Perturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function. III. Frequency-domain and time-domain results temporal point-spread function. III. Frequency-domain and time-domain results

摘要

We study the performance of a previously proposed perturbation theory for the diffusion equation in frequencynand time domains as they are known in the field of near infrared spectroscopy and diffuse optical tomography.nWe have derived approximate formulas for calculating higher order self- and mixed path length moments, upnto the fourth order, which can be used in general diffusive media regardless of geometry and initial distributionnof the optical properties, for studying the effect of absorbing defects. The method of Padé approximants is usednto extend the validity of the theory to a wider range of absorption contrasts between defects and background.nBy using Monte Carlo simulations, we have tested these formulas in the semi-infinite and slab geometries fornthe cases of single and multiple absorbing defects having sizes of interest (d=4–10 mm, where d is the diameternof the defect). In frequency domain, the discrepancy between the two methods of calculation (Padé approximantsnand Monte Carlo simulations) was within 10% for absorption contrasts u0001u0002au00030.2 mm−1 for alternatingncurrent data, and usually to within 1° for u0001u0002au00030.1 mm−1 for phase data. In time domain, the averagendiscrepancy in the temporal range of interest (a few nanoseconds) was 2%–3% for u0001u0002au00030.06 mm−1. The proposednmethod is an effective fast forward problem solver: all the time-domain results presented in this worknwere obtained with a computational time of less than about 15 s with a Pentium IV 1.66 GHz personalncomputer. © 2010 Optical Society of America