REFLECTIVE FREE-FORM KOHLER CONCENTRATOR

Abstract

One example of a solar photovoltaic concentrator has a primary mirror with multiple free-form panels, each of which forms a Köhler integrator with a respective panel of a lenticular secondary lens. The Köhler integrators are folded by a common intermediate mirror. The resulting plurality of integrators all concentrate sunlight onto a common photovoltaic cell. Luminaires using a similar geometry are also described.

Description

Reference is made to commonly-assigned International Patent Applications Nos. WO 2007/016363 to Miñano et al. and WO 2007/103994 to Benítez et al. which are incorporated herein by reference in their entirety.

Embodiments of the devices described and shown in this application may be within the scope of one or more of the following U.S. patents and patent applications and/or equivalents in other countries: U.S. Pat. Nos. 6,639,733, issued Oct. 28, 2003 in the names of Miñano et al., 6,896,381, issued May 24, 2005 in the names of Benítez et al., 7,152,985 issued Dec. 26, 2006 in the names of Benítez et al., and 7,460,985 issued Dec. 2, 2008 in the names of Benítez et al.; WO 2007/016363 titled “Free-Form Lenticular Optical Elements and Their Application to Condensers and Headlamps” to Miñano et al and US 2008/0316761 of the same title published Dec. 25, 2008 also in the names of Miñano et al; WO 2007/103994 titled “Multi-Junction Solar Cells with a Homogenizer System and Coupled Non-Imaging Light Concentrator” published Sep. 13, 2007 in the names of Benítez et al; US 2008/0223443, titled “Optical Concentrator Especially for Solar Photovoltaic” published Sep. 18, 2008 in the names of Benítez et al.; and US 2009/0071467 titled “Multi-Junction Solar Cells with a Homogenizer System and Coupled Non-Imaging Light Concentrator” published Mar. 19, 2009 in the names of Benítez et al.

GLOSSARY

Concentration-Acceptance Product (CAP)—A parameter associated with any solar concentrating architecture, it is the product of the square root of the concentration ratio times the sine of the acceptance angle. Some optical architectures have a higher CAP than others, enabling higher concentration and/or acceptance angle. For a specific architecture, the CAP is nearly constant when the geometrical concentration is changed, so that increasing the value of one parameter lowers the other.

Fresnel Facet—Element of a discontinuous-slope concentrator lens that deflects light by refraction.

TIR Facet—Element of a discontinuous-slope concentrator lens that deflects light by total internal reflection.

Primary Optical Element (POE)—Optical element that receives the light from the sun or other source and concentrates it towards the Intermediate Optical Element, if any, or to the Secondary Optical Element.

Intermediate Optical Element (JOE)—Optical element that receives the light from the Primary Optical Element and concentrates it towards the Secondary Optical Element.

Secondary Optical Element (SOE)—Optical element that receives the light from the Primary Optical Element or from the Intermediate Optical element, if any, and concentrates it towards the solar cell or other target.

Cartesian Oval—A curve (strictly a family of curves) used in imaging and non-imaging optics to transform a given bundle of rays into another predetermined bundle, if there is no more than one ray crossing each point of the surface generated from the curve. The so-called Generalized Cartesian Oval can be used to transform a non-spherical wavefront into another. See Reference [10], page 185, Reference [16].

BACKGROUND

Triple-junction photovoltaic solar cells are expensive, making it desirable to operate them with as much concentration of sunlight as practical. The efficiency of currently available multi-junction photovoltaic cells suffers when local concentration of incident radiation surpasses ˜2,000-3,000 suns. Some concentrator designs of the prior art have so much non-uniformity of the flux distribution on the cell that “hot spots” up to 9,000-11,000× concentration happen with 500× average concentration, greatly limiting how high the average concentration can economically be. Kaleidoscopic integrators can reduce the magnitude of such hot spots, but they are more difficult to assemble, and are not suitable for small cells.

There are two main design problems in Nonimaging Optics, and both are relevant here. The first is called “bundle-coupling” and its objective is to maximize the proportion of rays in a given input bundle that are transformed into a given output bundle. In a solar concentrator, that is effectively to maximize the proportion of the light power emitted by the sun or other source that is delivered to the receiver. The second problem, known as “prescribed irradiance,” has as its objective to produce a particular illuminance pattern on a specified target surface using a given source emission.

In bundle-coupling, the design problem consists in coupling two ray bundles M_i and M_o, called the input and the output bundles respectively. Ideally, this means that any ray entering into the optical system as a ray of the input bundle M_i exits it as a ray of the output bundle M_o, and vice versa. Thus the successfully coupled parts of these two bundles M_i and M_o comprise the same rays, and thus are the same bundle M_c. This bundle M_c is in general M_c=M_i∩M_o. In practice, coupling is always imperfect, so that M_c⊂M_i and M_c⊂M_o.

In prescribed-irradiance, however, it is only specified that one bundle must be included in the other, M_i in M_o. Any rays of M_i that are not included in M_o are for this problem disregarded, so that M_i is effectively replaced by M_c. In this type of solution an additional constraint is imposed that the bundle M_c should produce a prescribed irradiance on a target surface. Since M_c is not fully specified, this design problem is less restrictive than the bundle coupling one, since rays that are inconvenient to a particular design can be deliberately excluded in order to improve the handling of the remaining rays. For example, the periphery of a source may be under-luminous, so that the rays it emits are weaker than average. If the design edge rays are selected inside the periphery, so that the weak peripheral region is omitted, and only the strong rays of the majority of the source area are used, overall performance can be improved.

Efficient photovoltaic concentrator (CPV) design well exemplifies a design problem comprising both the bundle coupling problem and the prescribed irradiance problem. M_i comprises all rays from the sun that enter the first optical component of the system. M_o comprises those rays from the last optical component that fall onto the actual photovoltaic cell (not just the exterior of its cover glass). Rays that are included in M_i but are not coupled into M_o are lost, along with their power. (Note that in computer ray tracing, rays from a less luminous part of the source will have less flux, if there are a constant number of rays per unit source area.) The irradiance distribution of incoming sunlight must be matched to the prescribed (usually uniform) irradiance on the actual photovoltaic cell, to preclude hot-spots. Optimizing both problems, i.e., to obtain maximum concentration-acceptance product as well a uniform irradiance distribution on the solar cell's active surface, will maximize efficiency. Of course this is a very difficult task and therefore only partial solutions have been found.

Good irradiance uniformity on the solar cell can be potentially obtained using a light-pipe homogenizer, which is a well known method in classical optics. See Reference [1]. When a light-pipe homogenizer is used, the solar cell is glued to one end of the light-pipe and the light reaches the cell after some bounces on the light-pipe walls. The light distribution on the cell becomes more uniform with light-pipe length. The use of light-pipes for concentrating photo-voltaic (CPV) devices, however, has some drawbacks. A first drawback is that in the case of high illumination angles the reflecting surfaces of the light-pipe must be metalized, which reduces optical efficiency relative to the near-perfect reflectivity of total internal reflection by a polished surface. A second drawback is that for good homogenization a relatively long light-pipe is necessary, but increasing the length of the light-pipe both increases its absorption and reduces the mechanical stability of the apparatus. A third drawback is that light pipes are unsuitable for relatively thick (small) cells because of lateral light spillage from the edges of the bond holding the cell to the end of the light pipe, typically silicone rubber. Light-pipes have nevertheless been proposed several times in CPV systems, see References [2], [3], [4], [5], [6], and [7], which use a light-pipe length much longer than the cell size, typically 4-5 times.

Another strategy for achieving good uniformity on the cell is the Köhler illuminator. Köhler integration can solve, or at least mitigate, uniformity issues without compromising the acceptance angle and without increasing the difficulty of assembly.

Referring to FIG. 2, the first photovoltaic concentrator using Kohler integration was proposed (see Reference [8]) by Sandia Labs in the late 1980's, and subsequently was commercialized by Alpha Solarco. A Fresnel lens 21 was its primary optical element (POE) and an imaging single surface lens 22 (called SILO, for SIngLe Optical surface) that encapsulates the photovoltaic cell 20 was its secondary optical element (SOE). That approach utilizes two imaging optical lenses (the Fresnel lens and the SILO) where the SILO is placed at the focal plane of the Fresnel lens and the SILO images the Fresnel lens (which is uniformly illuminated) onto the photovoltaic cell. Thus, if the cell is square the primary can be square trimmed without losing optical efficiency. That is highly attractive for doing a lossless tessellation of multiple primaries in a module. On the other hand, the primary optical element images the sun onto the secondary surface. That means that the sun image 25 will be formed at the center of the SILO for normal incidence rays 24, and move towards position 25 on the secondary surface as the sun rays 26 move within the acceptance angle of the concentrator due to tracking perturbations and errors. Thus the concentrator's acceptance is determined by the size and shape of the secondary optical element.

Despite the simplicity and high uniformity of illumination on the cell, the practical application of the Sandia system is limited to low concentrations because it has a low concentration-acceptance product of approximately 0.3 (±1° at 300×). The low acceptance angle even at a concentration ratio of 300× is because the imaging secondary cannot achieve high illumination angles on the cell, precluding maximum concentration.

Another previously proposed approach uses four optical surfaces, to obtain a photovoltaic concentrator for high acceptance angle and relatively uniform irradiance distribution on the solar cell (see Reference [9]). The primary optical element (POE) of this concentrator should be an element, for example a double aspheric imaging lens, that images the sun onto the aperture of a secondary optical element (SOE). Suitable for a secondary optical element is the SMS (Simultaneous Multiple Surface) designed RX concentrator described in References [10], [11], [12]. This is an imaging element that works near the thermodynamic limit of concentration. In this notation, the surfaces of the optical device are listed in the order in which the light beam encounters them: I denotes a totally internally reflective surface, R denotes a refractive surface, and X denotes a reflective surface that may be opaque. If a light beam encounters the same surface twice, it is listed at both encounters with the correct type for each encounter.

