Research Of Phase Unwrapping Based On Quality Map

Phase unwrapping is one of the key steps of data processing in the field of the shape measurement of optical interference, interferometric synthetic aperture radar (INSAR) and medical magnetic resonance imaging, which determines the accuracy and reliability of measurement results to some extent. Over the years, people made a lot of research on phase unwrapping techniques, but the phase unwrapping problem has many issues worthy of in-depth study and discussion. Based on the literatures of phase unwrapping from home and abroad, the in-depth researches on the phase unwrapping method are carried out in this thesis. The main work of the thesis are as follows:First of all, we introduce the application of phase unwrapping in the optical shape measurement technology, discuss two main three-dimensional sensor technology, and highlight the principle of Fourier transform profilometry. Then we expound the principle of phase unwrapping, the basic concept of residues and quality map, and the mathematical framework for phase unwrapping algorithm. Two dimensional phase unwrapping problem is essentially a constrained optimization problem. Its norm optimization framework can be divided into path integral method and the minimum-norm method. We introduce the principle of path integral method, and simulate the disadvantage of the method. LpA quality map which characterizes the quality of the phase can guide phase unwrapping based on the traditional method of phase wrapping. By identifying datas of quality map , the phase path integral begins from the highest quality value, in order of the phase quality value. The unreliable regions which have low quality value are unwrapped at last so that the inevitable errors can be limited to minimum. We improve the maximum phase gradient quality map and propose a new quality map combined edge detection in the study of traditional quality map. For several typical phase discontinuities, such as noises, shadow and sheared plane, the simulations show the relatively optimal phase unwrapping results with several different quality maps. Therefore the quality maps we proposed have strong reliability and noise resistance.The least squares phase unwrapping algorithm can be seen as solving the Poisson equation with Neumann boundary conditions. The non-weighted minimum norm method is based on discrete cosine transform, and with its results as the initial conditions the weighted iterative minimum norm method is represented by Preconditioned Conjugate Gradient Method. Quality map and pixel mask can be the weight, such as previously proposed new quality map and the binary mask. They can distinguish non-residues and residues, and thus get a better phase unwrapping results. The simulations of the two methods for different wrapping phase show discrete cosine transform method is faster, but sometimes the results are not ideal, and preconditioned conjugate gradient method is slow as it involves a large number of matrix computation, but with quality map and pixel mask as the weight, can get a better result through iteration. At last the matrix theory of the minimum norm method about phase unwrapping from Hunt is derived and added as the basis of previous theory and algorithm.