Biomedical Optics

Chapter 5 - Radiative Transfer Equation and Diffusion Theory

5.1.   INTRODUCTION

Photon transport in biological tissue can be modeled analytically by the radiative
transfer equation (RTE), which is considered equivalent to the numerical Monte
Carlo method covered in Chapter 3. Because the RTE is difficult to solve, it
is often approximated to a diffusion equation, which provides solutions that are
more computationally efficient but less accurate than those provided by the Monte
Carlo method.

5.2.   DEFINITIONS OF PHYSICAL QUANTITIES

Spectral radiance Lv, the most general physical quantity discussed in this chapter,
is defined as the energy flow per unit normal area per unit solid angle per unit time
per unit temporal frequency (temporofrequency) bandwidth, where the normal
area is perpendicular to the flow direction. Radiance L is defined as the spectral
radiance integrated over a narrow frequency range [ν, ν + Δν]:

 

Here, denotes position, denotes unit direction vector, t denotes time, and the
parentheses enclose the unit of the physical quantity on the left-hand side of the
equation. The amount of radiant energy dE that is transported across differential
area element dA within differential solid angle element dΩ during differential
time element dt (Figure 5.1) is given by

 


Here, denotes the unit outward normal vector of dA; · denotes the dot
product of the two unit vectors, which equals the cosine of the angle between
them. The radiance is the dependent variable in the RTE (to be derived). Several
additional physical quantities can be derived from the radiance.

 

UNLIMITED FREE
ACCESS
TO THE WORLD'S BEST IDEAS

SUBMIT
Already a GlobalSpec user? Log in.

This is embarrasing...

An error occurred while processing the form. Please try again in a few minutes.

Customize Your GlobalSpec Experience

Category: X-ray Instruments and X-ray Systems
Finish!
Privacy Policy

This is embarrasing...

An error occurred while processing the form. Please try again in a few minutes.