Simple algorithm to estimate the absorption coefficients of two-layered scattering media from the spatially- and time-resolved reflectance

Abstract

A time-resolved diffuse reflectance from a semi-infinite homogeneous medium is compressed along the time axis and multiplied by appropriate factors. According to the photon diffusion equation, a gradient of the attenuation difference between the compressed reflectance and that measured with a smaller source-detector distance is proportional to the absorption coefficient. Using this property, a simple algorithm using spatially and time-resolved reflectance to measure the absorption coefficient of a homogeneous medium is proposed as an alternative to the procedure of fitting to the photon diffusion equation. In the case of a two-layered medium, the absorption coefficient of each layer can be estimated also using this simple algorithm if approximate values of the depth of the upper layer and the scattering coefficients of the two layers are known beforehand. For validation experiment, the time-resolved reflectance from a polyacetal block was measured at various source-detector distances and the estimated absorption coefficient of the block was compared to that obtained using the conventional method. As the result of <i>in vivo</i> experiment, the absorption coefficient of the lower layer of a human head was found to be larger than that of the upper layer under the assumption that the human head consisted of two layers.