Haar Transform Analysis of Photon Time-Of-Flight Measurements for Quantification of Optical Properties in Scattering Media

A method to independently quantify the absorption and the scattering properties of samples based on the analysis of the Haar transform (HT) of photon time-of-flight (TOF) distributions is described. A series of reflectance photon TOF measurements were acquired from absorbing /scattering milk samples of known composition (0 < (mu)a < 0.025 mm^-1 ; 100 < (mu)s < 250 mm^-1 ). The HT of the profiles was calculated, and the regression based on the most parsimonious subset of wavelets was determined by the genetic algorithm (GA). In addition, the utility of computing the logarithm of the profiles or of the absolute value of the wavelet coefficients before the GA was studied. Results show that the absorption coefficient could be estimated with a coefficient of variation (C.V.) of 6.7% and an r^2 of 0.99 by use of the log of selected wavelets of frequency less than 800 MHz. Scattering coefficients were estimated with a C.V. of 2.3% and an r^2 of 0.99 with the log of wavelets of frequency less than 400 MHz. The above results suggest that a simplified instrument based on low-frequency switches could be developed to quantify the optical properties of highly scattering media.