New approach to construct freeform surface by numerically differential formulation

Yu-Lin Tsai; Ming-Chen Chiang; Ray Chang; Chung-Hao Tien; Chin-Tien Wu

doi:10.1117/1.OE.53.3.031307

31 December 2013 New approach to construct freeform surface by numerically differential formulation

Yu-Lin Tsai, Ming-Chen Chiang, Ray Chang, Chung-Hao Tien, Chin-Tien Wu

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Optical Engineering, Vol. 53, Issue 3, 031307 (December 2013). https://doi.org/10.1117/1.OE.53.3.031307

Abstract

We proposed a new design method for single freeform reflective (or refractive) surface tailored to redistribute the radiant flux onto a prescribed illumination pattern. Unlike the conventional optimization approaches based on the grid mapping, in this study we estimated each segmental freeform surface by locally solving a second-order differential equation, which formulates the energy transportation between each domain cell. With finite element method via Hermite element, we validated a series of smooth reflective/refractive surfaces to reallocate the radiant flux from a point source toward a target plane with specific patterns. The proposed technique offers a large flexibility by varying the vectors of each ray with multiple refraction (or reflection), which imposes no restriction on the target distribution, collective solid angle, or even target topography.

CC BY: © The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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Yu-Lin Tsai, Ming-Chen Chiang, Ray Chang, Chung-Hao Tien, and Chin-Tien Wu "New approach to construct freeform surface by numerically differential formulation," Optical Engineering 53(3), 031307 (31 December 2013). https://doi.org/10.1117/1.OE.53.3.031307

Published: 31 December 2013

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