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Kim_slides - Analytical and numerical approximations to the radiative transport equation for light propagation in tissues Arnold D Kim School of

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Analytical and numerical approximations to the radiative transport equation for light propagation in tissues Arnold D. Kim School of Natural Sciences University of California, Merced
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We seek to give an overview of the analytical and numerical approximations used in studying light propagation in tissues. The theory of radiative transport governs light propagation in tissues. Typically, one make several simplifying assumptions to the general radiative transport equation. We wish to become familiar with some of the more common analytical and computational methods used in light propagation in tissues.
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Light propagation in tissues is governed by the radiative transport equation. This theory takes into account absorption and scattering due to inhomogeneities.
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We have made several assumptions in applying radiative transport theory to light propagation in tissues. There are no correlations between fields, so the addition of power (not the addition of fields) holds. The background is homogeneous. There is no time dependence. There is no polarization. In what follows, we discuss each of these assumptions.
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There are no correlations between fields, so the addition of power (not the addition of fields) holds. This is the key assumption in radiative transport theory. For a discrete random medium, this assumption corresponds to a medium being sufficiently dilute that scattered fields are not correlated, but dense enough that one can take a continuum limit. For a continuous random medium, the random fluctuations must be relatively small and vary on a scale on the order of the wavelength.
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The background is homogeneous. The theory of radiative transport can be extended readily to take into account a varying background refractive index. There have been several theories proposed for this problem. G. Bal [J. Opt. Soc. Am. A 23, 1639-1644 (2006)] has reviewed the existing theories and offered a mathematical explanation for the correct theory.
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There is no time dependence. The theory of radiative transport can be extended readily to take into account time dependence (for a sufficiently narrow bandwidth). For ultra-short pulses (broad bandwidth), one may need to consider a two-frequency radiative transport equation. See, for example, A. Ishimaru, J. Opt. Soc. Am. 68, 1045–1050 (1978) and A. C. Fannjiang, C. R. Physique 8 , 267-271 (2007).
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There is no polarization. The theory of radiative transport can be extended readily to take into account polarization through the so-called Stokes matrix. Here I is a 4-vector containing the Stokes parameters ( I , Q , U and V ) and S is a 4 x 4 scattering matrix. Polarization is neglected very often for mathematical simplicity. See M. Moscoso et al, J. Opt. Soc. Am. A
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This note was uploaded on 11/11/2011 for the course MATH 112 taught by Professor Jarvis during the Winter '08 term at BYU.

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Kim_slides - Analytical and numerical approximations to the radiative transport equation for light propagation in tissues Arnold D Kim School of

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