Neural-network methods for two-dimensional finite-source reflector design

TL;DR

This paper introduces neural-network-based methods for designing two-dimensional reflectors that efficiently transform light from finite sources into desired far-field patterns, outperforming traditional deconvolution approaches in speed and accuracy.

Contribution

The authors develop a neural network approach for 2D reflector design that improves accuracy and speed over existing methods, and demonstrate its effectiveness across various benchmarks.

Findings

Neural method achieves errors of about 2e-5 and 5e-5 within seconds.

Baseline deconvolution method has errors of 4e-3 and 5e-2 after hundreds of seconds.

Neural approach is more accurate and faster, supporting practical height constraints.

Abstract

We address the inverse problem of designing two-dimensional reflectors that transform light from a finite, extended source into a prescribed far-field distribution. The reflector height is represented by a neural network and optimized with two objective functions: a direct change-of-variables loss based on the closed-form inverse ray map, and a mesh-based loss that maps target cells back to the source and remains usable for discontinuous sources. Gradients are computed by automatic differentiation and minimized with a robust quasi-Newton method. As a baseline, we adapt a deconvolution pipeline built on a simplified finite-source approximation: a one-dimensional monotone map is recovered from flux balance, converted to a reflector by an integrating-factor ODE solve, and embedded in a modified Van Cittert iteration with nonnegativity clipping and ray-traced feedback. Across four benchmarks, covering continuous and discontinuous sources and minimum-height constraints, accuracy is measured by ray-traced normalized mean absolute error. On the two main benchmarks, the neural method reaches errors of about 2e-5 and 5e-5 within a few seconds on one NVIDIA RTX 4090 GPU, compared with 4e-3 and 5e-2 for the deconvolution baseline after several hundred seconds. The results show that the neural formulation is both more accurate and substantially faster, while still supporting practical height constraints. We also discuss extensions to rotationally symmetric and full three-dimensional reflector design through iterative correction schemes.