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21 August 1995 Iterative algorithm for reflector design for nonisotropic sources
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Until now the methods of nonimaging optics have been based on isotropic sources of radiation. In this paper we propose an iterative algorithm that extends the solution of the illumination problem to nonisotropic sources. Suppose the tailored edge-ray design (TED) procedure for the isotropic source Siso has given us a device with flux map Eiso((theta) ) whereas we really want to achieve the flux map E((theta) ) with the real source S. Now let us multiply the desired flux map by the correction factor f1((theta) ) proportional to E((theta) )/Eiso((theta) ) and design a new TED for the flux map f1((theta) ) E((theta) ). The correction factor enhances or reduces the flux map according to the observed discrepancy from the design goal. Repeat the correction procedure until it converges sufficiently close to the desired goal. We test this algorithm in 2D for the case where a nonisotropic virtual source is created by introducing a gap between a tubular real source and an involute reflector. The results show that the iterative algorithm does indeed improve the design; however, the convergence is slow. The iterative algorithm also appears promising for the solution of more complicated problems such as the design of 3D luminaires, designs with reflector materials of imperfect specularity, and designs where edge rays can undergo multiple reflections.
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Ari Rabl, Pang Teng Ong, Jeffrey M. Gordon, and Wen Cai "Iterative algorithm for reflector design for nonisotropic sources", Proc. SPIE 2538, Nonimaging Optics: Maximum Efficiency Light Transfer III, (21 August 1995);

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