Differentiable phase-space simulation for rapid irradiance estimation and optimization

Phase space optics is a powerful way to visualize illumination systems, where complex irradiance patterns arise from relatively simple phase space transformations. However, the full optical phase-space is four-dimensional and difficult to visualize, limiting the applicability to 2D optical systems. In this talk, we will present a direct phase-space simulation method that models light sources in phase-space as a sum of Gaussian radiance distributions, and traces these radiance distributions through the optical system to capture the underlying phase-space transformation. The approach extends naturally to 3D optical systems, and projects directly onto the target plane to deliver high-resolution irradiance estimates without requiring dense Monte Carlo sampling. We show through simple design-examples how this permits rapid simulation and gradient-based optimization of freeform optical surfaces, and also demonstrate how algorithms from machine learning like Gaussian splatting and backpropagation can be adapted to run these phase-space simulations rapidly and differentiably on the GPU.