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This paper introduces a neural network-based approach for designing 2D reflectors that transform light from a finite source into a desired far-field distribution. They propose two differentiable loss functions: a direct change-of-variables loss and a mesh-based loss, optimized using a quasi-Newton method. Experiments across various benchmarks demonstrate that the neural network approach outperforms a deconvolution baseline in terms of convergence speed and accuracy, while also naturally handling height constraints.
Neural networks can design optical reflectors that outperform traditional deconvolution methods, even with discontinuous light sources and height constraints.
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.