Iterative algorithm for reflector design for non-isotropic sources

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 non-isotropic sources. Suppose the tailored edge-ray design (TED) procedure for the isotropic source S_iso has given us a device with flux map E_iSo(θ) whereas we really want to achieve the flux map E(θ) with the real source S. Now let us multiply the desired flux map by the correction factor f₁(θ) proportional to E(θ)/E_iSo(θ) and design a new TED for the flux map f₁(θ) E(θ). 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 (two dimensions) for the case where a non-isotropic 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 three dimensional luminaires, designs with reflector materials of imperfect specularity, and designs where edge rays can undergo multiple reflections.