The Conjugate Refractive-Reflective Homogeniser in a 500X Cassegrain Concentrator: Design and Limits

In this study we present the Conjugate Refractive Reflective Homogeniser (CRRH) to be used 1 in a 500X Cassegrain photovoltaic concentrator. The CRRH is a dielectric crossed v-trough lined with a 2 reflective film whilst maintaining an air gap between them. This air gap between the two surfaces helps in 3 trapping the scattered light from the refractive geometry and ensures both total internal reflection (TIR) 4 and standard reflection of the escaped rays. A 10-42% drop in optical efficiency has been shown to occur 5 due to varying the surface roughness of the homogeniser in these ray trace simulations for the Cassegrain 6 set up. The CRRH increased the overall optical efficiency by a maximum of 7.75% in comparison to that 7 of a standard refractive homogeniser simulated within the same concentrator system. The acceptance angle 8 and flux distribution of these homogenisers was also investigated. The simple shape of the CRRH ensures 9 easy manufacturing and produces a relatively uniform irradiance distribution upon the receiver. The 10 theoretical benefit of the CRRH is also validated via practical measurements. Further research is required 11 but a 6.7% power increase was measured under a 1000 W/m solar simulator at normal incidence for the 12 experimental test. 13

A previous study has been carried out to determine the dimensions of the primary and secondary 103 reflectors as well as the homogeniser dimensions [31]. Overall, the design has a good acceptance angle 104 of >1°. The homogeniser geometry is set such that a perfect surface should only loose a negligible 105 percentage of energy due to light rays not meeting TIR (>0.01%). When increasing the misalignment with 106 the Sun up to 2°an increase in light loss occurs in this design due to interception by the homogeniser after 107 reflection from the large primary mirror ( fig.1a). At <0.5° misalignment this loss is almost negligible but 108 increases up to ~1.7% at ±2° solar misalignment. This will limit the air gap and thickness of the reflective 109 sleeve but would not be the case for other designs such as the Fresnel lens. In this study, simulations with 110 an increasing air gap between the refractive homogeniser surface and reflective film surface (figure 1b & c) 111 were carried out. The solar cell size was 1cm x 1cm and the geometrical concentration ratio was 500X. 112

Simulation method 113
Simulations were carried out using Breault's ASAP ray tracing software. The source was set to 114 imitate energy from the sun with 1000W/m 2 and a divergence angle of ±0.27°. The homogeniser material 115 is set as SHOTT BK7, with a dispersion curve as shown in figure 2. This is a commonly used medium and 116 has a higher refractive index than others such as PMMA. The homogeniser will be made out of a material 117 with a similarly stable and high refractive index to SHOTT BK7 (to improve TIR within). 118

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For measurements of the air gap thickness, the BSDF of the homogeniser was chosen to be similar to 122 that of standard polished aluminium, following the Harvey model. This model was chosen as the 123 homogeniser will be molded from an aluminium casing with polished inner surfaces. 124 Simulations were carried out assuming first the scenario of perfect surface qualities and 100% 125 reflectance for reflectors and 0% absorbance for the homogeniser. ~10% reflectance loss is then assumed 126 for the two reflective dishes assuming their surfaces follow the polished mirror BSDF (figure 3a). The 127 losses incurred when the light rays refract into the homogenisers entry aperture and are absorbed are 128 included next and finally a surface roughness is added to the homogeniser material.   Figure 4 confirms that no light rays are lost within the system at normal incidence as shown by the 150 Scatter angle from specular angle (°) As can be seen from figures 4 and 5, the addition of a 10% reflection loss on both dishes causes a 152 significant drop in optical efficiency. There are materials and coatings with improved reflectance [33]such 153 as silver (~97% reflectance) but degradation and/or expense are common problems with such high quality 154 reflective materials. All following simulations hence consider a 90% reflective primary and secondary dish 155 so as final results are more realistic. 156 There is a small loss of energy due to when the light refracts into the homogeniser and some portion 157 of the rays is reflected away. This can be improved with antireflection coatings and special textures of the 158 homogeniser surface but again this is expensive [34,35]. 159

