A set of basis functions to improve numerical calculation of Mie scattering in the Chandrasekhar-Sekera representation

Abstract

Numerical calculations of light propagation in random media demand the multiply scattered Stokes intensities to be written in a common fixed reference. In multiple-scattering schemes, a particularly useful way to perform automatically these basis transformations between reference frames is to write the scattered intensities in the Chandrasekhar-Sekera representation. The main drawback with this representation is the necessity of numerical tests to deal with the limiting situations of the small particle (Rayleigh) and forward/backward scattering. Here, a new set of basis functions is presented to describe the scattering of light by spherical particles (Mie scattering) in the Chandrasekhar-Sekera representation. These basis functions can be implemented in a new algorithm to calculate the Mie scattering amplitudes, which leads straightforwardly to all the scattering quantities. In contrast to the traditional implementation, this set of basis functions implies to natural numerical convergence to the above mentioned limiting cases, which are thoroughly discussed.

Keywords:

• Mie scattering
• Chandrasekhar-Sekera representation
• multiple scattering
• random media
• radiative transfer equation
• Monte Carlo simulation

Acknowledgments

The authors thank the very stimulating discussions with Felipe Arruda Pinheiro.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

A.S.M. holds grants from CNPq 309851/2018-1; J.R.A. and T.J.A. acknowledge financial support from the Brazilian agency FAPESP (Grants 2018/21694-4 and 2015/21194-3, respectively). This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.