Effect of finite terms on the truncation error of Mie series

TL;DR

This paper improves the formula for determining the number of terms needed in Mie series to accurately compute light scattering, enhancing efficiency in modeling scattering phenomena.

Contribution

An improved formula for the finite number of Mie series terms needed for accurate scattering calculations, incorporating error bounds.

Findings

Revised formula includes terms for prescribed relative error

Extended precision computations validate the improved formula

Applicable across various size parameters and refractive indices

Abstract

The finite sum of the squares of the Mie coefficients is very useful for addressing problems of classical light scattering. An approximate formula available in the literature, and still in use today, has been developed to determine a priori the number of the most significant terms needed to evaluate the scattering cross section. Here we obtain an improved formula, which includes the number of terms needed for determining the scattering cross section within a prescribed relative error. This is accomplished using extended precision computation, for a wide range of commonly used size parameters and indexes of refraction. The revised formula for the finite number of terms can be a promising and valuable approach for efficient modeling light scattering phenomena.