Analytical solutions to the simplified spherical harmonics equations using eigen decompositions.
Analytical solutions to the simplified spherical harmonics equations using eigen decompositions.
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DOI：
10.1364/ol.38.005462
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发表时间：
2013-12
期刊：
影响因子：
3.6
通讯作者：
Limin Zhang;Jiao Li;Xi Yi;Huijuan Zhao;F. Gao
中科院分区：
文献类型：
--
作者：
Limin Zhang;Jiao Li;Xi Yi;Huijuan Zhao;F. Gao
本文提出了一种简化球面谐波方程（SP(N)）解析解的改进方法。该方案利用特征分解将SP(N)偏微分方程解耦为独立方程，并基于特征向量和特征值计算光子迁移的格林函数。与基于原始耦合方程的已建立的解相比，所提出的推导在理论上是简洁的，并且普遍可扩展到其他规则几何。我们通过与蒙特卡罗模拟的无限散射介质和圆形几何作为边值问题的例子进行比较，验证了所提出的方法。
We develop a modified method to simplify the analytical solutions to the simplified spherical harmonics equations (SP(N)). The scheme decouples the SP(N) partial differential equations into independent equations using eigen decompositions and calculates the Green's function of the photon migrations based on the eigenvectors and eigenvalues. In contrast to the established solutions that are based on the original coupled equations, the proposed derivation is theoretically concise and universally extendable to other regular geometries. We validate the proposed method in comparison with Monte-Carlo simulations for an infinite scattering medium and a circular geometry as an example of the boundary value problems.