Density Estimation in Optical Phase Space for Optimizing Micro-Optical Elements on Freeform Surfaces

摘要

In imaging and non-imaging optical systems a microstructuring of the final surface of the system is often employed to further shape or diffuse the light distribution (e.g. in non-imaging luminaires or automotive headlights). While the geometry can be described in a parametric form by mapping the micro-optical features onto an underlying smooth freeform surface, ray-tracing an optical system composed of NURBS or polynomial B-spline surfaces for each optimization step can be costly. To reduce the computational overhead of ray-tracing the entire optical system for each optimization step, we perform a density estimation on the radiance distribution on the final smooth freeform surface. We employ a Gaussian Mixture Model (GMM) determined by Expectation Maximization (EM) and Multivariate Spline Approximation to estimate the power density in phase space. Using this continuous density, we gather the incident power on the detector and optimize parametric micro-optical elements on freeform surfaces. This is done in the context of purely specular surfaces, with the work focusing on the density estimation techniques and their side-effects in terms of precision and computational overhead. We demonstrate this density estimation approach for an LED collimator and compare the results to an unbiased Monte-Carlo ray-tracing ground truth.