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The thickness of the air gap was found to have very little effect on the efficiency with which 198 refracted light rays are caught as shown in figure 7, though there is a significant difference without an air 199 gap. Figure 7 shows the optimum air gap to be 0.01mm in these investigations, this would be nearly 200 impossible to cost effectively implement due to manufacturing limitations but it can be assumed as small 201 an air gap as is feasible considering manufacturing and cost would have the highest benefit. 202 Figure 7 shows that with no air gap (0mm), TIR is lost and all rays are reflected with specular losses 203 (10%) in energy due to the 90% reflectance of the reflective film. As soon as there is an air gap, even as 204 small as 0.01mm in these simulations, the optical efficiency sharply increases as shown in figure 7. This 205 increase in optical efficiency indicates how many reflections are experienced by the light rays and hence 206 the benefit TIR provides. The larger the increase in optical efficiency between the 0 and 0.01 air gap 207 marks in figure 7, the more reflections occurring within the homogeniser which will benefit from TIR. 208 This is why larger misalignment angles (except for 2 degrees misalignment where most rays completely 209 miss the homogeniser) have a more significant optical efficiency gain (vertical incline from 0mm to 210 0.01mm) in figure 7, because there are more reflections occurring. 211 212 213

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As can be seen from figure 8, the CRRH consistently improves the optical efficiency in comparison 233 to a standard refractive homogeniser of this type for a range of surface scattering profiles. The maximum 234 improvement is 7.75% with the BSDF of WH-1701 at normal incidence. Contrary to initial expectations 235 however, this improvement did not increase with larger solar misalignment angles. At increased incident 236 angles the benefit of the CRRH decreased until negligible at 2 degrees incidence angle as shown in figure  237 8 where the optical efficiency of the standard refractive homogeniser is almost zero. Misalignment with 238 the sun causes less light to reach the input surface of the homogeniser which can explain why the benefit 239 of the CRRH decreases with increasing incidence angle. Also, if too many reflections occur within the 240 homogeniser (due to the increased initial incidence angle), some light rays, despite being trapped at the 241 CCRH walls, can still be reflected back out the entry aperture of the CRRH. 242 It can be drawn from these results that as long as there is some percentage (>2%) of light reaching 243 the solar cell for the standard refractive homogeniser case, the CRRH will improve the optical efficiency 244 by a non-negligible amount (as shown for the case of 1.75° incidence angle in figure 8). At normal 245 incidence the smallest optical efficiency improvement by the CRRH was 4.82% with a BSDF of BK-2098.

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The irradiance distribution is improved due to the slight diffusion of the rays from the rough surface 266 of the homogeniser. In the case of the conjugate refractive reflective homogeniser, when the reflective 267 sleeve is added, the irradiance distribution is negligibly different to that without the reflective sleeve. The 268 difference between the maximum and minimum irradiance values are given in figure 10. This shows a 269 purely smooth and ideal optic to have the least homogeneous distribution, the addition of the rough surface 270 modelling has the most homogeneous irradiance distribution, and the CRRH has slightly less evenly 271 distributed irradiance upon the cell. As expected, with a higher misalignment angle, the distribution is less 272 even, especially at 1°, before falling lower due to less total light being focused successfully to the solar 273 cell. 274

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The measurements shown in figure 11a gave a 3.5% current increase and a 6.7% power increase. 288 When adding the reflective film to the refractive homogeniser (figures 11 b and c), care was taken that the 289 film did not optically stick to the refractive medium and prevent TIR. It was also ensured that the primary 290 optic (Fresnel lens) only focused to the centre of the homogeniser for both tests and the same 291 concentration ratio was maintained. With higher efficiency primary optics and higher concentration levels, 292 the final stage optic gains more influence on the overall optical efficiency and performance. These 293 practical measurements confirm the advantage of the CRRH over a plane refractive homogeniser. 294

Conclusion 295
The Conjugate Refractive Reflective Homogeniser has been presented within the Cassegrain 296 concentrator design. The CRRH has been shown to improve the optical efficiency by a maximum of 7.75% 297 when considering a realistic surface roughness upon the homogeniser and reflective optics within the 298 Cassegrain concentrator system. The benefits of the CRRH are limited by the Cassegrain concentrator 299 geometry and by the magnitude of surface roughness upon the homogeniser. A high quality homogenising 300 optic with almost ideal surface smoothness would not benefit from the addition of a reflective sleeve but 301 this is rarely the case due to difficult geometries and expense. Experimental tests confirmed the ray trace 302 simulation analysis and a 6.7% performance improvement with the CRRH in comparison to the original 303 refractive homogenizer was measured. Future work is required to fully understand the benefit conjugate 304 refractive reflective optics can have for solar concentrator technologies.