Simple but accurate variance reduction techniques for Monte Carlo ray tracing of stray light from optical surface scatter

Abstract

Variations of Monte Carlo ray tracing are the most popular techniques for computing stray light in optical systems. The simplest and easiest to implement version doesn’t require ray splitting so what an incident ray becomes at each interaction is determined by the probabilities of the possible physical processes there. Unfortunately, for a low probability process such as polished surface scatter (including particulate contamination), it requires a prohibitively large number of initial rays to get a sufficient ray density at a typical focal plane area. The details of several simple modifications that require far fewer rays for the same or better accuracy will be presented. These include universal techniques applicable also to illumination patterns such as smart binning (also called ‘pixel interpolation’) and the use of quasi-random instead of pseudo-random number generators. In addition, there is the ‘tweaked’ Monte Carlo method developed specifically for veiling glare (light from bright regions in an image bleeding into dark regions and thus reducing contrast). However, most available software for computing out-of-field stray light in general optical systems use importance sampling in the form of preferred scattering towards predetermined ‘importance areas’ limited by the usual approximations to modest solid angles. For nearly all optical surfaces, micro-roughness scatter (and particulate forward scatter) in direction-cosine space is rotationally symmetric about the specular direction. In this case, an efficient and accurate (even for large solid angles) version called an ‘Importance Sector’ is proposed as a replacement.