Particle sizing and optical constant measurement in granular samples using statistical descriptors of photon time-of-flight distributions

A method is described for optical constant estimation and particle sizing in granular samples using diffuse reflectance measurements. Statistical descriptors of the time-resolved photon distributions were used to obtain information inherent to absorption and scattering processes in a sample. Changes in a sampleʹs absorption and scattering properties and apparent particle diameter were simultaneously estimated using stepwise multi-linear regression (SMLR) and partial least squares regression (PLS). Models were constructed using time-distributions taken at both single and multiple radial displacements between source and detector. SMLR estimates of absorption and particle diameter required descriptors related to the trailing and rising edges of the time profiles, respectively. The inclusion of multi-perspective information allowed for improved estimates for all quantities. Using statistical descriptors, a robust means for simplifying complex photon time-distributions into measurable parameters was found. It was found that the SMLR model gave slightly better results compared with the PLS model. The absorption coefficient, scattering coefficient and apparent particle diameter were estimated to within 10, 9 and 7% of their respective reference values with SMLR. In the future, this approach may be used as a means in which to develop practical instrumentation for on-line, real-time characterisation of absorbing granular media.