Approximations for modeling light scattering by spheres with uncertainty in physical parameters

TL;DR

This paper introduces simplified trigonometric approximations for light scattering by spheres with uncertain parameters, significantly reducing computational costs while maintaining accuracy, applicable in astrophysics, biology, and atmospheric sensing.

Contribution

It presents a novel nested trigonometric approximation of Fraunhofer scattering coefficients for spheres, reducing evaluation costs by about 50 times without accuracy loss.

Findings

Approximation reduces computational cost significantly.

Maintains accuracy in scattering coefficient integrals.

Effective for parameterized lines of constant optical path.

Abstract

Uncertainty in physical parameters can make the solution of forward or inverse light scattering problems in astrophysical, biological, and atmospheric sensing applications, cost prohibitive for real-time applications. For example, given a probability density in the parametric space of dimensions, refractive index and wavelength, the number of required evaluations for the expected scattering increases dramatically. In the case of dielectric and weakly absorbing spherical particles (both homogeneous and layered), we begin with a Fraunhofer approximation of the scattering coefficients consisting of Riccati-Bessel functions, and reduce it into simpler nested trigonometric approximations. They provide further computational advantages when parameterized on lines of constant optical path lengths. This can reduce the cost of evaluations by large factors $\approx$ 50, without a loss of accuracy in the integrals of these scattering coefficients. We analyze the errors of the proposed approximation, and present numerical results for a set of forward problems as a demonstration.