A good strategy for increasing the optical efficiency of the system (which is a critical merit function) is to integrate multiple functions in fewer surfaces of the system, by designing the concentrator optical surfaces to have at least a dual function, e.g., to illuminate the cell with wide angles, at some specified approximation to uniformity. That entails a reduction of the degrees of freedom in the design compared to the ideal four-surface case. Consequently, there is a trade-off between the selected geometry and the homogenization method, in seeking a favorable mix of optical efficiency, acceptance angle, and cell-irradiance uniformity.

There are two ways to achieve irradiance homogenization. The first is a Köhler integrator, as mentioned before, where the integration process is along both dimensions of the ray bundle, meridional and sagittal. This approach is also known as a 2D Köhler integrator. The other strategy is to integrate in only one of the ray bundle's dimensions; thus called a 1D Köhler integrator. These integrators will typically provide a lesser homogeneity than is achievable with in 2D, but they are easier to design and manufacture, which makes them suitable for systems where uniformity is not too critical. A design method for calculating fully free-form 1D and 2D Köhler integrators was recently developed (see References [13], [14]), where optical surfaces are used that have the dual function of homogenizing the light and coupling the design's edge rays bundles.

In all the embodiments of the present invention, the primary optical element is reflective. The use of reflective primaries is old in solar concentrators, since the parabolic mirror has been in the public domain since centuries. More recently, advanced high-performance free-form asymmetric mirror designs that use a free-form lens with a short kaleidoscope homogenizer protruding from it [14]. designs have been developed. Also recently, the use of two-mirror Cassegrain type concentrators, common in antenna and telescope design, has been extended to solar concentrators with the addition of a kaleidoscope homogenizer [6], and with radial Kohler integration [14] [15].

SUMMARY

Embodiments of the present invention provide different photovoltaic concentrators that combine high geometric concentration, high acceptance angle, and high irradiance uniformity on the solar cell. In all the embodiments, the primary optical element is reflective in the sense that the light rays exit the primary on the same side that the light rays impinged from. Also in all the embodiments, the primary and secondary optical elements are each lenticulated to form a plurality of segments. In some embodiments, an intermediate optical element, not necessarily segmented, is used in between the primary and the secondary. A segment of the primary optical element and a segment of the secondary optical element combine to form a Köhler integrator. The multiple segments result in a plurality of Köhler integrators that collectively focus their incident sunlight onto a common target, such as a photovoltaic cell. Any hotspots are typically in different places for different individual Köhler integrators, with the plurality further averaging out the multiple hotspots over the target cell.

In some embodiments, the optical surfaces are modified, typically by lenticulation (i.e., the formation on a single surface of multiple independent lenslets that correspond to the segments mentioned before) to produce Köhler integration. Although the modified optical surfaces behave optically quite differently from the originals, they are macroscopically very similar to the unmodified surface. This means that they can be manufactured with the same techniques (typically plastic injection molding or glass molding) and that their production cost is the same.

An embodiment of the invention provides an optical device comprising: a primary optical element having a plurality of segments, which in an example are four in number; and a secondary optical element having a plurality of segments, which in an example are four lenticulations of an optical surface of a lens; wherein each segment of the primary optical element, along with a corresponding segment of the secondary optical element, forms one of a plurality of Köhler integrators. The plurality of Köhler integrators are arranged in position and orientation to direct light from a common source onto a common target. The common source, where the device is a light collector, or the common target, where the device is a luminaire, may be external to the device. For example, in the case of a solar photovoltaic concentrator, the source is the sun. Whether it is the common source or the common target, the other may be part of the device or connected to it. For example, in a solar photovoltaic concentrator, the target may be a photovoltaic cell. Further embodiments of the device, however, could be used to concentrate or collimate light between an external common source and an external common target.

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 design rays used for calculating the desired shape of a radial Köhler refractive lenticulation pair.

FIG. 2 shows certain principles of the Fresnel-SILO concentrator developed by Sandia Labs.

FIG. 3 shows a two mirror Cassegrain-type reflective concentrator of sunlight.

FIG. 4A shows a perspective view of a quad-lenticular XXR Köhler concentrator that uses azimuthal integration.

FIG. 4B shows aside view of the quad-lenticular XXR Köhler concentrator of FIG. 4A.

FIG. 5 is a first diagram of a design process for the concentrator shown in FIG. 4A.

FIG. 6 is a second diagram of the design process of FIG. 5.

FIG. 7 is a third diagram of the design process of FIG. 5.

FIG. 8 is a fourth diagram of the design process of FIG. 5.

FIG. 9 is a perspective view similar to part of FIG. 4A, illustrating a second stage of the design process of FIGS. 5 to 8.

FIG. 10A is an axial sectional view of another embodiment of XXR concentrator, showing ray paths in the plane of section.

FIG. 10B is a perspective view of the concentrator of FIG. 10A, showing ray paths over the whole area of the optical elements.

FIG. 11 is a graph of the performance of the concentrator of FIG. 10A.

FIG. 12A is an axial sectional view of another form of concentrator.

FIG. 12B is a perspective view of the concentrator of FIG. 12A.

FIG. 12C is a perspective view of a further form of concentrator.

FIG. 13 is a perspective view of another form of concentrator.

FIG. 14 is an axial sectional view of a further form of concentrator.

FIG. 15A is a perspective view of another form of concentrator.

FIG. 15B is an enlarged view of one mirror of the concentrator of FIG. 15A.

DETAILED DESCRIPTION OF THE EMBODIMENTS

A better understanding of various features and advantages of the present invention may be obtained by reference to the following detailed description of embodiments of the invention and accompanying drawings, which set forth illustrative embodiments in which various principles of the invention are utilized.

Two types of secondary optical elements are described herein: one comprising an array of refractors, the second an array of reflectors. Both exhibit overall N-fold symmetry. In the embodiments taught in this specification the primary reflective elements have the same N-fold symmetry as the secondary optic. In some embodiments the primary is asymmetric so the rest of elements are not located in front of the primary but on the side. Two types of intermediate optical elements are described herein: reflective type, and refractive type. The reflective intermediate optical element folds the ray path, permitting the removal of the secondary optical element and the solar cell (and heat-sink) from in front of the primary.

As may be seen from FIGS. 4 and 9 to 10B, symmetrical XXR configurations allow the photovoltaic cell to be placed close to, at, or even behind the primary mirror. Heat can then be removed to the rear of the primary mirror, greatly reducing the cooling problems of some prior designs, and the mounting for the PV cell can also be provided behind the primary mirror. Suitable heat sinks and mountings, are already known, and in the interests of clarity have been omitted from the drawings.

Several Köhler integrating solar concentrators are described herein. They are the first to combine a non flat array of Köhler integrators with concentration optics. Although, the embodiments of the invention revealed herein have quadrant symmetry, the invention does not limit embodiments to this symmetry but can be applied, by those skilled in the art, to other configurations (preferably N-fold symmetry, where N can be any number greater than two) once the principles taught herein are fully understood.

FIG. 1 shows lenticulation 10, comprising two refractive off-axis surfaces, primary optical element (POE) 11 and secondary optical element (SOE) 12, through which a light source outside the drawing illuminates cell 13. The final Radial Köhler concentrator will be the combination of several such lenticulation pairs, with common rotational axis 14 shown as a dot-dashed line. Solid lines 15 define the spatial edge rays and dotted lines 16 define the angular edge rays. They show the behavior of parallel and converging rays, respectively. In an embodiment, each optical element lenticulation 11, 12 may be one or more optical surfaces, each of which may be continuous or subdivided. For example, POE 11 may be a Fresnel lens, with one side flat and the other side formed of arcuate prisms.

Radial Köhler concentrators are 1D Köhler integrators with rotational symmetry. This makes the design process much easier than a 1D free-form Köhler integrator. Furthermore, rotational symmetry makes the manufacturing process as simple for a lenticular form as for any other aspheric rotational symmetry. The design process, however, first designs a 2D optical system, and then applies rotational symmetry.

Although the irradiance distribution produced by a radial Köhler concentrator has a hotspot, it is much milder than that produced by an imaging system. If α is the system acceptance angle, α_s is the sun's angular radius, and k is a constant that depends on the shape of the cell's active area (where k=1 for a round cell and k=4/π for a square cell), it can easily be seen that the hotspot generated by a radial Köhler approach is proportional to k*(α/α_s) times the average optical concentration, while the hotspot generated by an aplanatic device is proportional to k*(α/α_s)² times the average optical concentration. For instance, if α=1°, α_s=¼° (the angular radius of the sun as seen from Earth), and k=1, the hotspot created by a radial Köhler is around 4 times the average concentration, while the aplanatic design produces a hotspot 16 times the average concentration. For a square cell (k=4/π) the corresponding hotspots are 5 and 20 times the average concentration.

