Power Law Analysis Estimates of Analyte Concentration and Particle Size in Highly Scattering Granular Samples from Photon Time-of-Flight Measurements

Optical measurements of particle size and composition in granular samples are difficult to make due to complex light scattering from particles. These multiple scattering events bias absorption estimates and complicate the calculation of scattering and absorption coefficients used to estimate sample properties. Time series data, such as chromatograms and photon time-of-flight (TOF) profiles, contain self-repeating (fractal) characteristics. Power law analysis of photon TOF profiles allows the determination of absorption coefficients and particle sizes in a single experiment. A correlation dimension algorithm was used on photon TOF data from scattering samples. MLR models were then obtained from correlation dimension plots for the estimation of sample properties. Estimates of particle sizes and absorption coefficients were shown to agree well with theoretical values when compared using independent validation sets. Results show close to a 3-fold and up to a 5-fold decrease in the errors of estimation of dye concentration and particle size, respectively, as compared to steady-state measurements. The power law approach provides a useful means of determining sample properties in highly scattering media.