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Time domain Optical Coherence Tomography (TD-OCT), first reported in 1991, makes use of the low temporal coherence properties of a NIR broadband laser to create depth sectioning of up to 2mm under the surface using optical interferometry and point to point scanning. Prior and ongoing work in OCT in the research community has concentrated on improving axial resolution through the development of broadband sources and speed of image acquisition through new techniques such as Spectral domain OCT (SD-OCT). In SD-OCT, an entire depth scan is acquired at once with a low numerical aperture (NA) objective lens focused at a fixed point within the sample. In this imaging geometry, a longer depth of focus is achieved at the expense of lateral resolution, which is typically limited to 10 to 20 [micro]m. Optical Coherence Microscopy (OCM), introduced in 1994, combined the advantages of high axial resolution obtained in OCT with high lateral resolution obtained by increasing the NA of the microscope placed in the sample arm. However, OCM presented trade-offs caused by the inverse quadratic relationship between the NA and the DOF of the optics used. For applications requiring high lateral resolution, such as cancer diagnostics, several solutions have been proposed including the periodic manual re-focusing of the objective lens in the time domain as well as the spectral domain C-mode configuration in order to overcome the loss in lateral resolution outside the DOF. In this research, we report for the first time, high speed, sub-cellular imaging (lateral resolution of 2 [micro]m) in OCM using a Gabor domain image processing algorithm with a custom designed and fabricated dynamic focus microscope interfaced to a Ti:Sa femtosecond laser centered at 800 nm within an SD-OCM configuration. It is envisioned that this technology will provide a non-invasive replacement for the current practice of multiple biopsies for skin cancer diagnosis. The research reported here presents three important advances to this technology all of which have been demonstrated in full functional hardware conceived and built during the course of this research. First, it has been demonstrated that the coherence gate created by the femtosecond laser can be coupled into a scanning optical microscope using optical design methods to include liquid lens technology that enables scanning below the surface of skin with no moving parts and at high resolution throughout a 2x2x2 mm imaging cube. Second, the integration the variable-focus liquid lens technology within a fixed-optics microscope custom optical design helped increase the working NA by an order of magnitude over the limitation imposed by the liquid lens alone. Thus, this design has enabled homogenous axial and lateral resolution at the micron-level (i.e., 2 [micro]m) while imaging in the spectral domain, and still maintaining in vivo speeds. The latest images in biological specimens clearly demonstrate sub-cellular resolution in all dimensions throughout the imaging volume. Third, this new modality for data collection has been integrated with an automated Gabor domain image registration and fusion algorithm to provide full resolution images across the data cube in real-time. We refer to this overall OCM method as Gabor domain OCM (GD-OCM). These advantages place GD-OCM in a unique position with respect to the diagnosis of cancer, because when fully developed, it promises to enable fast and accurate screening for early symptoms that could lead to prevention. The next step for this technology is to apply it directly, in a clinical environment. This step is underway and is expected to be reported by the next generation of researchers within this group.

Spectroscopic techniques allow for studies of materials and organisms on the atomic and molecular level. Examples of such techniques are nuclear magnetic resonance (NMR) spectroscopy—one of the principal techniques to obtain physical, chemical, electronic and structural information about molecules—and magnetic resonance imaging (MRI)—an important medical imaging technique for, e.g., visualization of the internal structure of the human body. The less well-known spectroscopic technique of nuclear quadrupole resonance (NQR) is related to NMR and MRI but with the difference that no external magnetic field is needed. NQR has found applications in, e.g., detection of explosives and narcotics. The first part of this thesis is focused on detection and identification of solid and liquid explosives using both NQR and NMR data. Methods allowing for uncertainties in the assumed signal amplitudes are proposed, as well as methods for estimation of model parameters that allow for non-uniform sampling of the data. The second part treats two medical applications. Firstly, new, fast methods for parameter estimation in MRI data are presented. MRI can be used for, e.g., the diagnosis of anomalies in the skin or in the brain. The presented methods allow for a significant decrease in computational complexity without loss in performance. Secondly, the estimation of blood flow velo-city using medical ultrasound scanners is addressed. Information about anomalies in the blood flow dynamics is an important tool for the diagnosis of, for example, stenosis and atherosclerosis. The presented methods make no assumption on the sampling schemes, allowing for duplex mode transmissions where B-mode images are interleaved with the Doppler emissions.