Stochastic algorithm for creating highly accurate optimized scattering look-up tables for a large range of size parameters and optical constants

Abstract

We report a novel algorithm for generating optimized look-up tables suitable for rapid evaluation of various light scattering parameters and other hard-to-evaluate functions. Our method uses a stochastic algorithm to minimize the number of look-up table points needed while achieving high accuracy and speed. As an example, we present a general Mie scattering look-up table applicable to a large range of size parameters (0.02 < x < 200) and most materials (organics, inorganics, minerals, metals etc.) with real and imaginary parts of the refractive index ranging from 0.2 to 5 and 0 to 5, respectively. The look-up table is up to 3500 times faster than evaluating the Mie analytical expressions (in Matlab). This method opens up new possibilities in detection algorithm development (e.g. large synthetic datasets for machine learning), inverse problems and all other problems where a large number of Mie scattering coefficients needs to be rapidly evaluated. Furthermore, this method is applicable to other, related scattering problems. For example, we also present look-up tables for scattering efficiencies for spheres on various substrates.