Analysis and development of phase retrieval algorithms for ptychography

Ptychography, a relatively new form of phase retrieval, can reconstruct both intensity and phase images of a sample from a group of diffraction patterns, which are recorded as the sample is translated through a grid of positions. To recover the phase information lost in the recording of these diffraction patterns, iterative algorithms must optimise an objective function full of local minima, in a huge multidimensional space. Many such algorithms have been developed, each aiming to converge rapidly whilst avoiding stagnation. This thesis aims to set a standard error metric for comparing some of the more popular algorithms, to determine their advantages and disadvantages under a range of different conditions, and hence develop a more adaptive algorithm that combines the advantages of these ancestors. In this thesis, different algorithms are explained together with their reconstruction results from both simulated and practical data. Modifications for mPIE, ADMM and RAAR are suggested to either reducing the number of parameters or improving their computation efficiency. An improved spatial error metric, which can evaluate the reconstruction quality by removing inherent ambiguities, is introduced to compare these algorithms. Based on the explained phase retrieval algorithms, a new algorithm, i.e., adaptive PIE, is developed. It has。 a faster converging speed and better accuracy comparing to its ancestors