Reconstruction of optical coefficients in turbid media using time-resolved reflectance and calibration-free instrument response functions.

Measurements of time-resolved reflectance from a homogenous turbid medium can be employed to retrieve the absolute values of its optical transport coefficients. However, the uncertainty in the temporal shift of the experimentally determined instrument response function (IRF) with respect to the real system response can lead to errors in optical property reconstructions. Instrument noise and measurement of the IRF in a reflectance geometry can exacerbate these errors. Here, we examine three reconstruction approaches that avoid requiring direct measurements of photon launch times. They work by (a) fitting relative shapes of the reflectance profile with a pre-determined constraint on the scattering coefficient, (b) calibrating launch-time differences via a reference sample, and (c) freely fitting for the launch-time difference within the inverse problem. Analysis methods that can place a tight bound on the scattering coefficient can produce errors within 5-15% for both absorption and scattering at source-detector separations of 10 and 15 mm. Including the time-shift in the fitting procedure also recovered optical coefficients to under 20% but showed large crosstalk between extracted scattering and absorption coefficients. We find that the uncertainty in the temporal shift greatly impacts the reconstructed reduced scattering coefficient compared to absorption.