Analytical solutions of the simplified spherical harmonics equations for infinite and semi-infinite scattering medium based on Eigen method

Limin Zhang; Wei Zhang; Feng Gao; Jiao Li; Huijuan Zhao

doi:10.1117/12.2003014

25 March 2013 Analytical solutions of the simplified spherical harmonics equations for infinite and semi-infinite scattering medium based on Eigen method

Limin Zhang, Wei Zhang, Feng Gao, Jiao Li, Huijuan Zhao

Author Affiliations +

Proceedings Volume 8578, Optical Tomography and Spectroscopy of Tissue X; 85782G (2013) https://doi.org/10.1117/12.2003014
Event: SPIE BiOS, 2013, San Francisco, California, United States

Abstract

We derive a modification method to simplify the SP_N coupled partial differential equations into some independent equations. The modification leads to significant mathematical simplifications and can be used to calculate the Green’s function of the SP_N equations for infinite and semi-infinite turbid medium. The obtained analytical solutions depend on eigenvectors and eigenvalues. Compared with the derived methods based on coupled equations, the derivation process of our proposed method is general, fast and simple. The derived analytical solutions are successfully verified by comparisons with Monte Carlo simulations.

Citation Download Citation

Limin Zhang, Wei Zhang, Feng Gao, Jiao Li, and Huijuan Zhao "Analytical solutions of the simplified spherical harmonics equations for infinite and semi-infinite scattering medium based on Eigen method", Proc. SPIE 8578, Optical Tomography and Spectroscopy of Tissue X, 85782G (25 March 2013); https://doi.org/10.1117/12.2003014

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