Improving numerical stability of the separation of variables method for light scattering by spheroids with size parameters beyond 1000

This study analyzes the numerical instability associated with using the separation of variables method (SVM) to solve light scattering by spheroids. An accurate and numerically stable solution to the single-scattering properties of a spheroidal particle is obtained. The numerical instability causes inaccurate calculation of the scattered field expansion coefficients with even expansion degrees (n) at expansion order m = 0. Relying on a quantitative analysis using numerical linear algebra techniques, we find that this problem originates in the expression of the linear equation system used to solve the expansion coefficients. A pseudoinverse method is adopted to substantially improve the numerical stability of the expansion coefficient calculation. The new SVM improved by the pseudoinverse method can be used to accurately compute single-scattering properties of spheroidal particles with size parameters beyond 1000.