Investigations and improvements in ptychographic imaging

This thesis has been devoted to investigate and improve ptychography, which is a newly developed coherent diffractive imaging technique that can achieve quantitative imaging (both modulus and phase) at diffraction-limited resolution without imaging lenses. \nIn particular, this thesis has first looked into two solutions of partial coherence in ptychography: the Wigner distribution deconvolution method (WDDM) and mixed state decomposition. WDDM is a non-iterative solution and with it partial coherence was first mathematically demonstrated solvable. We have improved the performance of WDDM, especially in the presence of noise, by proposing three tools that can be used together: a projection strategy, design of a favourable probe, and an iterative method. Furthermore, the reconstruction of spatial partial coherence via WDDM has been successfully demonstrated using a model calculation for the first time. \nMixed state decomposition is an iterative solution. It provides much more flexibility and is able to solve any experimental instability (not just partial coherence) that can be modelled as a set of mutually orthogonal states. According to the formation of the mixed states, it can be divided into spatially mixed state ptychography and temporally mixed state ptychography. For spatially mixed state reconstruction, we have mathematically and experimentally demonstrated an inherent linear ambiguity in the reconstructions and also that the ambiguity can be broken by using an orthogonality constraint or phase-only constraint. Besides, the effects of a diffused probe on the reconstructions have been investigated using a spatial partial coherent x-ray experiment. For temporally mixed state ptychography, we have mathematically and experimentally demonstrated the breakdown of the linear ambiguity. In addition, an iterative algorithm \nvi \nhas been proposed to remove the static background noise from the measurements by treating the background as the diffraction pattern from an extra temporal state. \nMoreover, this thesis has also explored two ways to extend ptychography for three-dimensional (3D) imaging: multislice ptychography and ptychographic tomography. The multislice method has already been introduced into ptychography to provide 3D information before. In this thesis, we have further extended it into a Fourier variant of ptychography – Fourier ptychography – by applying a parallel update for the aperture reconstruction and reforming the iterative algorithm to involve the specimen plane. Also, the reconstruction resolution has been discussed via the Ewald sphere construction and demonstrated via model calculations. \nPtychographic tomography utilises ptychography to acquire 2D projection images at different orientations and makes use of tomography to achieve isotropic 3D reconstruc-tions at high resolution. In this thesis, we have demonstrated this technique step by step via an x-ray experiment and shown how the inherent ptychographic reconstruction ambiguities are removed prior to the tomographic reconstruction. The possibility of electron ptychographic tomography is also discussed based on the scale calculation with the x-ray experiment.