arXiv subjects

Wilbert IJzerman

Publications and source records attributed to Wilbert IJzerman.

9 recordsLinked to original sources

arXiv2026

Direct Optimization of a 3D Finite-Source Reflector via Neural-Network Parameterization

We present a direct optimization method for three-dimensional freeform reflectors that transform the light of a finite-\'etendue 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.

physics.optics↗

arXiv2026

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

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.

cs.LG↗

arXiv2025

An inverse design method for generalized zero-\'etendue sources and two targets

We present an inverse method to compute freeform optical surfaces that transform a light distribution, parameterized by two source planes, into two separate target distributions. The surfaces can be reflectors or lenses, and control both the spatial and directional source and target coordinates of light rays. From energy conservation we derive Jacobian equations for optical mappings, and the optical path length provides generating functions for the optical surfaces. A three-stage least-squares algorithm numerically solves the resulting equations. We present examples with complex source and target distributions.

physics.optics↗

arXiv2025

Inverse freeform design of a parallel-to-two-target reflector system

We present an inverse method for transforming a given parallel light emittance to two light distributions at different parallel target planes using two freeform reflectors. The reflectors control both the spatial and directional target coordinates of light rays. To determine the shape and position of the reflectors, we derive generating functions and use Jacobian equations to find the optical mappings to the two targets. The model is solved numerically by a three-stage least-squares algorithm. A feasibility condition is derived, which ensures that the reflectors are not self-intersecting. Several examples validate this condition and demonstrate the algorithm's capability of realizing complex distributions.

physics.optics↗

arXiv2024

A neural network approach for solving the Monge-Amp\`ere equation with transport boundary condition

This paper introduces a novel neural network-based approach to solving the Monge-Amp\`ere equation with the transport boundary condition, specifically targeted towards optical design applications. We leverage multilayer perceptron networks to learn approximate solutions by minimizing a loss function that encompasses the equation's residual, boundary conditions, and convexity constraints. Our main results demonstrate the efficacy of this method, optimized using L-BFGS, through a series of test cases encompassing symmetric and asymmetric circle-to-circle, square-to-circle, and circle-to-flower reflector mapping problems. Comparative analysis with a conventional least-squares finite-difference solver reveals the competitive, and often superior, performance of our neural network approach on the test cases examined here. A comprehensive hyperparameter study further illuminates the impact of factors such as sampling density, network architecture, and optimization algorithm. While promising, further investigation is needed to verify the method's robustness for more complicated problems and to ensure consistent convergence. Nonetheless, the simplicity and adaptability of this neural network-based approach position it as a compelling alternative to specialized partial differential equation solvers.

cs.LG↗

arXiv2024

Three-Dimensional Freeform Reflector Design with a Microfacet Surface Roughness Model

This manuscript will unify inverse freeform reflector design and surface light scattering to design freeform reflectors with a scattering surface. We use microfacets, which are small, tilted mirrors superimposed on a smooth surface. We form a simple model of surface roughness and light scattering based on the orientations of the microfacets. Using a least-squares solver to compute the smooth reflector as a starting point, we can subsequently alter the surface using an optimization procedure to account for the scattering. After optimization, the resulting reflector surface produces the desired scattered light distribution. We verify the resulting reflector using raytracing.

physics.optics↗

arXiv2023

Concatenated Backward Ray Mapping on the Compound Parabolic Concentrator

Concatenated backward ray mapping is an alternative for ray tracing in 2D. It is based on the phase-space description of an optical system. Phase space is the set of position and direction coordinates of light rays intersecting a surface. The original algorithm is limited to optical systems consisting of only straight surfaces; we generalize it to accommodate curved surfaces. The algorithm is applied to a standard optical system, the compound parabolic concentrator. We compare the accuracy and speed of the generalized algorithm, the original algorithm and Monte Carlo ray tracing. The results show that the generalized algorithm outperforms both other methods.

physics.optics↗

arXiv2023

Three-Dimensional Freeform Reflector Design with a Scattering Surface

We introduce a novel approach to calculating three-dimensional freeform reflectors with a scattering surface. Our method is based on optimal transport and utilizes a Fredholm integral equation to express scattering. By solving this integral equation through a process similar to deconvolution, which we call `unfolding,' we can recover a typical specular design problem. Consequently, we consider freeform reflector design with a scattering surface as a two-step process wherein the target distribution is first altered to account for scattering, and then the resulting specular problem is solved. We verify our approach using a custom raytracer that implements the surface scattering model we used to derive the Fredholm integral.

physics.optics↗

arXiv2022

Two-Dimensional Freeform Reflector Design with a Scattering Surface

We combine two-dimensional freeform reflector design with a scattering surface modelled using microfacets, i.e., small specular surfaces representing surface roughness. The model results in a convolution integral for the scattered light intensity distribution, which yields an inverse specular problem after deconvolution. Thus, the shape of a reflector with a scattering surface may be computed using deconvolution, followed by solving the typical inverse problem of specular reflector design.

physics.optics↗