Renormalization of the highly forward-peaked phase function using the double exponential formula for radiative transfer
Renormalization of the highly forward-peaked phase function using the double exponential formula for radiative transfer
复制标题
使用辐射传输双指数公式对高前向峰值相位函数进行重整化
DOI：
10.1007/s10910-016-0670-3
复制
发表时间：
2016
影响因子：
1.7
通讯作者：
M.
中科院分区：
文献类型：
--
作者：
Fujii;H.;Okawa;S.;Yamada;Y.;Hoshi;Y.;Watanabe;M.
利用辐射传输方程（RTE）数值计算光子在生物组织中的迁移是生物医学光学和成像领域的研究热点。由于生物组织是一种高度前向峰值散射介质，在RTE的数值计算中，相函数的重正化是至关重要的。本文提出了一种利用双指数公式对相函数进行重正化的简单方法。首先，在高前向峰值散射条件下，通过与传统方法计算的极散射角余弦平均值的数值比较，验证了该方法的有效性.结果表明，平均余弦的计算收敛速度使用所提出的方法比使用传统的离散角方向的总数增加。接下来，使用所提出的方法的RTE的数值解的准确性进行了检查，通过比较的数值解与解析解的RTE在一个均匀的介质中具有高度前向峰值散射。结果发现，所提出的方法减少了使用传统的数值解的误差，特别是在方向总数的一个小的值。这一结果表明，所提出的方法有可能提高高散射介质中的RTE的数值结果的精度。
Numerical calculation of photon migration in biological tissue using the radiative transfer equation (RTE) has attracted great interests in biomedical optics and imaging. Because biological tissue is a highly forward-peaked scattering medium, renormalization of the phase function in numerical calculation of the RTE is crucial. This paper proposes a simple approach of renormalizing the phase function by the double exponential formula, which was heuristically modified from the original one. Firstly, the validity of the proposed approach was tested by comparing numerical results for an average cosine of the polar scattering angle calculated by the proposed approach with those by the conventional approach in highly forward-peaked scattering. The results show that calculation of the average cosine converged faster using the proposed approach than using the conventional one as a total number of discrete angular directions increases. Next, the accuracy of the numerical solutions of the RTE using the proposed approach was examined by comparing the numerical solutions with the analytical solutions of the RTE in a homogeneous medium with highly forward-peaked scattering. It was found that the proposed approach reduced the errors of the numerical solutions from those using the conventional one especially at a small value of the total number of the directions. This result suggests that the proposed approach has a possibility to improve the accuracy for the numerical results of the RTE in the highly scattering medium.