The radial Köhler concept has been applied in CPV systems to a two-mirror Cassegrain-type reflective concentrator (see Reference [15] and above-referenced WO 2007/103994). FIG. 3 shows a prior art two-mirror Cassegrain-type reflective concentrator 30, comprising lenticulated primary mirror 31, secondary mirror 32, and encapsulated solar cell 33 mounted on heat sink 34. Each concave reflector-lenticulation segment 31L is an annulus, and reflects incoming rays 35 as converging rays 36 focusing onto a corresponding annular lenticulation segment of secondary mirror 32, which in turn spreads them over cell 33, a 1 cm² cell of the triple junction type. Concentrator 30 is designed to work at C_g=650× with ±0.9° of acceptance angle, and has optical efficiency of 78%, with a maximum irradiance peak on the cell of 1200 suns. In the Radial Köhler design of FIG. 3, integration takes place only in the radial (meridional) direction, and not in the azimuthal or tangential (sagittal) direction. Also, the Kohler integrators are all different, because they are concentric rings, which both increases complexity and reduces uniformity. It is possible to configure the radial Köhler device to produce uniform irradiation of the photovoltaic cell with the sun on axis, but a hot spot then appears when the sun is off axis. In addition, Kohler integration with circular primary segments produces a circular irradiation on the photovoltaic cell, which is less than optimal because most commercially available PV cells are square.

In this Radial Köhler design, the average concentration and the peak concentration can be high, so that it is necessary to introduce a further degree of freedom in the radial Köhler design, in order to keep the irradiance peak below 2000 suns. To perform the integration in a second direction, the present application comprises a concentrator with four subsystems (having quad-symmetry), hereinafter referred to as segments, that symmetrically compose a whole that achieves azimuthal integration, while keeping each of the four subsystems rotationally symmetric and thus maintaining ease of manufacture, since each is actually a part of a complete rotationally symmetric radial Köhler system, analogous to those of FIG. 2 and FIG. 3.

Better homogenization is produced when using a two-directional free-form Köhler integrator instead of a rotational-symmetric one. A possible type of free-form Köhler system is the same XXR, comprising a primary reflector, and intermediate reflector and a secondary refractor, in which the Kohler integration is performed between the primary and secondary elements. FIG. 4A and FIG. 4B show an embodiment of an XXR Köhler concentrator 40, comprising four-fold segmented primary mirror 41, four-fold segmented secondary lens 42, an intermediate mirror 44 and photovoltaic cell 43.

The photovoltaic receiver has preferably a square flat active area, and without loss of generality can be considered as located in a coordinate system in which the receiver plane is z=0 and the sides of the active area are parallel to the x and y axes, and the origin is in the center of the active area. Because of the symmetry, defining the unit in the region x>0, y>0 fully defines the primary optical element. The intermediate optical element will preferably have rotational symmetry around the z axis. The secondary optical element will preferably have the same four-fold symmetry as the primary. In the particular embodiment shown in FIG. 4A and FIG. 4B, the units of the primary and secondary optical elements in regions x>0, y>0 are Köhler pairs, but other correspondences are obviously possible.

The design process has then three stages. First, the diagonal cross section profiles of the primary and intermediate mirrors are designed as in two dimensions using the SMS2D method (detailed below) with the conditions that the edge rays impinging on the entry aperture tilted +α and −α (α being the design acceptance angle) are focused in two dimensions (i.e., all the rays are contained in a plane) on close to the boundary points A and B of its corresponding lenticulation of the secondary lens, see FIG. 5. Second and third stages correspond to the design in three dimensions of the free-form surface of the primary and secondary, respectively.

The first stage of the design is done with the following process, illustrated by FIG. 5 to FIG. 8, and generates a cross-section through the three optical surfaces in the x=y plane 90 (see FIG. 9).

1. Choose β, which is the direction of the normal to the optical surface at B.

2. Choose the x coordinates of R (& R′), which are the corner points of the active area of the PV cell 43, the x and z coordinates of point B and of point E, which is the outer corner of the selected lenticulation of the primary 41, and the z coordinate of point D, which is on the rim of the intermediate optical element 44.

3. Calculate the x coordinate of D by tracing the reversed ray R′-B-D.

4. Calculate the optical path length R′-B-D-E.

5. Choose α.

6. Calculate the normal vector at E so as to reflect the known reversed ray D-E into the direction −α.

7. Choose the z coordinate z_A of point A, Calculate the x coordinate of point A using the formula x_A=(2^1/2−1)/(2^1/2+1)x_B.

8. Calculate the line of the intermediate mirror from D to C as a “distortion-free imaging oval” so that there is a linear mapping between tilt (sin) angles of rays at E in the range +/−α and points along the straight segment A to B. (See FIG. 6).

9. Calculate the points of the secondary lens, starting from B, so that the rays from E reflected off the intermediate mirror are focused by refraction to R′ (using the optical path length condition, if desired). This is most conveniently done at the same time each point of the intermediate mirror is calculated.

10. The secondary lens calculated in step 9 will usually not pass through the previously chosen point A. The intersection of the secondary lens with the line x=x_A gives a better estimation of z_A. So go back to step 7, substitute the new value of z_A, and do an “iteration loop of z_A,” repeating steps 8 and 9, and optionally repeating this step 10.

11. Calculate the primary and intermediate mirrors with SMS2D to form an image of the incident light from angle −α in B and of the incident light from angle +α in A. (See FIGS. 7 and 8.)

12. When the primary arrives at the z-axis, if the ray from +α at G after refraction at A does not reach R but a different point R″ on the receiver surface, go back to step 5 and choose a better a with value α *|R′R|/|R′R″|. Then repeat the subsequent steps.

13. If the x-coordinate of the last calculated point of the intermediate mirror (i.e., the closest to the z-axis) is not properly allocated (for instance, is negative), go back to step 2 and choose a different value for the coordinate x_B of point B. Then repeat the subsequent steps.

14. Generate the three-dimensional intermediate mirror by revolution of the profile with respect to the z-axis.

In the second stage of the design, illustrated in FIG. 9, the section x>0, y>0 of primary optical element 91 is designed in three-dimensions as the free-form mirror that forms an approximate image of the sun on the paired section of the secondary optical element through the rotationally symmetric intermediate mirror 94. Such a free-form primary mirror can be designed, for instance, as the Generalized reflective Cartesian oval that focuses all the +α rays in three dimensions, which are parallel to direction (−sin α, −sin α, −cos α), onto the point A after reflection on the intermediate mirror.

In the third step of the design, the secondary free-form lens is designed to form an image of the paired section of the primary optical element, reflected in the intermediate optical element, on the solar cell. Again, such a free-form lens can be designed, for instance, as the Generalized refractive Cartesian oval that receives rays passing through corner point E of the primary and reflected on the rotational intermediate mirror, and focuses them in three dimensions on the corner point R of the cell.

Note that the calculation in three dimensions of the primary and secondary is consistent with the two dimensional design, which means that the curves 95 and 96 contained in the free-form mirror and lens at the intersection of the diagonal x=y plane 90 in FIG. 9A coincide with the profiles calculated in the two-dimensional plane of FIG. 5 to FIG. 8.

The contour of the primary mirror in three dimensions is given by the image of the photovoltaic cell projected by the secondary lens. A notional cell larger than the real cell can be considered here, to allow for cell placement tolerances. The minimum contour size of the secondary lens units is defined by the image of the three-dimensional acceptance area (that is, the cone of radius α).

The intermediate mirror designed as described in the first stage differs very significantly from the aplanatic two mirror imaging design used in reference [6]. The aplanatic design produced focusing of the on-axis input rays onto an on-axis point, while the focal region of the on-axis input rays in the intermediate mirror designed according to the present embodiment is approximately centered in the off-axis segment AB. The difference is specially clear if the three-dimensional design is done using the intermediate mirror described in reference [6] and both +α rays and −α rays are traced as in FIG. 7 and FIG. 8, respectively. Even though the primary mirror is redesigned in three dimensions to perfectly focus the +a rays (rays incident parallel to (−sin α, −sin α, −cos α)) onto A, the use of the mirror of reference [6] as the intermediate optical element causes the focal region of the −α rays (parallel to (+sin α, +sin α, −cos α)) to be formed very far from the rim B of the secondary, specifically at a much higher z.

In another preferred embodiment, the intermediate mirror is also free-form and the primary and intermediate mirrors are designed using the SMS3D method, so four edge rays of the acceptance angle cone are approximately focused on four points at the rim of its corresponding lenticulation of the secondary in 3D geometry.

Referring to FIGS. 10A and 10B (collectively “FIG. 10”), FIG. 10A shows an XXR system similar to that of FIG. 4B with rays contained in a diagonal plane. FIG. 10B shows a close-up view of converging rays (in this case traced though the whole aperture) focusing to points 101 on the surface of secondary lens 103 (shown de-emphasized), and then spread out to uniformly cover cell 102. The irradiance thereupon is the sum of the four images of the primary mirror segments.

An embodiment of the XXR Köhler in FIG. 10 achieves a geometric concentration Cg=2090× (ratio of primary projected aperture area to cell area) with an acceptance of ±0.85°, which is a very good result for this concentration level as compared to the prior art. This high concentration level allows reduced cell costs in the system, and the acceptance angle is still high enough to provide the manufacturing tolerances needed for low cost. Shadowing of primary mirror 41 by intermediate mirror 45 is smaller than 5%.

FIG. 11 shows graph 110 with abscissa 111 plotting off-axis angle and ordinate 112 plotting relative transmission 113 of the XXR Köhler in FIG. 10. Vertical dashed line 114 corresponds to 0.85°, and horizontal dashed line 115 corresponds to the 90% threshold at which the acceptance angle is defined. The spectral dependence of the optical performance (optical efficiency, acceptance angle and irradiance distribution) is very small (which is an advantage of using mirrors).

