Framework for freeform reflective mirror design in uniform illumination systems

A typical digital light processing (DLP) projection system revolves around a digital micro-mirror device and fundamentally consists of an illumination structure and a projection lens. Designing high-performance freeform reflective mirrors for uniform illumination in DLP systems remains computationally challenging due to the iterative nature of traditional ray tracing methods. This paper presents a differentiable ray tracing framework that enables gradient-based optimization of mirror surfaces through automatic differentiation. A hybrid parametrization strategy combining quadratic base functions with multilayer perceptron (MLP) corrections is employed to represent the mirror surface, effectively capturing both global curvature and local refinements. This optimization utilizes a composite loss function incorporating Wasserstein distance approximation, entropy regularization, and efficiency penalties, implemented through an adaptive multi-stage training strategy. The framework was evaluated in a representative off-axis illumination scenario with an extended Lambertian source. In a constrained DMD illumination scenario, simulation results show the framework achieves an optical efficiency of 72.8% and an illuminance uniformity of 94.3% along the Y direction. The optimization process typically converges within 10–20 min on a single GPU, demonstrating high computational efficiency. Furthermore, the framework remains functional on standard multi-core CPUs, achieving convergence in under 40 min. Preliminary validation using LightTools shows qualitative agreement with computational results, with minor discrepancies attributed to sampling differences. This automated workflow reduces the need for manual parameter tuning, providing a practical tool for rapid freeform optical prototyping.