χ^2 analysis for estimating the accuracy of optical properties derived from time resolved diffuse-reflectance

Abstract

Weighted residuals and the reduced chi(2) (chi(R) (2)) value are investigated with regard to their relevance for assessing optical property estimates using the diffusion equation for time-resolved measurements in turbid media. It is shown and explained, for all photon counting experiments including lifetime estimation, why chi(R) (2) increases linearly with the number of photons when there is a model bias. Only when a sufficient number of photons has been acquired, chi(R) (2) is a pertinent value for assessing the accuracy of mu(a) and mu(s)' estimates. It was concluded that chi(R) (2) is of particular interest for cases of small interfiber separation, low-level scattering, strong absorption and incorrect measurement of instrument response function. It was also found that chi(R) (2) is less pertinent for judging mu(a) in case of air boundary effects.