Modeling interference using Monte Carlo ray trace
Monte Carlo ray tracing has been shown to be both a robust and reliable method for optical modeling of illumination systems. The typical approach traces rays through an optical system and averages the rays in spatial and angular bins to provide estimates of the illuminance and intensity. While Monte Carlo methods are commonly used with incoherent sources, they can also be used with coherent sources. The primary difference between the two simulation types is the inclusion of the phase difference between binned rays in the illuminance and intensity calculations. The phase information can be stored in a ray’s optical path length, which is updated as a ray is traced through a system and when a ray encounters specific interfaces, such as the π phase shift due to a reflection from a surface of higher index. Thus, when careful consideration is given to the phase changes that occur during a ray trace, it is possible to use Monte Carlo methods to model illumination systems that require coherent sources, such as interferometers. Furthermore, with the ability to model coherent sources, beamlet based approaches are also effective. Comparisons are presented. In general, a common challenge for Monte Carlo simulations is the large number of needed rays to overcome statistical noise. However, it is possible to reduce the number of traced rays using various methods, such as: source aiming, scatter aiming, and Backwards Ray Trace. These methods minimize the number of traced rays by using knowledge of the system to selectively avoid tracing rays which will not contribute meaningful data to the output distribution. Monte Carlo ray tracing can also be computationally expensive. To prevent rerunning a costly simulation, it is advantageous to save the traced rays and post process the data for further analysis and studies. For example, the rays can be defocused to a plane at a different distance, re-binned for a difference receiver resolution, or filters can be used to remove rays based on specific criteria like whether they passed through a specific surface. This paper is organized with three main sections. First, we discuss Monte Carlo ray tracing to model interference. The second discusses Monte Carlo ray tracing for modeling diffraction using a Huygens-Fresnel approach. The last summarizes the paper.
Synopsys, Inc. (United States)
Dr. Bill Cassarly, a Synopsys Scientist, is a driving force in the movement to develop the field of computer-aided illumination engineering. He submitted the winning solutions for the 2006 IODC and 2010 IODC Illumination Design Problems, teaches illumination design courses, holds 50 US patents, and is a key contributor to many features available in LightTools®.