Finite element solution of the forward imaging problem associated with timeand frequency-domain measurements of photon migration

摘要

Abstract: Finite element (FEM) predictions of the solution to the forward imaging problem are presented. In this study, the forward imaging problem consisted of predicting time-dependent photon migration measurements from information regarding the presence, location, geometry, and optical properties of a single heterogeneity obscured within a uniform, homogeneous random medium. FEM solutions which predict time-domain measurements of emitted light, I(t), suggest that the successful use of these measurements in an inverse imaging algorithm may be limited in the range of heterogeneity volumes and optical properties by factors such as the source/detector geometry. Two dimensional plots of fluence rate, $Phi@(p,t), illustrate the physical basis of photon migration as described by particle, photon density wave, and optical wave transport theories. FEM solutions which predict frequency-domain measurements of phase-shift, $Theta@(f), and modulation, M(f) illustrate the physical basis of interfering photon density wave measurements for detection and localization of a single absorber. !21