25 March 2013 Analytical solutions of the simplified spherical harmonics equations for infinite and semi-infinite scattering medium based on Eigen method
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Abstract
We derive a modification method to simplify the SPN 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 SPN 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.
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Limin Zhang, Limin Zhang, Wei Zhang, Wei Zhang, Feng Gao, Feng Gao, Jiao Li, Jiao Li, Huijuan Zhao, 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); doi: 10.1117/12.2003014; https://doi.org/10.1117/12.2003014
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