Monte Carlo ray-trace diffraction based on the Huygens-Fresnel principle.

Abstract

The goal of this effort is to establish the conditions and limits under which the Huygens-Fresnel principle accurately describes diffraction in the Monte Carlo ray-trace (MCRT) environment. This goal is achieved by systematic intercomparison of dedicated experimental, theoretical, and numerical results. We evaluate the success of the Huygens-Fresnel principle by predicting and carefully measuring the diffraction fringes produced by both single slit and circular apertures. We then compare the results from the analytical and numerical approaches with each other and with dedicated experimental results. We conclude that use of the MCRT method to accurately describe diffraction requires that careful attention be paid to the interplay among the number of aperture points, the number of rays traced per aperture point, and the number of bins on the screen. This conclusion is supported by standard statistical analysis, including the adjusted coefficient of determination, Radj2, the rms deviation, and the reduced chi-square statistic, χv2.