Tables 1 to 3 (placed at the end of the description) provide an example of a concentrator according to FIG. 10. Table 1 contains the X-Y-Z coordinates of points of the free-form primary mirror of said design. The points correspond to the octant X>0, Y>X. Corresponding points in the remaining octants can be generated by interchanging the X and Y coordinates and/or changing the sign of the X and/or Y coordinate. Table 2 contains the p-Z coordinates of the profile points of the intermediate mirror. Since the design is rotationally symmetric, the whole mirror can be generated by rotation of the given coordinates around the Z axis. Finally, Table 3 contains the X-Y-Z coordinates of points of the free-form secondary lens of said design, also in the octant X>0, Y>X.

FIG. 15A shows a device 150 which is a modification of the XXR design of FIG. 10 using grooved reflectors 151 and 152 and the same secondary 153 as in FIG. 10. Grooved reflectors are described in U.S. patent application Ser. No. 12/456,406 (Publication Number: US 2010/0002320 A) titled “Reflectors Made of Linear Grooves,” filed 15 Jun. 2009, which is incorporated herein by reference in its entirety, and in which is disclosed how arbitrary rotational aspheric and free-form mirrors can be substituted by dielectric free-form structured equivalents that work by Total Internal Reflection (TIR). TIR is of interest in this XXR device to reduce the reflection losses due to metallic reflection, save the mirror coating cost and avoid the risk of the metal coating corrosion. FIG. 15B shows a detail of the intermediate mirror 152, and the ray 154 coming from the primary is twice totally internal reflected on free-form facets 155 and 156. In a CPV implementation, the mirrors 150, 152 are typically formed as the back surfaces of thin sheets of transparent material. In FIGS. 15A and 15B the refractive front surfaces of the dielectric grooved reflectors are not shown for clarity. In other embodiments, the space between the grooved reflectors 150, 152 may be a solid block of dielectric material with the grooved reflectors formed on opposite surfaces.

The present embodiments are a particular realization of the devices described in the above-mentioned patent application WO 2007/016363 to Miñano et al.

Variations can be obtained by designers skilled in the art. For instance, the number of cells, also called sections or lenslets, on each of the primary and secondary optical elements can be increased, for instance, to nine. Also the cell can be rectangular and not square, and then the four units of the primary mirror will preferably be correspondingly rectangular, so that each unit still images easily onto the photovoltaic cell. Alternatively, or in addition, the number of array units could be reduced to two, or could be another number that is not a square, so that the overall primary is a differently shaped rectangle from the photovoltaic cell. Where each segment is further subdivided into lenslets, the desirable number of lenslets in each primary and secondary lens segment may depend on the actual size of the device, as affecting the resulting size and precision of manufacture of the lens features.

Examples of such variations are shown in FIG. 12A to FIG. 14. FIGS. 12A and 12B show an embodiment of a two-unit array XR concentrator comprising an asymmetric tilted primary mirror and a refractive secondary to illuminate solar cell 120, so no intermediate optical element is used in this case. The Kohler pairs are 122a-122b and 121a-121b. The tilt of the mirror allows the secondary to be placed outside the beam of light incident on the primary, avoiding the shading produced by the secondary and heat sink in conventional centered systems. FIG. 12C shows a similar XR configuration with Kohler integration using four units: 123a to 136a and 123b to 126b.

FIG. 13 shows a four-unit tilted XR, in which compared to the previous ones the unit is rotated 45 degrees with respect to an axis normal to its surface passing through its center, so the full primary mirror 131 shows the same 45 degree rotation. Each unit has its own secondary lens 130 and PV cell 137 placed at the outer corner of the primary mirror opposite its own primary mirror 131, in the arrangement shown in FIG. 13. Note that the primary 131 receives light from the sun as shown by ray 132 and illuminates the PV cell located behind the secondary 130. Each primary mirror 131 and each secondary lens 130 is segmented into the Kohler lenticulations, as 133 to 136. This relative positioning of the primaries and secondaries allows the whole primary to be supported from the secondary positions at the corners, and even the heatsink 137 can be extended along the perimeter to become a supporting frame that eventually can also support a front glass cover.

FIG. 14 shows an example in which the intermediate optical surface 144 is not a mirror but a lens, while both primary (141a and 142a) and secondary Kohler integrating surfaces (141b and 142b) work by reflection. One secondary reflector 141b is metalized (XRX) and the other is a TIR surface (XRI).

Although various specific embodiments have been shown and described, the skilled reader will understand how features of different embodiments may be combined in a single photovoltaic collector, luminaire, or other device to form other devices within the scope of the present invention. When the photovoltaic cell is replaced by an LED or an LED array, or other light source, the present embodiments provide optical devices that can collimate the light with a quite uniform intensity for the directions of emission, because all points on the source are carried to every direction. This can be used to mix the colors of different LEDs of a source array or to make the intensity of the emission more uniform without the need to bin the chips.

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.

