This preview shows pages 1–9. Sign up to view the full content.
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
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 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.
Light propagation in tissues is governed by the
radiative transport equation.
This theory takes into account absorption and scattering due to
inhomogeneities.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 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.
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.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 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, 16391644 (2006)] has
reviewed the existing theories and offered a mathematical
explanation for the correct theory.
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 ultrashort pulses (broad bandwidth), one may need to
consider a twofrequency radiative transport equation. See, for
example, A. Ishimaru, J. Opt. Soc. Am.
68,
1045–1050 (1978)
and A. C. Fannjiang, C. R. Physique
8
, 267271 (2007).
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document There is no polarization.
The theory of radiative transport can be extended readily to
take into account polarization through the socalled Stokes
matrix.
Here I is a 4vector 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
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 11/11/2011 for the course MATH 112 taught by Professor Jarvis during the Winter '08 term at BYU.
 Winter '08
 JARVIS
 Approximation

Click to edit the document details