ABSTRACT
In the previous two chapters, we have covered the basic concepts of light and optical theories as well as light interactions with the tissue in the form of absorption, reflection, and scattering. In this chapter, we first define the basic radiometric quantities that are needed for describing light propagation in food and biological materials. Radiative transfer theory is then derived, according to the principle of conservation of energy. As the radiative transfer theory equation is generally too complex to solve, diffusion approximation theory needs to be introduced to simplify the mathematical description of light propagation in food and biological materials. It is then followed with a discussion of the three boundary conditions commonly used for solving the diffusion equation. Moreover, analytical solutions to the diffusion equation under several special light illumination conditions are presented, which form the theoretical foundation for a number of modern, noninvasive, or in vivo optical property measurement techniques, including a spatially-resolved, time-resolved, frequency domain, and spatial-frequency domain. Numerical methods such as the finite element analysis offer flexibility in dealing with complex geometries and nonhomogeneous or layered scattering media, and hence are useful in studying light propagation in food and biological materials. Finally, application examples are given of using the finite element method (FEM) for modeling light propagation in semi-infinite scattering media and for predicting the reflectance at the surface.
