Beam spread functions calculated using Feynman path integrals. (July 2017) - Kilgo, Paul; Tessendorf, Jerry
Abstract: A method of solving the radiative transfer equation using Feynman path integrals (FPIs) is discussed. The FPI approach is a mathematical framework for computing multiple scattering in participating media. Its numerical behavior is not well known, and techniques are being developed to solve the FPI approach numerically. A missing numerical technique is detailed and used to calculate beam spread functions (BSFs), a commonly studied experimental property of many types of media. The calculations are compared against measured BSFs of sea ice. Analysis shows differently-shaped BSFs, and suggests the width parameter of the calculated BSF's Gaussian fit approaches a value in the limit of the number of path segments. A projection is attempted, but suggests a larger number of path segments would not increase the width of the calculated BSF. The trial suggests the approach is numerically stable, but requires further testing to ensure scientific accuracy. Abstract : Highlights: Methodology is introduced for calculating radiative transfer using path integrals. Calculated beam spread functions are differently-shaped from experimental ones. Extrapolation of a numerical parameter shows diminishing returns for the shape of the BSF.