Photon time-of-flight and spectroscopic characterization of scattering samples using analysis of self-similarity

Scattering samples such as tissue or milk are difficult to analyze using spectroscopy. Due to scattering, the path length of light through samples varies. However, diffuse scattering is repetitive, and can therefore be considered to be a self-similar process. This thesis shows that mathematical techniques which characterize self-similarity can significantly improve spectroscopic quantification in absorbing/scattering media.Often, quantification in scattering samples relies on multivariate analysis of near-infrared (NIR) spectra. Using data from wheat samples and tissue phantoms, it is shown that Haar transform (HT) preprocessing improves quantification. Wavelet domain calibration reduces the need for trial and error preprocessing of spectra, and yields more parsimonious models and lower errors than single wavelength selection. In particular, preprocessing with Haar "son" wavelets gives simple calibrations which are useful to design future simplified data acquisition schemes.Time-resolved intensity measurements compliment NM spectroscopy by providing information on absorption and scattering coefficients (mua and mu s). Haar wavelets are shown to be useful for constructing simple models to determine optical properties of tissue phantoms from times-of-flight (TOFs) of transmitted or diffusely reflected photons. For TOF distributions collected with a research-grade instrument, three wavelets at frequencies less than 800 MHz accurately quantify mua and mus (less than 8% and 3% error, respectively). Furthermore, when the light source is simplified to a portable nanosecond rise-time laser diode, three wavelets of frequencies less than 400 MHz yield accurate estimates from transmitted photon data. Based on the above results, simplifications to the light source and electronics of photon TOF instruments are suggested.Fractal correlation dimension calculations further improve the analysis of photon TOF distributions. Compared to HT analysis, models based on the correlation sum use fewer variables to quantify mua and mu s, while maintaining comparable accuracy. A simple method of analysis that is forgiving to instrumental drift is obtained.Overall, analysis of self-similarity facilitates quantification in highly scattering samples. By using wavelets or correlation dimension calculations to analyze NIR spectra or TOF distributions, simple yet accurate models are obtained to estimate optical properties. Improvements proposed in this thesis could serve to make measurements at the bedside of a patient feasible