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Most of the freeform lens optimization methods for LED beam shaping are focused on producing rectangular illumination patterns. Here we demonstrate the generation of non-rectangular irradiance distributions by optimizing the 'uv'-polynomial freeform surface, where (u,v) are stereographic coordinates. An initial freeform surface is designed with an optimal transport ray mapping method that is suitable for unconventional boundaries. Simulated annealing is then used to optimize the polynomial coefficients based on an automated workflow that links Matlab (central platform and optimization engine), Rhinoceros (3D molding) and LightTools (Ray tracing).
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