Phase Unwrapping Based On Path-Following And Two-Wavelength Interferometry

The phase contains a lot of useful information. For example, in Interferometric Synthetic Aperture Radar, the phase is corresponding to the ground elevation information; in Optical Measurement, the phase information reflects the three-dimensional shape of the object; in Magnetic Resonance Imaging, the phase information indicates the clinical relevance of physiological parameters. However, the obtained phase is generally not the real true continuous phase information, but the wrapped phase, as it is usually determined by the inverse trigonometric function. Phase unwrapping seeks to reconstruct the true continuous phase information by retrieving the missing number of periods from the wrapped phase. The phase unwrapping has important application in many fields such as Interferometric Synthetic Aperture Radar, Optical Measurement and Magnetic Resonance Imaging.In the past decades, the phase unwrapping problem has been widely studied. Various engineering mathematical methods have been used in phase unwrapping, and a variety of different phase unwrapping algorithms have been emerged. Generally speaking, there are two kinds of methods of the phase unwrapping in the present phase, which are based on path-following methods (local method) and minimum-norm methods (global method). In practice, it is often difficult to achieve accurate unwrapping phase because of the noise, the lack of sampling and other factors. But so far, there is still no way to solve the problem of phase unwrapping perfectly, and the approximate solution is obtained by all kinds of algorithms.In this thesis, we focus on the commonly phase unwrapping algorithms and the main works are as follows:(1) The development of phase unwrapping is introduced systematically. The phase unwrapping algorithms based on path-following and minimum-norm have been studied, and the basic principles and idea, strengths and weaknesses, and the applicable conditions of these algorithms have been analyzed in detail.(2) Aiming at the problem of the classical Goldstein phase unwrapping algorithm, this thesis makes some improvements on the traditional branch-cut algorithm using the idea that the branch-cut problem is equivalent to the Traveling Salesman Problem. The proposed algorithm uses a multiple population genetic and simulated annealing algorithm to calculate optimized combination of residues, which effectively reduces the total length of the branch cuts and avoids the large "isolated island" phenomenon that appears in the Branch-Cut algorithm for phase unwrapping. The experiments on simulated and real data validate the effectiveness of the proposed approach.(3) It is often difficult to achieve accurate unwrapping by numerical methods, which attributes to the fact that the phase data is inconsistent with the basic continuous conditions of phase unwrapping caused by noise, the lack of sampling and other reasons. In addition, the pure numerical method can not deal with the step type objects. In order to overcome these defects, the phase unwrapping algorithm based on two-wavelength interferometry is studied in this thesis, and the effectiveness of the algorithm is verified by simulation experiments.