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Random Processes in Physics and Finance$
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Melvin Lax, Wei Cai, and Min Xu

Print publication date: 2006

Print ISBN-13: 9780198567769

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198567769.001.0001

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Random walk of light in turbid media

Random walk of light in turbid media

(p.227) 13 Random walk of light in turbid media
Random Processes in Physics and Finance

Melvin Lax

Wei Cai

Min Xu

Oxford University Press

The random motion of particles in a turbid medium, due to multiple elastic scattering, obeys the classic Boltzmann transport equation. This chapter shows how the center position and the diffusion coefficients of an incident collimated beam into an infinite uniform turbid medium are derived using an elementary analysis of the random walk of photons in a turbid medium. Light propagation in a multiple scattering (turbid) medium such as the atmosphere, colloidal suspensions, and biological tissue is commonly treated by the theory of radiative transfer. The basic equation of radiative transfer is the elastic Boltzmann equation, a nonseparable integro-differential equation of first order for which an exact closed form solution is not known except for the case for isotropic scatterers. Solutions are often based on truncation of the spherical harmonics expansion of the photon distribution function or resort to numerical calculation including Monte Carlo simulations. Macroscopic and microscopic statistics in the direction space are also discussed, along with the generalised Poisson distribution.

Keywords:   random walk, light propagation, turbid medium, Boltzmann transport equation, diffusion coefficients, collimated beam, photons, direction space, generalised Poisson distribution

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