Phase-sensitive Imaging and Image Processing for Optical Coherence Tomography Applications

This work is concerned with the topic of phase-sensitive imaging techniques suitable for the investigation of structures in the micron range, and shows the potential for quantitative analysis resulting from an appropriate image processing for the investigated specimens. The probed samples are mostly of technical nature, but the methods are in general not restricted to technical applications. Moreover, several imaging aspects have originated from biological applications, being recently transfered to technical material sciences. Concerning imaging technique, we focus on optical coherence tomography (OCT) and in particular on its phase-sensitive modifications: Polarization-sensitive OCT (PS-OCT) and differential phase contrast OCT (DPC-OCT). The comparison to quantitative imaging in phase contrast microscopy techniques (classical phase contrast microscopy, differential interference contrast microscopy, and advanced versions of phase microscopy) has been done to illustrate the similarities, differences, and limitations of both techniques. We propose two procedures comprehending the measurement, the enhancement and the quantitative analysis of phase-related quantities: In case of PS-OCT we consider the reconstruction of retardation and birefringence distributions, and in case of DPC-OCT imaging, the extraction of the phase gradient fields and the reconstruction of the optical path length maps therefrom. From the point of view of physics we demonstrate how existing phase-sensitive OCT techniques can be modified in their imaging setup to allow an advanced data acquisition. Especially, we consider how one-dimensional measurement schemes in DPC-OCT can be extended to allow a two-dimensional solution of the phase reconstruction problem. From the point of view of signal processing we illustrate the potential given by extending also the analysis of PS-OCT retardation images from one-dimensional signal processing to two-dimensional image analysis. We include demodulation schemes, based on generalized analytic signal theory and originally developed for two-dimensional fringe pattern analysis of conventional interferometry, in PS-OCT imaging applications. From the point of view of mathematics we show how the existing image processing schemes can be adapted and improved to become suitable for the measured PS-OCT and DPC-OCT images. Especially the necessity of an appropriate pre-processing (as image denoising and decomposition), tailored to the features of phase-based OCT imaging, is illustrated. We have demonstrated the performance of the described methods to obtain spatially-resolved and quantitative information about internal material states, as birefringence and stress, or about the topography of embedded phase structures. Suggestions for further improvements of the reconstruction scheme are discussed. We have exemplified the proposed procedures for different test samples in real-world applications and situations being relevant in the field of material testing. The thesis is written deliberately in the field spanned between physics, in particular optics, and mathematics, in particular image processing. The work should illustrate the potential, which can be obtained by the interdisciplinary consideration of optical measurement techniques, mathematical data analysis, and aspects of material sciences.