Hybrid Method for Solving the Radiative Transport Equation

Hybrid Method for Solving the Radiative Transport Equation

The spherical harmonics method (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>N</mi></msub></semantics></math></inline-formula> method) is of...

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Bibliographic Details
Main Authors: André Liemert, Dominik Reitzle, Alwin Kienle
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Photonics
Subjects:
radiative transport
spherical harmonics method
photon migration
turbid media
light propagation in tissues
Online Access:https://www.mdpi.com/2304-6732/12/5/409
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Summary:The spherical harmonics method (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>N</mi></msub></semantics></math></inline-formula> method) is often used for solving the radiative transport equation in terms of analytical functions. A severe and unsolved problem in this context was the evaluation of the angle-resolved radiance near sources and boundaries, which is a serious limitation of this method in view of concrete applications, e.g., in biomedical optics for investigating the different types of optical microscopy, within NIR spectroscopy, such as for the determination of ingredients in foods or in pharmaceuticals, and within physics-based rendering. In this article, we report on a hybrid method that enables accurate evaluation of the angle-resolved radiance directly at the boundary of an anisotropically scattering medium, avoiding the problems of the traditional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>N</mi></msub></semantics></math></inline-formula> methods. The derived integral equation needed for the realization of the hybrid <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>N</mi></msub></semantics></math></inline-formula> method is formally valid for an arbitrary convex bounded medium. The proposed approach can be evaluated with practically the same computational effort as the traditional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>N</mi></msub></semantics></math></inline-formula> method while being far more accurate.
ISSN:2304-6732

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