TABLE 1
x	y	z
192.287	195.167	58.140
56.261	163.672	−12.523
57.652	167.477	−10.307
1.976	2.092	−57.289
1.719	2.311	−57.288
1.168	2.702	−57.285
0.578	3.028	−57.281
−0.041	3.290	−57.274
5.427	5.579	−57.309
4.679	6.201	−57.308
3.873	6.744	−57.305
3.453	6.985	−57.302
2.581	7.407	−57.296
2.134	7.587	−57.292
1.221	7.889	−57.283
0.758	8.011	−57.278
0.058	8.159	−57.269
9.454	9.667	−57.230
8.171	10.737	−57.228
7.065	11.481	−57.225
6.489	11.815	−57.222
5.300	12.404	−57.215
4.690	12.660	−57.211
3.446	13.095	−57.200
2.814	13.274	−57.194
2.178	13.428	−57.187
0.896	13.662	−57.172
0.253	13.743	−57.164
12.965	13.232	−57.085
11.397	14.580	−57.083
10.052	15.538	−57.079
9.353	15.975	−57.076
7.910	16.764	−57.068
7.168	17.115	−57.063
5.652	17.732	−57.050
4.880	17.997	−57.043
3.313	18.443	−57.026
2.522	18.623	−57.017
0.927	18.899	−56.996
0.125	18.996	−56.984
19.039	19.394	−56.643
18.231	20.140	−56.644
16.530	21.533	−56.642
14.730	22.789	−56.637
13.797	23.364	−56.634
11.874	24.406	−56.624
10.887	24.873	−56.618
8.870	25.698	−56.603
7.843	26.057	−56.594
5.759	26.666	−56.574
4.705	26.916	−56.562
1.508	27.453	−56.521
−0.102	27.602	−56.497
22.715	23.123	−56.261
20.824	24.804	−56.261
19.832	25.587	−56.260
17.764	27.035	−56.256
15.598	28.321	−56.249
14.483	28.902	−56.244
12.196	29.939	−56.231
11.029	30.395	−56.223
8.654	31.180	−56.205
7.449	31.510	−56.194
5.015	32.045	−56.169
3.788	32.251	−56.155
1.323	32.539	−56.124
0.086	32.623	−56.107
26.721	26.173	−55.821
25.697	27.162	−55.822
24.638	28.112	−55.822
22.420	29.890	−55.819
20.080	31.497	−55.813
18.870	32.236	−55.809
16.378	33.580	−55.796
15.099	34.185	−55.789
12.486	35.258	−55.770
11.155	35.726	−55.758
8.452	36.524	−55.732
7.083	36.854	−55.718
4.318	37.374	−55.685
1.529	37.710	−55.647
0.129	37.808	−55.626
30.068	30.583	−55.222
28.898	31.669	−55.224
27.687	32.708	−55.224
25.800	34.178	−55.224
23.165	35.966	−55.222
21.802	36.785	−55.219
18.996	38.269	−55.211
16.098	39.549	−55.199
13.874	40.374	−55.187
10.854	41.294	−55.167
9.325	41.676	−55.155
6.237	42.288	−55.126
4.681	42.517	−55.110
1.557	42.821	−55.073
−0.009	42.897	−55.053
34.298	34.875	−54.472
31.643	37.265	−54.473
30.252	38.385	−54.472
27.356	40.468	−54.468
25.092	41.888	−54.462
23.544	42.766	−54.457
20.363	44.355	−54.443
18.734	45.065	−54.435
16.250	46.022	−54.419
14.570	46.589	−54.407
12.017	47.330	−54.387
10.297	47.752	−54.371
6.822	48.420	−54.336
3.314	48.855	−54.296
1.552	48.985	−54.274
−0.211	49.056	−54.250
40.643	41.311	−53.125
37.574	44.096	−53.126
34.320	46.656	−53.121
30.898	48.980	−53.112
27.329	51.063	−53.097
23.629	52.897	−53.076
19.815	54.478	−53.048
15.907	55.802	−53.014
11.920	56.865	−52.972
7.871	57.666	−52.923
3.777	58.201	−52.867
1.719	58.369	−52.836
−0.344	58.469	−52.804
43.944	44.660	−52.319
42.325	46.180	−52.321
40.653	47.642	−52.321
37.163	50.382	−52.319
35.350	51.657	−52.315
32.551	53.449	−52.308
30.637	54.562	−52.302
26.702	56.587	−52.285
24.687	57.498	−52.274
20.572	59.115	−52.246
18.477	59.820	−52.230
14.224	61.020	−52.191
12.070	61.515	−52.169
7.719	62.293	−52.120
5.527	62.575	−52.092
0.015	62.969	−52.014
51.111	51.931	−50.333
47.346	55.353	−50.335
44.373	57.740	−50.334
42.325	59.244	−50.331
39.161	61.364	−50.325
36.994	62.685	−50.318
34.784	63.932	−50.310
32.534	65.103	−50.301
30.247	66.198	−50.289
27.925	67.216	−50.276
25.570	68.156	−50.260
23.186	69.019	−50.243
20.775	69.803	−50.223
18.340	70.507	−50.201
15.882	71.132	−50.176
13.405	71.677	−50.150
10.910	72.141	−50.121
8.402	72.525	−50.090
5.881	72.827	−50.056
3.351	73.047	−50.021
0.814	73.184	−49.983
−0.456	73.221	−49.963
55.323	56.204	−48.984
51.268	59.873	−48.990
48.064	62.427	−48.993
45.855	64.032	−48.994
42.443	66.291	−48.994
40.106	67.695	−48.993
37.724	69.017	−48.990
35.298	70.256	−48.986
32.833	71.412	−48.980
30.332	72.483	−48.973
27.797	73.469	−48.963
25.231	74.369	−48.952
22.637	75.184	−48.939
20.019	75.913	−48.924
17.378	76.555	−48.906
14.718	77.110	−48.887
12.041	77.578	−48.865
9.351	77.959	−48.840
6.649	78.252	−48.814
3.940	78.457	−48.785
1.226	78.574	−48.754
−0.132	78.600	−48.737
62.828	63.819	−46.338
58.291	67.964	−46.339
54.710	70.864	−46.336
52.244	72.693	−46.332
45.824	76.892	−46.313
41.813	79.148	−46.295
39.079	80.539	−46.281
36.300	81.838	−46.264
33.479	83.046	−46.245
30.620	84.159	−46.224
27.724	85.179	−46.200
24.796	86.103	−46.174
21.838	86.931	−46.145
18.853	87.662	−46.114
15.845	88.296	−46.080
12.815	88.831	−46.043
9.769	89.268	−46.004
6.707	89.605	−45.963
3.635	89.842	−45.918
0.555	89.979	−45.872
65.901	66.937	−45.142
61.161	71.270	−45.144
57.420	74.301	−45.140
54.844	76.214	−45.136
48.138	80.607	−45.117
45.358	82.204	−45.105
42.526	83.707	−45.091
39.646	85.116	−45.075
36.721	86.429	−45.057
33.753	87.645	−45.036
30.746	88.764	−45.013
27.704	89.783	−44.987
24.628	90.703	−44.958
21.522	91.522	−44.927
18.390	92.239	−44.893
15.234	92.855	−44.856
12.058	93.368	−44.816
8.865	93.777	−44.774
4.052	94.195	−44.706
0.831	94.344	−44.657
75.988	77.170	−40.786
70.575	82.117	−40.791
63.362	87.761	−40.787
54.124	93.697	−40.768
47.658	97.129	−40.744
44.344	98.682	−40.729
37.569	101.458	−40.689
30.624	103.788	−40.637
27.095	104.782	−40.607
23.535	105.661	−40.573
16.332	107.072	−40.497
12.697	107.602	−40.453
5.378	108.309	−40.357
1.701	108.484	−40.304
−0.140	108.527	−40.276
80.478	81.726	−38.607
74.754	86.936	−38.617
67.119	92.865	−38.627
57.340	99.076	−38.632
50.498	102.648	−38.627
46.991	104.260	−38.622
39.829	107.128	−38.604
32.491	109.517	−38.577
28.767	110.530	−38.559
25.011	111.420	−38.538
17.419	112.831	−38.487
13.591	113.350	−38.457
5.890	114.014	−38.387
2.026	114.158	−38.347
0.092	114.183	−38.326
85.008	86.323	−36.318
78.994	91.826	−36.322
70.980	98.107	−36.319
60.715	104.718	−36.299
53.528	108.538	−36.275
49.842	110.267	−36.260
40.394	114.046	−36.210
34.582	115.936	−36.172
30.658	117.036	−36.143
26.697	118.006	−36.112
18.684	119.553	−36.040
14.641	120.129	−36.000
6.502	120.880	−35.911
2.416	121.054	−35.863
0.370	121.091	−35.837
94.197	95.645	−31.214
87.579	101.716	−31.216
78.766	108.658	−31.206
75.085	111.225	−31.197
65.531	117.096	−31.165
61.579	119.220	−31.147
57.558	121.214	−31.126
53.474	123.075	−31.101
45.127	126.394	−31.043
36.573	129.163	−30.970
32.229	130.338	−30.929
27.846	131.371	−30.884
18.980	133.008	−30.783
14.506	133.609	−30.727
10.011	134.065	−30.667
0.978	134.536	−30.537
−1.286	134.562	−30.502
97.395	98.890	−29.308
90.566	105.157	−29.310
81.470	112.325	−29.299
77.672	114.975	−29.291
67.812	121.038	−29.258
63.733	123.232	−29.240
59.584	125.291	−29.218
55.368	127.213	−29.193
46.753	130.641	−29.134
37.924	133.500	−29.061
33.440	134.713	−29.019
28.915	135.780	−28.974
19.763	137.469	−28.872
15.145	138.089	−28.816
10.506	138.558	−28.756
1.181	139.042	−28.625
−1.156	139.067	−28.590
107.402	109.043	−22.913
99.909	115.927	−22.915
89.931	123.805	−22.902
85.764	126.720	−22.891
79.341	130.831	−22.870
74.949	133.393	−22.852
68.208	136.963	−22.819
63.618	139.157	−22.792
58.957	141.201	−22.762
49.440	144.827	−22.691
42.150	147.137	−22.628
37.227	148.478	−22.582
32.259	149.658	−22.531
22.208	151.531	−22.419
17.136	152.221	−22.357
12.039	152.744	−22.291
1.795	153.290	−22.149
−0.773	153.321	−22.111
111.075	112.769	−20.379
103.326	119.870	−20.387
93.005	127.983	−20.389
88.694	130.980	−20.387
79.786	136.534	−20.375
75.200	139.087	−20.366
70.531	141.486	−20.354
65.785	143.731	−20.338
60.966	145.818	−20.320
51.132	149.516	−20.272
43.603	151.864	−20.227
38.520	153.224	−20.192
33.392	154.418	−20.153
23.024	156.304	−20.063
17.793	156.993	−20.011
12.539	157.511	−19.956
1.983	158.033	−19.832
−0.662	158.055	−19.799
121.459	123.305	−12.789
113.030	131.058	−12.789
101.808	139.934	−12.772
97.123	143.220	−12.759
87.440	149.322	−12.723
82.453	152.132	−12.700
77.375	154.778	−12.673
72.212	157.257	−12.641
66.969	159.568	−12.606
50.807	165.462	−12.474
39.725	168.507	−12.365
34.109	169.758	−12.304
22.753	171.710	−12.167
17.026	172.408	−12.093
5.501	173.242	−11.930
−0.284	173.376	−11.842
124.320	126.208	−10.568
115.701	134.134	−10.569
104.226	143.211	−10.553
99.435	146.570	−10.540
89.534	152.809	−10.506
84.434	155.681	−10.483
79.242	158.386	−10.456
73.963	160.921	−10.425
68.601	163.282	−10.390
52.075	169.306	−10.260
40.744	172.418	−10.151
35.002	173.696	−10.089
23.391	175.690	−9.954
17.535	176.402	−9.879
5.752	177.252	−9.717
−0.163	177.387	−9.629
133.343	135.362	−3.215
124.122	143.840	−3.218
111.847	153.546	−3.205
106.720	157.139	−3.194
98.816	162.206	−3.173
93.412	165.365	−3.153
87.906	168.346	−3.131
82.304	171.145	−3.104
76.611	173.761	−3.073
70.833	176.190	−3.038
64.976	178.430	−2.999
59.045	180.479	−2.955
43.934	184.749	−2.827
37.791	186.112	−2.767
25.373	188.234	−2.634
19.111	188.990	−2.560
6.510	189.888	−2.400
0.186	190.027	−2.313
136.402	138.466	−0.604
126.981	147.136	−0.604
114.440	157.066	−0.585
109.203	160.743	−0.572
101.129	165.931	−0.544
95.608	169.167	−0.521
89.982	172.221	−0.493
84.259	175.091	−0.462
78.442	177.772	−0.426
72.537	180.263	−0.386
66.551	182.562	−0.342
60.489	184.665	−0.293
45.042	189.052	−0.150
38.762	190.454	−0.085
26.065	192.639	0.058
19.660	193.420	0.137
6.773	194.352	0.308
0.304	194.500	0.399
146.053	148.259	8.057
135.987	157.523	8.056
122.586	168.133	8.073
116.990	172.062	8.086
105.427	179.358	8.124
99.471	182.719	8.149
87.241	188.850	8.212
80.978	191.614	8.251
68.187	196.525	8.341
61.672	198.668	8.394
48.434	202.313	8.514
41.724	203.812	8.582
28.157	206.151	8.733
21.314	206.988	8.816
7.544	207.989	8.997
0.631	208.151	9.094
149.453	151.709	11.263
139.157	161.180	11.260
125.450	172.025	11.273
119.726	176.040	11.284
107.897	183.492	11.315
101.804	186.924	11.336
89.292	193.179	11.390
82.886	195.998	11.423
69.802	201.001	11.502
63.139	203.181	11.548
49.600	206.884	11.653
42.739	208.402	11.713
28.868	210.763	11.845
21.873	211.602	11.918
7.800	212.590	12.078
0.737	212.737	12.165
146.886	170.086	19.368
132.458	181.527	19.393
126.433	185.765	19.410
113.983	193.639	19.458
107.571	197.268	19.488
94.400	203.890	19.564
87.655	206.877	19.609
73.878	212.188	19.714
66.859	214.506	19.774
52.596	218.453	19.911
45.366	220.077	19.987
30.744	222.616	20.154
23.368	223.526	20.246
8.523	224.621	20.444
1.070	224.802	20.551
160.387	162.802	22.070
149.371	172.949	22.072
134.709	184.578	22.098
128.587	188.886	22.115
115.935	196.890	22.164
109.418	200.578	22.195
96.033	207.310	22.272
89.179	210.347	22.318
75.177	215.746	22.425
68.044	218.103	22.486
53.549	222.117	22.624
46.200	223.768	22.701
31.340	226.350	22.870
23.843	227.275	22.963
8.756	228.389	23.163
1.182	228.573	23.271
165.711	168.203	27.618
154.342	178.677	27.620
139.209	190.679	27.645
132.891	195.126	27.663
119.833	203.387	27.712
113.107	207.194	27.743
99.292	214.143	27.821
92.218	217.278	27.867
77.767	222.851	27.974
70.405	225.283	28.036
55.444	229.425	28.175
47.859	231.129	28.253
32.522	233.793	28.424
24.784	234.748	28.517
9.212	235.895	28.720
1.395	236.085	28.829
168.389	170.920	30.478
156.842	181.559	30.481
141.474	193.751	30.508
135.057	198.268	30.527
121.796	206.662	30.577
114.965	210.530	30.610
100.936	217.590	30.690
93.751	220.775	30.737
79.074	226.439	30.848
71.597	228.911	30.911
56.401	233.121	31.053
48.697	234.853	31.132
33.118	237.561	31.306
25.259	238.532	31.401
173.887	176.499	36.502
161.975	187.475	36.505
146.121	200.055	36.533
139.500	204.715	36.551
125.819	213.376	36.603
118.772	217.367	36.636
104.297	224.651	36.716
96.884	227.937	36.764
81.742	233.780	36.875
74.027	236.330	36.939
176.578	179.229	39.525
164.486	190.370	39.527
148.391	203.137	39.553
141.670	207.867	39.571
127.782	216.654	39.619
120.628	220.704	39.651
105.934	228.095	39.729
98.409	231.428	39.775
83.039	237.355	39.884
182.202	184.935	45.998
169.736	196.423	46.001
153.144	209.591	46.030
146.216	214.470	46.050
131.898	223.536	46.103
124.523	227.714	46.138
109.375	235.340	46.222
185.063	187.838	49.375
172.405	199.502	49.378
155.557	212.869	49.405
148.522	217.821	49.423
133.983	227.022	49.474
126.494	231.262	49.506
139.296	235.862	58.265
194.459	197.371	60.841
181.184	209.612	60.848
163.518	223.648	60.886
156.141	228.850	60.911
161.667	236.846	69.607
203.483	206.524	72.398
189.612	219.316	72.405
171.152	233.983	72.444
210.278	213.418	81.456

