Diffraction models of radiation entering an aperture for use in a Monte Carlo ray-trace environment

Abstract

This manuscript presents multiple modeling efforts to describe diffraction of monochromatic radiant energy passing through an aperture for use in the Monte-Carlo ray-trace environment. Described is a deterministic model, based upon Heisenberg's uncertainty principle, which predicts the angle at which an approaching ray is diffracted. The result is a curve which approximates the analytical interference pattern, but does not model the side fringes (i.e. secondary maxima). This model is applicable to either Fraunhofer (far-field) or Fresnel (near- field) diffraction situations. In addition to this model, a diffraction model is presented that approximates the interference pattern including the secondary maxima, as produced by radiation passing through a slit or a circular aperture. This model, based on the Huygens-Fresnel principle with a correcting obliquity factor, is useful for predicting Fraunhofer (far-field) diffraction in the Monte-Carlo ray- trace environment. The motivation for this work is the need to properly model the diffraction of radiant energy as it approaches a detector intended for monitoring the Earth's radiation budget from a geo-stationary orbit. The proposed detector, a linear-array of thermopile elements, is housed in a wedge-shaped cavity with a 60-$micrometer slit through which radiant energy between wavelengths of 0.1 micrometer and 40 micrometer must pass. A radiative model of this cavity which does not account for diffraction effects has already been developed using the Monte Carlo ray-trace method. This detector was originally intended to fly on the Geo-Stationary Earth Radiation Budget (GERB) instrument.