The Use of Statistical Characteristics of Photon Trajectories for the Tomographic Studies of Optical Macroheterogeneities in Strongly Scattering Objects

摘要

Application possibilities of the statistical characteristics of photons for the study of macroheterogeneities, in strongly scattering tissue-like objects by means of optical computer tomography are considered. The presented technique is based on the approximation of the diffusion equation and is suitable for the subsequent application in the algorithm of reconstruction of the structure of an inhomogeneous object. It is demonstrated that the shadow from an inhomogeneity inside an object of any shape can be calculated with the use of a presentation of integrals along the mean trajectory of the photons. The influence of the shape of an object on the statistical characteristics of the photons trajectories is studied, namely: the trajectory R(#tau#) of the center of the statistical distribution of photons, RMS deviation #DELTA#(#tau#) and the quantity d#tau#/(dl) (#tau#) inverse proportional to the speed of motion of the center of distribution. The comparative study of three main geometries of objects (semiinfinite medium, flat layer, and rectangular sector) showed that the trajectory R(#tau#) can be approximated with sufficient accuracy by a three-step broken line and that the RMS deviation #DELTA#(#tau#) and the quantity d#tau#/(dl) (#tau#) can be replaced, in the general case, by simplified functions. The dependences that allow one to determine the parameters of the sh