Computational Methods and Applications in Optical Imaging and Spectroscopy

Open Access
Author:
Mehta, Nikhil N
Graduate Program:
Electrical Engineering
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
September 30, 2015
Committee Members:
  • Zhiwen Liu, Dissertation Advisor
Keywords:
  • Nonlinear optics
  • spectroscopy
  • ultrafast optics
  • two dimensional phase retrieval
  • coherent Raman spectroscopy
  • compressive sensing
  • ultrashort pulse characterization
Abstract:
This dissertation presents my work in application of computational techniques and the resulting enhancements to several non-linear and ultrafast optical imaging and spectroscopy modalities. The importance of novel computational optical imaging schemes which aim to overcome the limitations of conventional imaging techniques by leveraging the availability of computational resources and the vast body of literature in computational signal processing is emphasized. In particular the computational techniques of compressive sensing and two dimensional phase retrieval are introduced in the broad context as inversion techniques suitable for optical applications including coherent anti-Stokes Raman holography, non-linear spectroscopy, and ultrashort pulse characterization. It is shown that both computational techniques seek to improve key signal metrics such as higher signal to noise ratio (SNR) and better resolution than can be obtained traditionally within the specific imaging modality. Coherent anti-Stokes Raman scattering (CARS) holography is a novel imaging modality which combines the principles of coherent anti-Stokes Raman scattering and holography to provide label-free, chemical selective, scanning-free, and single shot 3D imaging modality. Compressive CARS holography is introduced as a sparsity constrained holographic image reconstruction technique to enhance the optical sectioning capability of CARS holography by suppressing out-of-focus background noise inherent in 3D images processed from a typical single 2D hologram. The advantages of compressive sensing guided signal acquisition strategy in optical spectroscopy is presented by proposing ‘compressive multi-heterodyne optical spectroscopy’ as a novel technique for ultra-high resolution frequency comb spectroscopy. Using numerical simulations, our proposed compressive frequency comb spectroscopy technique is shown to be well-suited for recording narrow line spectra at ultra-high sampling over broad spectral range by leveraging sparsity inherent in such spectra. We next present applications of phase retrieval in optical imaging and spectroscopy. In particular we use 2D phase retrieval technique to enhance the resolution of sum frequency generation vibrational spectroscopy (SFG-VS) whose unique surface selectivity enables qualitative and quantitative study of chemical species at surfaces/interfaces. Specifically, our key contribution is that we show that our 2D phase retrieval based inversion algorithm enables measurement of characteristic molecular vibrational spectra of air/dimethyl sulfoxide interface at resolutions significantly better than that achievable in conventional SFG-VS acquisition system. Lastly, we address the limitation of the commonly used pulse characterization technique: frequency resolved optical gating (FROG) to spatio-temporally characterize the ultrafast pulse. Using a simple spectral holographic recording technique, we present a modified 2D phase retrieval based algorithm to measure the spectral phase at every spatial location in the vicinity of focus of an objective and thereby track the spatio-temporal evolution of the pulse along its optical axis.