Consistently smooth merit functions in algorithmic differentiable ray tracing for illumination design

Optics Express, vol. 34, pp. 30764

Abstract

In illumination design, a common goal is to determine the parameters of an optical system that produce a desired irradiance distribution. One approach to this problem is to employ optimization methods based on differentiable algorithmic ray tracing, which enables efficient derivative computation. However, conventional Monte Carlo ray tracing simulation of irradiance distributions is not directly differentiable with automatic differentiation. To address this, current methods use smooth measurement functions that weight ray contributions based on distance from pixel centers, effectively smoothing the simulated irradiance. Yet these methods typically leave the desired irradiance distribution unsmoothed. This creates a mismatch where the optimization compares a smoothed simulation to an unsmoothed target. We show that this inconsistency degrades performance, especially if wider kernels are used to reduce noise. We propose a fully smoothed residual merit function that applies the same Gaussian convolution to both the simulated and desired distributions and eliminates this mismatch. We present two examples that demonstrate the stability and accuracy of the proposed merit function.

Authors 2

1. Martin Pflaum Aachen Fraunhofer Institute for Laser Technology ILT

   Fraunhofer Institute for Laser Technology

   Affiliation as printed

   Fraunhofer Institute for Laser Technology ILT

2. Hakon Johnsen