Technology Category
Search and Optimization: Non-convex OptimizationMachine Learning: OptimizationComputer Vision: Learning & Optimization for CV
Neural network methods for two-dimensional finite-source reflector design
🤖 AI Summary
This work proposes a neural network–based inverse design method for two-dimensional reflectors tailored to finite extended sources, aiming to accurately generate prescribed far-field intensity distributions. The reflector height is parameterized via a neural network, and two differentiable objective functions are formulated: a forward loss based on variable transformation and a backward loss derived from grid-based ray-tracing integration. Leveraging automatic differentiation and the L-BFGS quasi-Newton optimizer, the method enables efficient and robust optimization. Notably, it is the first to integrate neural networks into reflector design for finite sources, inherently satisfying height constraints, maintaining continuous optimization even under discontinuous source distributions, and significantly enhancing robustness. Across four benchmark cases, the approach consistently outperforms conventional flux-balancing deconvolution baselines, achieving faster convergence and lower normalized mean absolute error (NMAE).
Technology Category
Application Category
📝 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. We propose a neural network parameterization of the reflector height and develop two differentiable objective functions: (i) a direct change-of-variables loss that pushes the source distribution through the learned inverse mapping, and (ii) a mesh-based loss that maps a target-space grid back to the source, integrates over intersections, and remains continuous even when the source is discontinuous. Gradients are obtained via automatic differentiation and optimized with a robust quasi-Newton method. As a comparison, we formulate a deconvolution baseline built on a simplified finite-source approximation: a 1D monotone mapping is recovered from flux balance, yielding an ordinary differential equation solved in integrating-factor form; this solver is embedded in a modified Van Cittert iteration with nonnegativity clipping and a ray-traced forward operator. Across four benchmarks -- continuous and discontinuous sources, and with/without minimum-height constraints -- we evaluate accuracy by ray-traced normalized mean absolute error (NMAE). Our neural network approach converges faster and achieves consistently lower NMAE than the deconvolution method, and handles height constraints naturally. We discuss how the method may be extended to rotationally symmetric and full three-dimensional settings via iterative correction schemes.
Problem
Research questions and friction points this paper is trying to address.
reflector design
inverse problem
finite-source
far-field distribution
optical design
Innovation
Methods, ideas, or system contributions that make the work stand out.
neural network reflector design
differentiable rendering
inverse optics
finite extended source
mesh-based loss
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