Direct Optimization of a 3D Finite-Source Reflector via Neural-Network Parameterization
Abstract
We present a direct optimization method for three-dimensional freeform reflectors that transform the light of a finite-étendue source into a prescribed far-field angular intensity distribution. The reflector profile is represented by a small neural network (a multilayer perceptron), which is trained end-to-end through a differentiable ray-tracing objective. We furthermore parameterize the emission directions in gnomonic coordinates, and show how we use this to ensure that every emitted ray intersects the reflector. At each iteration, the network is converted to a bicubic spline representation for ray-tracing efficiency, and intersections with this smooth surface are solved by a damped Newton solve, with gradients computed via the implicit function theorem. The traced output distribution is compared with the desired target on a 'soft' histogram, under an H−1-type spectral weighting that emphasizes long-range transport of flux to improve convergence. Optimization is performed using a BFGS method with self-scaled Broyden updates and a plateau-perturbation rule to prevent stalling. The method converges reliably within seconds on a single GPU for all examples tested.
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BibTeX
@misc{hacking2026direct,
title = {{Direct Optimization of a 3D Finite-Source Reflector via Neural-Network Parameterization}},
author = {Roel Hacking and Lisa Kusch and Martijn Anthonissen and Wilbert IJzerman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00899},
eprint = {2609.00899},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00899},
}
RIS
TY - UNPB
TI - Direct Optimization of a 3D Finite-Source Reflector via Neural-Network Parameterization
AU - Roel Hacking
AU - Lisa Kusch
AU - Martijn Anthonissen
AU - Wilbert IJzerman
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00899
UR - https://arxiv.org/abs/2609.00899
AB - We present a direct optimization method for three-dimensional freeform reflectors that transform the light of a finite-étendue source into a prescribed far-field angular intensity distribution. The reflector profile is represented by a small neural network (a multilayer perceptron), which is trained end-to-end through a differentiable ray-tracing objective. We furthermore parameterize the emission directions in gnomonic coordinates, and show how we use this to ensure that every emitted ray intersects the reflector. At each iteration, the network is converted to a bicubic spline representation for ray-tracing efficiency, and intersections with this smooth surface are solved by a damped Newton solve, with gradients computed via the implicit function theorem. The traced output distribution is compared with the desired target on a 'soft' histogram, under an H^−1-type spectral weighting that emphasizes long-range transport of flux to improve convergence. Optimization is performed using a BFGS method with self-scaled Broyden updates and a plateau-perturbation rule to prevent stalling. The method converges reliably within seconds on a single GPU for all examples tested.
ER -