TABLE 2
ρ      z
0.000  78.022
0.085  78.013
0.255  78.005
0.388  77.999
0.475  77.996
0.647  77.988
0.816  77.981
0.981  77.975
1.142  77.968
1.300  77.962
1.454  77.955
1.605  77.949
1.753  77.943
1.896  77.938
2.037  77.932
2.173  77.927
2.372  77.920
2.563  77.913
2.746  77.907
2.921  77.901
3.088  77.895
3.399  77.886
3.589  77.881
3.808  77.875
4.005  77.870
4.182  77.867
4.380  77.864
4.576  77.862
4.762  77.861
4.937  77.862
5.109  77.864
5.278  77.866
5.443  77.867
5.604  77.869
5.762  77.871
5.917  77.873
6.215  77.877
6.499  77.882
6.736  77.886
6.994  77.891
7.238  77.896
7.440  77.900
7.685  77.906
7.937  77.913
8.167  77.920
8.396  77.928
8.565  77.935
8.866  77.947
9.106  77.959
9.348  77.974
9.481  77.984
9.695  77.999
9.903  78.014
10.107 78.029
10.304 78.044
10.496 78.059
10.683 78.073
10.865 78.087
11.041 78.102
11.211 78.116
11.568 78.146
11.722 78.159
11.899 78.175
12.069 78.190
12.231 78.205
12.386 78.220
12.557 78.236
12.719 78.252
12.890 78.270
13.050 78.287
13.213 78.304
13.406 78.326
13.608 78.350
13.803 78.374
13.963 78.396
14.141 78.421
14.316 78.446
14.487 78.470
14.655 78.494
14.819 78.518
14.980 78.542
15.138 78.565
15.292 78.588
15.443 78.611
15.591 78.633
15.735 78.656
15.876 78.677
16.014 78.699
16.181 78.725
16.344 78.751
16.501 78.777
16.653 78.801
16.800 78.826
16.942 78.849
17.079 78.872
17.211 78.895
17.363 78.921
17.508 78.947
17.645 78.971
17.797 78.998
17.940 79.024
18.091 79.053
18.327 79.098
18.648 79.161
18.951 79.225
19.229 79.286
19.499 79.345
19.762 79.403
20.307 79.526
20.547 79.581
20.780 79.635
20.969 79.679
21.153 79.722
21.367 79.773
21.574 79.823
21.806 79.879
21.998 79.926
22.183 79.972
22.361 80.016
22.533 80.059
22.751 80.115
22.907 80.155
23.080 80.200
23.245 80.243
23.401 80.285
23.647 80.352
23.903 80.422
24.034 80.459
24.251 80.521
24.363 80.553
24.573 80.615
24.725 80.660
24.875 80.705
25.023 80.750
25.170 80.794
25.314 80.837
25.457 80.881
25.599 80.924
25.739 80.967
25.876 81.009
26.013 81.051
26.147 81.093
26.280 81.134
26.411 81.175
26.541 81.215
26.669 81.255
26.795 81.295
26.919 81.334
27.042 81.373
27.164 81.412
27.283 81.450
27.401 81.488
27.517 81.526
27.632 81.563
27.857 81.636
28.075 81.707
28.287 81.777
28.492 81.845
28.691 81.912
28.884 81.977
29.071 82.041
29.252 82.103
29.426 82.163
29.595 82.221
29.758 82.278
29.914 82.333
30.065 82.387
30.210 82.439
30.349 82.489
30.483 82.537
30.610 82.583
30.733 82.628
30.849 82.671
30.960 82.713
31.066 82.752
31.174 82.793
31.349 82.859
31.464 82.902
31.579 82.946
31.749 83.011
31.862 83.054
31.974 83.096
32.086 83.139
32.197 83.182
32.471 83.287
32.687 83.370
32.900 83.453
33.111 83.535
33.318 83.616
33.524 83.697
33.876 83.836
34.074 83.914
34.269 83.992
34.462 84.069
34.651 84.145
34.839 84.221
34.978 84.277
35.206 84.369
35.385 84.442
35.562 84.515
35.737 84.586
35.909 84.657
36.078 84.727
36.245 84.796
36.410 84.865
36.572 84.933
36.731 85.000
36.888 85.066
37.043 85.131
37.195 85.196
37.345 85.259
37.493 85.322
37.638 85.385
37.781 85.446
37.990 85.537
38.195 85.625
38.394 85.712
38.588 85.798
38.778 85.881
38.962 85.962
39.141 86.042
39.315 86.120
39.484 86.196
39.637 86.265
39.778 86.329
39.919 86.393
40.060 86.457
40.199 86.520
40.338 86.584
40.477 86.647
40.615 86.710
40.752 86.773
40.889 86.835
41.025 86.898
41.161 86.960
41.296 87.022
41.430 87.084
41.564 87.146
41.697 87.207
41.830 87.269
41.962 87.330
42.093 87.391
42.289 87.482
42.484 87.573
42.678 87.663
42.870 87.753
43.061 87.843
43.251 87.932
43.439 88.021
43.626 88.109
43.812 88.197
43.997 88.285
44.181 88.372
44.363 88.459
44.544 88.545
44.724 88.631
44.903 88.717
45.080 88.802
45.256 88.887
45.432 88.971
45.605 89.055
45.778 89.138
45.950 89.222
46.120 89.304
46.289 89.387
46.457 89.469
46.624 89.550
46.790 89.631
46.955 89.712
47.118 89.793
47.280 89.873
47.442 89.952
47.602 90.031
47.761 90.110
47.919 90.188
48.075 90.266
48.231 90.344
48.386 90.421
48.539 90.498
48.691 90.574
48.843 90.650
48.993 90.726
49.142 90.801
49.290 90.875
49.437 90.950
49.583 91.024
49.728 91.097
49.872 91.170
50.015 91.243
50.157 91.316
50.344 91.411
50.483 91.483
50.622 91.554
50.759 91.624
50.895 91.695
51.122 91.812
51.306 91.907
51.490 92.002
51.673 92.097
51.947 92.239
52.128 92.333
52.310 92.428
52.491 92.522
52.671 92.616
52.852 92.710
53.031 92.804
53.210 92.897
53.389 92.991
53.568 93.084
53.746 93.178
53.923 93.271
54.100 93.364
54.277 93.457
54.453 93.549
54.629 93.642
54.804 93.734
54.979 93.827
55.154 93.919
55.328 94.011
55.502 94.103
55.675 94.195
55.848 94.287
56.020 94.378
56.193 94.470
56.364 94.561
56.536 94.652
56.707 94.743
56.877 94.834
57.047 94.925
57.217 95.016
57.386 95.106
57.555 95.197
57.724 95.287
58.060 95.468
58.228 95.558
58.395 95.647
58.561 95.737
58.728 95.827
58.894 95.916
59.059 96.006
59.225 96.095
59.389 96.184
59.554 96.273
59.718 96.362
59.882 96.451
60.045 96.540
60.208 96.628
60.371 96.717
60.533 96.805
60.695 96.893
60.857 96.981
61.018 97.069
61.179 97.157
61.340 97.245
61.500 97.333
61.660 97.420
61.820 97.508
61.979 97.595
62.138 97.682
62.297 97.769
62.455 97.856
62.613 97.943
62.771 98.030
62.928 98.117
63.085 98.203
63.241 98.290
63.398 98.376
63.554 98.462
63.709 98.549
63.865 98.635
64.020 98.721
64.174 98.806
64.329 98.892
64.483 98.978
64.636 99.063
64.790 99.149
64.943 99.234
65.096 99.319
65.248 99.404
65.401 99.489
65.552 99.574
65.704 99.659
65.855 99.744
66.006 99.828
66.157 99.913
66.307 99.997
66.458 100.081
66.607 100.165
66.757 100.250
66.906 100.333
67.055 100.417
67.204 100.501
67.352 100.585
67.500 100.668

