RADIATIVE TRANSFER THEORY

All non-invasive optical medical diagnostic systems work on the principle of solving inverse problems of optics of light-scattering media. The main physical and mathematical theory describing the propagation and scattering of light in light-scattering media is the scalar radiative transfer theory. However, the radiative transfer theory still lacks precise and closed-form analytical solutions of the main model problems, which complicates the creation of algorithms for diagnostic data processing and analyzing. The Monte Carlo method and other numerical methods are poorly applicable in this case, because for the real-time systems, it is necessary to solve the inverse problem with an error of no more than 10% for a time of no more than 0.01 seconds. This is possible only if there is an exact and closed-form analytical solution to the direct problem. Our research is aimed at finding such solutions. Results will be reported in our publications. See our “Publications” Section.

We are considering the problem of a continuous absorbing medium with discrete scatterers. Previously, the problem have been solved in the one-dimensional (1D) formulation with any scattering and absorption properties and with any scattering multiplicity (single, multiple). Recently, we solved the problem in 2D and 3D spaces at a single scattering approximation and for a pencil-like incident beam. Also, it is shown that the classical Monte Carlo method has a small systematic error for the absorbing medium with discrete scatterers, which cannot be eliminated by increasing the number of photons. Thus, contrary to the generally accepted opinion, the Monte Carlo method is not accurate for all problems in biomedical optics.