Expansion of scattered phase matrix based on Zernike polynomials

Haishui Ye; Zhishan Gao; Qianwen Wang; Kexin Bao; Xiaowei Yang

doi:10.1117/12.999481

11 December 2012 Expansion of scattered phase matrix based on Zernike polynomials

Haishui Ye, Zhishan Gao, Qianwen Wang, Kexin Bao, Xiaowei Yang

Proceedings Volume 8553, Optics in Health Care and Biomedical Optics V; 85532L (2012) https://doi.org/10.1117/12.999481
Event: Photonics Asia, 2012, Beijing, China

Abstract

There exists three variables in the radiative transfer equation based on dynamic energy conservation, including polar angle, azimuth angle and normalized penetrate depth. In order to solute this equation with double integral on polar angle and azimuth angle, the first step is to introduce proper method to isolate azimuthal dependency from polar angle. In this paper, we propose a novel phase matrix expansion with Zernike polynomials, which represents the probability of scattering events. The results show that it can provide a new improved strategy for the solution of radiative transfer equations in Discrete-Ordinate Method (DOM), which is different from commonly used Fourier series and Legendre polynomials expansion and we make conclusion that there are three principles for polynomials’ selection, including orthogonal performance, special theorem for polynomial derivation and triangle function generation.

Citation Download Citation

Haishui Ye, Zhishan Gao, Qianwen Wang, Kexin Bao, and Xiaowei Yang "Expansion of scattered phase matrix based on Zernike polynomials", Proc. SPIE 8553, Optics in Health Care and Biomedical Optics V, 85532L (11 December 2012); https://doi.org/10.1117/12.999481

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