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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 differ- ential 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 restric- tion on the target distribution, collective solid angle, or even target topog- raphy. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attri- bution of the original publication, including its DOI. (DOI: 10.1117/1.OE.53.3.031307) Subject terms: freeform design; uniform illumination; nonimaging optics.
Highlights
Construction of a freeform surface to reallocate the radiant flux is a substantial challenge in terms of nonimaging optics
The basic concept is to convert the radiant flux emitted from a point source onto a prescribed illumination, usually in Cartesian coordinate
The segmental differential formulation is capable of taking numerical error into account in each step
Summary
Construction of a freeform surface to reallocate the radiant flux is a substantial challenge in terms of nonimaging optics. Parkyn[1] firstly pioneered a tessellation method to map the cell area between a point source in polar grid with a particular rectangular illumination in Cartesian grid. The surface can be made smooth and the resulted radiant flux can be less distorted via the above mentioned approaches, the amount of energy deviation is still difficult to be estimated before the freeform surface is constructed. Tsai et al.: New approach to construct freeform surface by numerically differential formulation curious if there exists a systematic way to construct the freeform in which the surface is guaranteed to be smooth, and the correspondence between light source and target plane is ensured under a controllable energy deviation. All the main restrictions influencing the target distribution, collective solid angle, or source distribution are discussed, alongside the viability of realizing an optical surface for different specific requests
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