Radiative transfer with delta-Eddington-type phase functions

详细信息    查看全文

• 作者：Weimin Han ; ^a ; ^{weimin-han@uiowa.edu} ; Feixiao Long^b ; Wenxiang Cong^b ; Xavier Intes^b ; Ge Wang^b
• 关键词：Radiative transfer equation ; Generalized delta-Eddington phase function ; Existence ; Uniqueness ; Continuous dependence
• 刊名：Applied Mathematics and Computation
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：300
• 期：Complete
• 页码：70-78
• 全文大小：1035 K
• 卷排序：300

文摘

The radiative transfer equation (RTE) arises in a wide variety of applications, in particular, in biomedical imaging applications associated with the propagation of light through the biological tissue. However, highly forward-peaked scattering feature in a biological medium makes it very challenging to numerically solve the RTE problem accurately. One idea to overcome the difficulty associated with the highly forward-peaked scattering is through the use of a delta-Eddington phase function. This paper is devoted to an RTE framework with a family of delta-Eddington-type phase functions. Significance in biomedical imaging applications of the RTE with delta-Eddington-type phase functions are explained. Mathematical studies of the problems include solution existence, uniqueness, and continuous dependence on the problem data: the inflow boundary value, the source function, the absorption coefficient, and the scattering coefficient. Numerical results are presented to show that employing a delta-Eddington-type phase function with properly chosen parameters provides accurate simulation results for light propagation within highly forward-peaked scattering media.