## Truncated Fourier-series approximation of the time-domain radiative transfer equation using finite elements |

JOSA A, Vol. 30, Issue 3, pp. 470-478 (2013)

http://dx.doi.org/10.1364/JOSAA.30.000470

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### Abstract

The radiative transfer equation (RTE) is widely accepted to accurately describe light transport in a medium with scattering particles, and it has been successfully applied as a light-transport model, for example, in diffuse optical tomography. Due to the computationally expensive nature of the RTE, most of these applications have been in the frequency domain. In this paper, an efficient solution method for the time-domain RTE is proposed. The method is based on solving the frequency-domain RTE at multiple modulation frequencies and using the Fourier-series representation of the radiance to obtain approximation of the time-domain solution. The approach is tested with simulations. The results show that the method can be used to obtain the solution of the time-domain RTE with good accuracy and with significantly fewer computational resources than are needed in the direct time-domain solution.

© 2013 Optical Society of America

**OCIS Codes**

(000.3860) General : Mathematical methods in physics

(030.5620) Coherence and statistical optics : Radiative transfer

(170.3660) Medical optics and biotechnology : Light propagation in tissues

(170.6920) Medical optics and biotechnology : Time-resolved imaging

(170.7050) Medical optics and biotechnology : Turbid media

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: October 23, 2012

Manuscript Accepted: January 9, 2013

Published: February 21, 2013

**Virtual Issues**

Vol. 8, Iss. 4 *Virtual Journal for Biomedical Optics*

**Citation**

Aki Pulkkinen and Tanja Tarvainen, "Truncated Fourier-series approximation of the time-domain radiative transfer equation using finite elements," J. Opt. Soc. Am. A **30**, 470-478 (2013)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-3-470

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