Computational and statistical approaches to optical spectroscopy

Abstract

Compact and smart optical sensors have had a major impact on people's lives over the last decade. Although the spatial information provided by optical imaging systems has already had a major impact, there is untapped potential in the spectroscopic domain. By transforming molecular information into wavelength-domain data, optical spectroscopy techniques have become some of the most popular scientific tools for examining the composition and nature of materials and chemicals in a non-destructive and non-intrusive manner. However, unlike imaging, spectroscopic techniques have not achieved the same level of penetration due to multiple challenges. These challenges have ranged from a lack of sensitive, miniaturized, and low-cost systems, to the general reliance on domain-specific expertise for interpreting complex spectral signals. In this thesis, we aim to address some of these challenges by combining modern computational and statistical techniques with physical domain knowledge. In particular, we focus on three aspects where computational or statistical knowledge have either enabled realization of a new instrument-with a compact form factor yet still maintaining a competitive performance-or deepened statistical insights of analyte detection and quantification in highly mixed or heterogeneous environments. In the first part, we utilize the non-paraxial Talbot effect to build compact and high-performance spectrometers and wave meters that use computational processing for spectral information retrieval without the need for a full-spectrum calibration process. In the second part, we develop an analyte quantification algorithm for Raman spectroscopy based on spectral shaping modeling. It uses a hierarchical Bayesian inference model and reversible-jump Markov chain Monte Carlo (RJMCMC) computation with a minimum training sample size requirement. In the last part, we numerically investigate the spectral characteristics and signal requirements for universal and predictive non-invasive glucose estimation with Raman spectroscopy, using an in vivo skin Raman spectroscopy dataset. These results provide valuable advancements and insights in bringing forth smart compact optical spectroscopic solutions to real-world applications.