Equation (13.1) showed that if a high concentration is needed to reduce the receiver cost and a sufficiently high acceptance angle a is needed to make the system practical, the illumination angles в on the receiver must, of necessity, be high. A first consequence of illuminating the cell with wide angles в is that such an illumination will make the cell design (especially antireflection coatings, thickness of tandem cells, etc) more difficult and, in general, for the same cost, the final cell performance will be worse than for the case of a low illumination angle в.
The higher the angles a and в are the more difficult the design problem for achieving good illumination uniformity will be, which can be critical as we have just seen in section 13.1.5. The difficulty that corresponds to the acceptance angle a can be illustrated as follows: if a were equal to the sun radius as (which probably makes the system impractical because of the low tolerances), then any simple point-focus imaging concentrator (i. e. one that images the sun on the cell) would provide a nearly-uniformly illuminated disk on the cell (the sun image). When a is bigger, for instance, a = 4as, the imaging concentrator will produce a disk with a 16 times higher concentration with an area 16 times smaller on the cell, and this sun image will move around the cell when the sun (due to tracking errors) moves within the acceptance area. For high concentration cells (usually with Jlt s > Vt), such local concentration levels will produce a dramatic reduction in the conversion efficiency and, thus, the imaging concentrator is useless for this high a.
Therefore, a practical concentrator design cannot perform as the imaging concentrator, it must be different to obtain good illumination uniformity without reducing the acceptance angle a too much. It should be noted that concentrator efficiency records are usually obtained with imaging concentrators (Fresnel lenses) with a small acceptance angle to have good illumination uniformity and low в to maximize the cell performance. Such records are obviously good for showing the limiting performance but are not representative of the achievable efficiency in practical systems. Of course, this is not exclusive to concentration systems and also happens in some one-sun records: there are record cells that achieve a very high efficiency for normal incidence but significantly lower efficiency for non-normal rays, so they are not practical for static one-sun modules (since their daily average efficiency will not be that high).
Designing for good illumination uniformity without reducing the acceptance angle so that it is close to that of the sun is a difficult task. There are two methods in classical optics that potentially can achieve this, if conveniently adapted to the PV requirements. The two methods specifically used for condenser designs in projection optics are the light-pipe homogenizer and the Kohler illuminator (commonly called an integrator) .
The light-pipe homogenizer uses the kaleidoscopic effect created by multiple reflections inside a light pipe, which can be hollow with metallic reflection or solid with total internal reflections (TIR). This strategy has been proposed several times in PVs [11,16-18] essentially by attaching the cell to the light-pipe exit and making the light-pipe entry the receiver of a conventional concentrator. It can potentially achieve (with the appropriate design for the pipe walls and length) good illumination on a squared light-pipe exit with the sun in any position within the acceptance angle. For achieving high illumination angles в, the design can include a final concentration stage by reducing the light-pipe cross section near the exit. However, this approach has not yet been proven to lead to practical PV systems (neither has any company commercialized it as a product yet).
However, the integrating concentrator consists of two imaging optical elements (primary and secondary) with positive focal length (i. e. producing a real image of an object at infinity, as a magnifying glass does). The secondary element is placed at the focal plane of the primary, and the secondary images
the primary on the cell. This configuration ensures that the primary images the sun on the secondary aperture and, thus, the secondary contour defines the acceptance angle of the concentrator. As the primary is uniformly illuminated by the sun, the irradiance distribution is also uniform and the illuminated area will have the contour of the primary, which will remain unchanged when the sun moves within the acceptance angle (equivalently when the sun image moves within the secondary aperture). If the primary is tailored to be square, the cells will be uniformly illuminated in a squared area. A squared aperture is usually the preferred contour to tessellate the plane when making the modules, while a squared illuminated area on the cell is also usually preferred as it fits the cell’s shape.
Integrator optics for PV was first proposed  by Sandia Labs in the late 1980s and it was commercialized later by Alpha Solarco. This approach uses a Fresnel lens as the primary and a single-surface imaging lens (called SILO, from SIngLe Optical surface) that encapsulates the cell as secondary, as illustrated in figure 13.7.
This simple configuration is excellent for getting a sufficient acceptance angle a and highly uniform illumination but it is limited to low concentrations because it cannot get high в. Imaging secondaries achieving high в (high numerical aperture, in the imaging nomenclature) have, up to now, proved impractical. Classical solutions, which would be similar to high power microscopes objectives, need many lenses and would achieve в ^ 60°. A simpler solution that nearly achieves в = 90° is the RX concentrator [20,21] (see figure 13.8). Although the Lens+RX integrator is still not practical, it is
Figure 13.8. The use of an RX concentrator as the imaging secondary in the integrator (not shown to scale on the left) with a double aspheric imaging primary shows that it is theoretically possible to come very close to optimum PV concentrator performance.
theoretically interesting, because it encourages the definition of an optimum PV concentrator performance and shows that it is (at least) nearly attainable.
Let us define the optimum PV concentrator performance as that provided by a squared aperture concentrator collecting all rays within the acceptance angle a (this being several times the sun radius as) and achieving isotropic illumination of the cell (в = 90°), producing a squared uniform irradiance covering the whole cell, independently of the sun position within the acceptance area. Note that since all rays reaching the cell come from the rays within a cone of angular radius a no rays outside this cone can be collected by the optimum concentrator.
As an example, for a = 1°, this optimum performance concentrator will have a geometrical concentration Cg = 7387x, which is the thermodynamic concentration limit for that acceptance angle.
This definition of optimum PV concentrator performance is just a definition and it does not try to be general. For instance, as already mentioned, the high reflectivity of non-textured cells for glazing angles may make the isotropical illumination useless. As another example, illuminating a squared area inside the cell is perfect for back-contacted solar cells but it may be not so perfect for front-contacted cells, for which an inactive area is needed to make the front contacts (breaking the squared shape active area restriction). Finally, for medium concentration systems (say, Cg = 100) the aforementioned optimum performance would imply an ultra-wide acceptance angle a = 8.6°. As pointed out in section 13.1.4, it seems logical that over a certain acceptance angle, there must be no cost benefits due to the relaxation of accuracies (and 8.6° seems to be above
Figure 13.9. The difference between imaging and non-imaging optical systems is that in the former a specific point-to-point correspondence between the source and the receiver is required.
such a threshold). If this is the case, coming close to the optimum performance seem to be unnecessary for this medium concentration level.
The present challenge in optical designs for high-concentration PV systems is to design concentrators that approach the optimum performance and, at the same time, are efficient and suitable for low-cost mass production.