Application of low-discrepancy sequences for evaluation of illumination optical systems

Abstract

In this article, we introduce the quasi-Monte Carlo (QMC) method that applies a low-discrepancy sequence (LDS) for the evaluation of illumination optical systems. LDS is used in sequence-generation methods for numerical calculation, with high-order integration, and a characteristic of the QMC method that adopts a LDS is that it can deliver faster convergence than the Monte Carlo (MC) method, which uses random numbers. In this study, we have applied a LDS to the evaluation of illumination optical systems, which are conventionally evaluated by using the MC method, and verified its effectiveness. By assuming the evaluated system to have a gradient-index (GRIN) lens and comparing its illuminance distribution with the theoretical illuminance distribution, we confirmed that by using the QMC method, the evaluation process could be sped up by approximately five times compared to the MC method at the equivalent precision level. Furthermore, we established a method to reconstruct the image by using the QMC method that applies a LDS to evaluate the image-forming characteristics of the lens system and compared its results with those of the conventional MC method. It was found that the QMC method that applies a LDS was superior to the MC method even in this case, in both precision and conversion speed. On the basis of these results, it is evident that the QMC method that applies a LDS is extremely useful in the evaluation of illumination optical systems.