The purpose of this book and the enclosed software is to provide a tool with dual functionality. The text summarizes the theory of light propagation through diffusive media, while the software serves as a computational tool giving users an interactive approach to understanding the link between theory and real calculations. Through this two-pronged approach, the authors believe that this tool will be valuable both for research investigations and educational purposes.
The software on the CD-ROM is designed to calculate the solutions of the diffusion equation (DE) â solutions that can be verified by comparing against the enclosed set of reference Monte Carlo (MC) results. The text describes the basic theory of photon transport along with analytical solutions of the diffusion equation for several geometries. The book also includes a description of the software, related materials, and their use.
We will show that propagation of light through turbid media (i.e., media with scattering and absorption properties) can be accurately described with the radiative transfer equation (RTE), a complex integro-differential equation of which analytical solutions are not available for geometries of practical interest. The DE is an approximation that can be obtained from the RTE by making some simplifying assumptions. For the DE, analytical solutions are available in many geometries, but it is necessary to stress that these solutions are approximate. Therefore, each application should be checked to verify that the accuracy of these approximations is sufficient. This check can be performed by comparing the approximate solutions against reference solutions of the RTE. For this purpose, the CD-ROM also includes examples of numerical solutions of the RTE obtained with MC simulations for different geometries.
Diffusive media are turbid media for which the solutions of the DE provide a sufficiently accurate description of light propagation. Through these media, photons propagate in a diffusive regime, i.e., the path followed by any photon migrating from the source to the detector looks like a random walk (zigzag trajectory). This occurs when photons undergo a sufficiently high number of scattering events that their trajectories become randomized. Section 2.5 lists a number of media common in daily life for which a diffusive regime of propagation can be assumed.