from the optical axis to the rim, due to the progressively smaller separation of the Kohler integrator pairs. 
         [0052]      FIG. 13  illustrates a Kohler radial homogenizer optical system that is comprised of volumes  130 ,  131 ,  132  and  133  of different refractive indices; and the Kohler radial homogenization is done between the inner surface of the top cover  1302  and the secondary mirror  1304 . In one embodiment, material  1301  is air and dielectric material materials  1300  and  1302  are identical (so interface  1002  does not exist), so that it can be manufactured as a single piece. 
         [0053]      FIG. 14  illustrates a Kohler radial homogenizer optical system that is comprised of volumes  140 ,  141 ,  142  and  143  of different refractive indices; and the Kohler radial homogenization is done between the inner surface of the top cover  1402  and the exit surface  1405 . In one embodiment, material  141  is air and dielectric material materials  140  and  142  are identical (so interface  1402  does not exist), so that it can be manufactured as a single piece. In one embodiment, the material  112  is air, so the lens segments of exit surface  1405  are concave. In another embodiment, the material  142  is a dielectric and  143  is air, so the lens segments of exit surface  1405  are convex. 
         [0054]    The use of the inner surface instead of outer surface of the cover (for example,  1202  in  FIG. 12  instead of  901  in  FIG. 9 ) to allocate the Kohler integrator segments is beneficial in case the system is used outdoors (as it is usually the case in photovoltaic applications), because the slope discontinuities between segments in top surface will accumulate dust and thus will need a higher cleaning maintenance. 
         [0055]      FIG. 15  illustrates a Kohler radial homogenizer optical system that is comprised of volumes  150 ,  151 ,  152  and  153  of different refractive indices; and the Kohler radial homogenization is done between the primary mirror  1503  and the exit surface  1505 . In one embodiment, the material  152  is air, so the lens segments of exit surface  1505  are concave. In another embodiment, the material  152  is a dielectric and  153  is air, so the lens segments of exit surface  1505  are convex. 
         [0056]      FIG. 16  illustrates a Kohler radial homogenizer optical system that is comprised of volumes  160 ,  161 ,  162  and  163  of different refractive indices; and the Kohler radial homogenization is done between the secondary mirror  1604  and the exit surface  1605 . In one embodiment, the material  162  is air, so the lens segments of exit surface  1605  are concave. In another embodiment, the material  162  is a dielectric and  163  is air, so the lens segments of exit surface  1605  are convex. When the exit surface is to be selected, it is possible to shape it to improve even more the uniformity of the Kohler homogenizing device when the sun is on-axis, provided that there is a significant refractive index difference at both sides of the exit surface.  FIGS. 17A  &amp; B illustrates how to provide the uniformity-improvement: the exit surface profile should have a concavity  171  or a convexity  172  at the center, when the cell side  173  has a higher or lower refractive index, respectively. This profiles cause the rays  174  going to the cell-center to be deflected closer to the cell edge. 
         [0057]    It should be understood that various changes and modifications referred to in the embodiment described herein would be apparent to those skilled in the art. Such changes and modification can be made without departing from the spirit and scope of the present invention.