Biomedical Optics

Chapter 6 - Hybrid Model of Monte Carlo Method and Diffusion Theory

6.1.   INTRODUCTION

The Monte Carlo method and the diffusion theory have complementary attributes
for modeling photon transport in a scattering medium. The Monte Carlo method
is accurate but computationally inefficient, whereas the diffusion theory is inaccurate
but computationally efficient. A hybrid of the two approaches, however,
is constructed to combine the advantages of both. The hybrid model computes as
much as 100 times faster than the Monte Carlo method yet improves the accuracy
of the diffusion theory.

6.2.   DEFINITION OF PROBLEM

A pencil beam is normally incident on a slab of homogeneous scattering medium.
The geometric and optical properties of the slab are described by thickness d,
relative refractive index nrel, absorption coefficient μa, scattering coefficient μs,
and scattering anisotropy g, where nrel is the ratio of the refractive index of the
scattering medium to that of the ambient medium. The Henyey–Greenstein phase
function is assumed. Cylindrical coordinates (r, φ, z) are used; the origin is the
point of incidence of the pencil beam on the top surface of the slab; the z axis
points along the pencil beam. The diffuse reflectance and the diffuse transmittance
versus r are computed.

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