Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium

TLDR

The study investigates improved diffusion‑equation solutions for time‑resolved and steady‑state spatially resolved reflectance to determine optical coefficients of semi‑infinite turbid media such as tissue. The authors derive these solutions under various boundary conditions, fit relative reflectance data in the time domain, and analyze relative and absolute reflectance in the steady‑state domain, comparing results with Monte Carlo simulations. The improved solutions yield substantially lower errors in optical‑coefficient estimation, especially for steady‑state spatially resolved reflectance, and experimental data confirm these advantages.

Abstract

Improved solutions of the diffusion equation for time-resolved and steady-state spatially resolved reflectance are investigated for the determination of the optical coefficients of semi-infinite turbid media such as tissue. These solutions are derived for different boundary conditions at the turbid-medium–air interface and are compared with Monte Carlo simulations. Relative reflectance data are fitted in the time domain, whereas relative and absolute reflectance are investigated in the steady-state domain. It is shown that the error in deriving the optical coefficients is, especially for steady-state spatially resolved reflectance, considerably smaller for the solutions under study than for the commonly used solutions. Analysis of experimental measurements of absolute steady-state spatially resolved reflectance confirms these results.