TABLE 3
x	y	z
0.900	15.153	16.072
0.971	15.042	16.990
1.005	14.908	17.770
0.979	14.562	19.181
0.924	14.353	19.822
0.773	13.916	20.901
0.672	13.678	21.386
0.543	13.412	21.864
0.412	13.151	22.283
0.267	12.879	22.674
0.110	12.597	23.037
−0.060	12.305	23.373
1.812	15.270	15.168
1.983	15.100	17.054
1.969	14.626	19.302
1.840	14.219	20.516
1.754	14.001	21.044
1.651	13.771	21.538
1.535	13.530	21.999
1.391	13.260	22.457
1.247	12.997	22.858
1.090	12.725	23.233
0.922	12.443	23.583
0.742	12.151	23.907
0.533	11.830	24.226
0.330	11.520	24.502
0.115	11.200	24.756
−0.111	10.871	24.987
2.788	15.254	15.172
2.887	15.195	16.140
2.923	14.653	19.296
2.592	13.819	21.613
2.033	12.809	23.357
1.867	12.536	23.720
1.689	12.254	24.058
1.500	11.964	24.373
1.283	11.644	24.684
1.188	11.502	24.812
1.072	11.336	24.953
0.973	11.189	25.071
0.851	11.019	25.200
0.747	10.868	25.309
0.619	10.693	25.426
0.510	10.538	25.525
0.377	10.358	25.630
0.262	10.199	25.719
0.123	10.014	25.813
0.003	9.851	25.892
−0.142	9.660	25.975
3.763	15.160	15.533
3.701	14.252	20.515
3.613	14.051	21.069
3.500	13.825	21.620
3.111	13.122	22.989
2.943	12.852	23.416
2.416	12.036	24.473
1.995	11.430	25.084
1.778	11.124	25.347
1.675	10.979	25.463
1.313	10.487	25.811
1.201	10.333	25.907
1.065	10.155	26.012
0.948	9.998	26.099
0.807	9.814	26.192
0.685	9.653	26.270
0.538	9.465	26.352
0.411	9.299	26.419
0.126	8.935	26.548
−0.172	8.561	26.655
4.714	14.978	16.279
4.756	14.771	17.988
4.540	14.110	20.696
3.751	12.738	23.599
3.302	12.070	24.514
3.108	11.791	24.835
2.790	11.348	25.287
2.572	11.049	25.556
2.106	10.427	26.033
1.973	10.255	26.147
1.721	9.926	26.345
1.458	9.589	26.523
1.185	9.243	26.681
0.901	8.888	26.819
0.300	8.148	27.031
0.009	7.791	27.102
5.515	14.839	15.487
5.560	14.439	18.890
5.433	14.113	20.231
5.122	13.525	21.921
4.692	12.838	23.327
4.059	11.925	24.680
3.970	11.798	24.834
3.863	11.652	25.005
3.769	11.522	25.150
3.656	11.371	25.309
3.559	11.237	25.445
3.441	11.082	25.593
3.321	10.925	25.737
3.216	10.786	25.858
3.091	10.625	25.991
2.983	10.482	26.102
2.852	10.316	26.225
2.740	10.169	26.327
2.487	9.849	26.533
2.225	9.520	26.720
1.953	9.182	26.887
1.672	8.836	27.034
1.515	8.647	27.105
1.217	8.287	27.222
0.908	7.916	27.318
0.614	7.563	27.388
0.282	7.172	27.443
−0.063	6.770	27.473
6.346	14.599	15.560
6.410	14.458	17.399
6.216	13.900	20.295
6.116	13.714	20.922
6.010	13.527	21.473
5.821	13.219	22.258
5.671	12.992	22.764
5.522	12.768	23.211
5.362	12.535	23.632
5.192	12.294	24.030
5.096	12.162	24.233
4.997	12.028	24.429
4.911	11.908	24.596
4.498	11.358	25.279
4.285	11.080	25.578
4.063	10.794	25.858
3.833	10.500	26.118
3.345	9.890	26.581
3.088	9.573	26.785
2.822	9.247	26.969
2.260	8.571	27.281
1.965	8.220	27.409
1.659	7.859	27.516
1.342	7.488	27.602
1.013	7.107	27.668
0.672	6.715	27.712
0.348	6.341	27.732
−0.019	5.925	27.730
−0.223	5.697	27.718
7.164	14.294	16.059
7.187	14.230	16.950
7.164	14.078	18.228
7.143	14.016	18.621
7.121	13.957	18.954
7.089	13.885	19.320
7.052	13.809	19.673
7.010	13.728	20.015
6.971	13.654	20.305
6.921	13.567	20.626
6.867	13.475	20.936
6.757	13.295	21.492
6.487	12.888	22.543
6.328	12.661	23.039
6.002	12.208	23.892
5.824	11.969	24.282
5.425	11.449	25.021
5.006	10.915	25.652
4.783	10.636	25.938
4.293	10.035	26.470
3.786	9.423	26.908
3.243	8.778	27.273
2.958	8.444	27.427
2.824	8.285	27.492
2.664	8.100	27.562
2.524	7.938	27.619
2.359	7.748	27.679
2.215	7.581	27.726
2.044	7.386	27.775
1.895	7.215	27.813
1.744	7.041	27.847
1.564	6.838	27.880
1.408	6.660	27.904
1.221	6.450	27.925
1.059	6.267	27.939
0.895	6.081	27.947
0.698	5.862	27.950
0.527	5.671	27.948
0.322	5.445	27.937
0.145	5.247	27.923
−0.036	5.046	27.903
7.892	13.989	15.461
7.932	13.878	17.322
7.852	13.656	18.943
7.693	13.367	20.302
7.469	13.021	21.499
7.342	12.835	22.027
7.203	12.639	22.527
7.041	12.420	23.029
6.881	12.205	23.474
6.697	11.966	23.921
6.516	11.734	24.317
6.326	11.493	24.691
6.128	11.244	25.043
5.905	10.970	25.397
5.689	10.705	25.708
5.464	10.433	26.000
5.231	10.153	26.273
5.103	10.001	26.411
4.990	9.866	26.527
4.857	9.710	26.655
4.741	9.571	26.763
4.603	9.411	26.881
4.483	9.269	26.980
4.340	9.104	27.089
4.216	8.959	27.180
4.069	8.789	27.279
3.941	8.640	27.362
3.789	8.467	27.451
3.657	8.314	27.525
3.500	8.136	27.605
3.364	7.979	27.670
3.202	7.796	27.739
3.061	7.636	27.796
2.894	7.448	27.855
2.748	7.283	27.903
2.575	7.090	27.952
2.425	6.921	27.990
2.091	6.548	28.058
1.746	6.165	28.104
1.417	5.800	28.127
1.048	5.394	28.130
0.664	4.975	28.108
0.265	4.542	28.060
−0.116	4.128	27.991
8.633	13.611	15.815
8.591	13.389	18.441
8.343	12.979	20.535
8.233	12.819	21.122
8.100	12.636	21.711
7.963	12.452	22.232
7.816	12.259	22.724
7.647	12.042	23.220
7.478	11.830	23.659
7.384	11.713	23.883
7.287	11.594	24.101
7.201	11.487	24.286
7.100	11.364	24.492
7.010	11.254	24.667
6.904	11.126	24.862
6.795	10.996	25.050
6.699	10.880	25.210
6.143	10.224	26.005
6.018	10.079	26.157
5.780	9.803	26.428
5.649	9.652	26.565
5.534	9.519	26.680
5.139	9.069	27.032
4.313	8.136	27.597
3.881	7.654	27.815
2.933	6.607	28.135
2.437	6.064	28.228
1.916	5.499	28.275
1.545	5.097	28.279
1.160	4.683	28.259
0.760	4.255	28.214
0.377	3.845	28.147
−0.134	3.307	28.024
9.329	13.195	16.088
9.328	13.144	17.034
9.299	13.071	17.850
9.207	12.912	19.037
9.126	12.789	19.716
9.021	12.643	20.395
8.909	12.492	20.992
8.774	12.318	21.592
8.636	12.143	22.122
8.558	12.046	22.393
8.476	11.945	22.656
8.316	11.750	23.129
8.226	11.642	23.370
8.133	11.531	23.605
8.051	11.432	23.805
7.953	11.317	24.027
7.853	11.200	24.243
7.764	11.095	24.426
7.660	10.973	24.630
7.567	10.864	24.803
7.346	10.610	25.183
7.012	10.229	25.689
6.677	9.848	26.131
6.307	9.433	26.550
5.917	9.000	26.927
5.529	8.570	27.248
5.103	8.101	27.543
4.678	7.637	27.786
4.378	7.309	27.930
4.067	6.974	28.055
3.748	6.629	28.162
3.419	6.274	28.250
3.079	5.910	28.318
2.728	5.535	28.365
2.020	4.781	28.396
1.633	4.371	28.378
1.449	4.177	28.361
1.231	3.947	28.335
1.041	3.746	28.306
0.847	3.542	28.270
0.615	3.300	28.221
0.335	3.009	28.151
0.037	2.701	28.065
9.967	12.760	15.331
9.863	12.522	18.814
9.821	12.465	19.190
9.555	12.125	20.852
9.127	11.616	22.512
8.875	11.325	23.242
8.600	11.013	23.912
8.304	10.682	24.529
7.989	10.331	25.096
7.300	9.575	26.089
6.946	9.189	26.500
6.556	8.767	26.890
6.148	8.328	27.238
5.742	7.893	27.531
5.296	7.418	27.799
4.854	6.947	28.015
4.540	6.614	28.140
4.217	6.273	28.247
3.884	5.923	28.335
3.727	5.757	28.369
3.541	5.562	28.403
3.379	5.391	28.428
3.187	5.191	28.451
3.020	5.015	28.466
2.850	4.838	28.477
2.649	4.628	28.483
2.474	4.445	28.483
2.266	4.228	28.477
2.084	4.039	28.466
1.680	3.619	28.424
1.489	3.420	28.396
1.294	3.218	28.362
1.062	2.978	28.314
0.781	2.690	28.245
0.483	2.385	28.161
0.134	2.028	28.047
10.606	12.270	15.924
10.528	12.142	18.131
10.249	11.807	20.296
9.829	11.337	22.084
9.583	11.067	22.850
9.022	10.462	24.203
8.381	9.779	25.347
7.923	9.294	25.991
7.682	9.040	26.285
7.434	8.779	26.561
7.159	8.491	26.836
6.895	8.214	27.075
6.623	7.930	27.296
6.343	7.638	27.500
6.055	7.338	27.686
5.918	7.197	27.767
5.454	6.715	28.007
4.487	5.714	28.352
3.983	5.196	28.459
3.458	4.655	28.523
2.907	4.089	28.541
2.329	3.497	28.509
1.720	2.874	28.422
0.907	2.047	28.225
11.096	11.633	18.186
11.012	11.543	18.970
10.908	11.433	19.700
10.794	11.314	20.342
10.658	11.172	20.985
10.518	11.026	21.553
10.355	10.858	22.124
10.192	10.689	22.630
9.524	10.004	24.238
9.205	9.678	24.833
8.867	9.333	25.380
8.511	8.970	25.880
8.154	8.607	26.316
8.020	8.470	26.465
7.622	8.066	26.866
7.226	7.664	27.209
6.793	7.225	27.529
6.363	6.789	27.795
5.893	6.313	28.035
5.747	6.165	28.099
5.576	5.992	28.168
5.426	5.841	28.224
5.250	5.663	28.284
5.096	5.507	28.331
4.915	5.324	28.380
4.241	4.643	28.512
3.703	4.100	28.562
3.499	3.894	28.569
3.321	3.715	28.569
3.110	3.502	28.564
2.925	3.316	28.554
2.322	2.708	28.485
1.608	1.989	28.339
1.308	1.688	28.256
0.957	1.336	28.144
0.593	0.970	28.011
0.259	0.635	27.873

