The Diffusion Approximation in Three Dimensions
The diffusion approximation of the radiative transport equation is used extensively because closed-form analytical solutions can be obtained. The previous chapter gave closed-form solutions to the one-dimensional diffusion equation. In this chapter, the classic searchlight problem of a finite beam of light normally incident on a slab or semi-infinite medium will be solved in the timeindependent diffusion approximation. The solution follows naturally once the Green’s function for the problem is known, and so the Green’s function subject to homogeneous Robin boundary conditions will be given for semi-infinite and slab geometries. The diffuse radiant fluence rates are then found for impulse, flat (constant), and Gaussian shaped finite beam irradiances.
KeywordsCatheter Attenuation Expense Convolution Refraction
Unable to display preview. Download preview PDF.
- 8.Patterson MS, Schwartz E, Wilson BC. “Quantitative reflectance spectrophotometry for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” in Photodynamic Therapy Mechanisms, Vol. 1065, SPIE Optical Engineering Press, 1989, pp. 115–122.Google Scholar
- 9.Allen V, McKenzie AL. “The modifiied diffusion dipole model,” Phys. Med. Biol. 36: 1621— 1638 (1991).Google Scholar
- 11.Ishimaru A. Wave Propagation and Scattering in Random Media, Vo1. 1, Academic Press, New York, 1978.Google Scholar
- 13.Moulton JD. “Diffusion modeling of picosecond laser pulse propagation in turbid media,” Master’s thesis, McMaster University, Hamilton, Ontario, Canada, 1990.Google Scholar