Chi2 analysis for estimating the accuracy of optical properties derived from time resolved diffuse-reflectance

Area of Science:

• Biomedical Optics
• Photonics
• Medical Physics

Background:

• Accurate optical property estimation (mu(a), mu(s)') is vital for time-resolved measurements in turbid media using the diffusion equation.
• Assessing the reliability of these estimates often involves analyzing weighted residuals and the reduced chi-squared (chi(R)(2)) value.

Purpose of the Study:

• To investigate the relevance of weighted residuals and chi(R)(2) for evaluating optical property estimates.
• To understand the behavior of chi(R)(2) in photon counting experiments, particularly concerning model bias and photon count.

Main Methods:

• Analysis of the diffusion equation for time-resolved measurements in turbid media.
• Investigation of weighted residuals and the reduced chi-squared (chi(R)(2)) metric.
• Examination of photon counting experiments, including lifetime estimation.

Main Results:

• chi(R)(2) increases linearly with photon count when model bias is present.
• chi(R)(2) becomes a pertinent metric for mu(a) and mu(s)' accuracy only after acquiring a sufficient number of photons.
• chi(R)(2) is particularly useful for small interfiber separation, low scattering, high absorption, and incorrect instrument response function measurements.

Conclusions:

• Sufficient photon acquisition is necessary for chi(R)(2) to reliably assess optical property estimates.
• chi(R)(2) is a valuable tool for specific challenging conditions in turbid media analysis.
• The pertinence of chi(R)(2) for mu(a) estimation can be limited by air boundary effects.