REFERENCES

• [1] W. Cassarly, “Nonimaging Optics: Concentration and illumination”, in the Handbook of Optics, 2nd ed., pp. 2.23-2.42, (McGraw-Hill, New York, 2001)
• [2]H. Ries, J. M. Gordon, M. Laxen, “High-flux photovoltaic solar concentrators with Kaleidoscope based optical designs”, Solar Energy, Vol. 60, No. 1, pp. 11-16, (1997)
• [3] J. J. O'Ghallagher, R. Winston, “Nonimaging solar concentrator with near-uniform irradiance for photovoltaic arrays” in Nonimaging Optics: Maximum Efficiency Light Transfer VI, Roland Winston, Ed., Proc. SPIE 4446, pp. 60-64, (2001)
• [4] D. G. Jenkings, “High-uniformity solar concentrators for photovoltaic systems” in Nonimaging Optics Maximum Efficiency Light Transfer VI, Roland Winston, Ed., Proc. SPIE 4446, pp. 52-59, (2001)
• [5] http://www.daido.co.jp/english/rd/7503.pdf
• [6] http://www.solfocus.com/, also U.S. 2006/0207650, 2006/0274439
• [7] www.sol3g.com
• [8] L. W. James, “Use of imaging refractive secondaries in photovoltaic concentrators”, SAND 89-7029, Albuquerque, N. Mex., (1989)
• [9] Chapter 13, “Next Generation Photovoltaics”, (Taylor & Francis, CRC Press, 2003)
• [10] R. Winston, J. C. Miñano, P. Benítez, “Nonimaging Optics”, (Elsevier-Academic Press, New York, 2005)
• [11] J. C. Miñano, P. Benítez, J. C. González, “RX: a nonimaging concentrator”, Appl. Opt. 34, pp. 2226-2235, (1995)
• [12] P. Benítez, J. C. Miñano, “Ultrahigh-numerical-aperture imaging concentrator”, J. Opt. Soc. Am. A, 14, pp. 1988-1997, (1997)
• [13] J. C. Miñano, M. Hernandez, P. Benítez, J. Blen, O. Dross, R. Mohedano, A. Santamaria, “Free-form integrator array optics”, in Nonimaging Optics and Efficient Illumination Systems II, SPIE Proc., R. Winston & T. J. Koshel ed. (2005)
• [14] US and other patents and patent applications: U.S. Pat. No. 6,639,733; U.S. Pat. No. 6,896,381; U.S. Pat. No. 7,152,985; U.S. Pat. No. 7,460,985; WO 2007/016363; US 2009/0071467; US 2008/0223443; US 2008/0316761.
• [15] P. Benítez, A. Cvetkovic, R. Winston, G. Diaz, L. Reed, J. Cisneros, A. Tovar, A. Ritschel, J. Wright, “High-Concentration Mirror-Based Köhler Integrating System for Tandem Solar Cells”, 4th World Conference on Photovoltaic Energy Conversion, Hawaii, (2006).
• [16] J. Chaves, “Introduction to Nonimaging Optics”, CRC Press, 2008, Chapter 17.

Claims

1. An optical device comprising a primary optical element, an intermediate optical element, and a secondary optical element, wherein: each of the primary and secondary optical elements comprises a plurality of sections;each section of the primary optical element and a respective section of the secondary optical element form a Köhler integrator arranged to transmit light from a source common to the lenticulations to a target common to the sections; andlight passing between the primary and secondary optical elements is deflected by the intermediate optical element.

2. The optical device of claim 1, wherein the primary and intermediate optical elements are reflective and the secondary optical element is refractive.

3. The optical device of claim 1, wherein the primary and secondary optical elements are reflective and the intermediate optical element is refractive.

4. The optical device of claim 1, wherein the intermediate optical element comprises a single smooth optical surface common to the sections.

5. The optical device of claim 1, wherein the primary and secondary optical elements are free-form and the intermediate optical element is rotationally symmetric.

6. The optical device of claim 1, wherein the Köhler integrators are operative to integrate light in both sagittal and meridional directions.

8. The optical device of claim 1, which is a solar concentrator, and wherein the target is a photovoltaic device attached to the secondary optical element.

9. The optical device of claim 1, wherein the segments of the primary optical element are so arranged as to produce substantially coincident images of their respective segments of the secondary optical element at the common source, and wherein the segments of the secondary optical element are so arranged as to produce substantially coincident images of their respective segments of the primary optical element at the common target.

10. The optical device of claim 1, wherein at least one of the primary and secondary optical elements is operative to concentrate or collimate light reaching that element from the common source or being directed by that element onto the common target.

11. The optical element of claim 1, wherein the primary and secondary optical elements each comprise sections symmetrically arranged around a common axis and displaced from each other in rotation about the common axis.

12. The optical device of claim 1, further comprising a central axis, wherein the common target further comprises a device for converting light into another form of energy, and wherein each of the plurality of Köhler integrators is arranged to direct collimated light incident parallel to said central axis over the common target.

13. The optical device of claim 12, wherein the device for converting energy is a photovoltaic cell.

14. The optical device of claim 1, wherein the secondary optical element is a dielectric element having the plurality of segments formed in one surface and having the common source or common target at another surface.

15. An optical device comprising a primary optical element and a secondary optical element, wherein: each of the primary and secondary optical elements comprises a plurality of sections;each section of the primary optical element and a respective section of the secondary optical element form a Köhler integrator arranged to transmit light from a source common to the sections to a target common to the sections; andthe secondary optical element is outside the beam of light from the source to the primary optical element that is deflected by the primary optical element to the secondary optical element.

16. The optical device of claim 13, wherein the primary and secondary optical elements are free-form.

17. The optical device of claim 15, which is a solar concentrator, and wherein the target is a photovoltaic device attached to the secondary optical element.

18. The optical device of claim 15, wherein the secondary optical element is a refractive surface on a dielectric element that extends from the refractive surface to the target.

19. The optical device of claim 15, wherein the secondary optical element is a reflective rear surface on a dielectric element that extends from the reflective surface to the target.

20. The optical device of claim 15, comprising a plurality of said primary optical elements and a corresponding plurality of secondary optical element, wherein each secondary element is separated from its associated primary optical element by another primary optical element.