Investigating Ptychographic Phase Retrieval in Terms of Vibration Correction, Online Data Analysis, and Direct 3D Reconstruction

X-ray ptychography is becoming increasingly popular. The semi-transparency of matter to X-rays allows to look into their structure and thereby lay the foundation to understand their functionality. X-ray Ptychography achieves a spatial resolution down to the single nanometer regime. A broad range of materials are well suited for investigation, such as biological samples, catalysts or microchips. Modern synchrotron radiation sources allow to perform ptychographic scans in minutes, which enables the investigation of fast dynamic processes. Furthermore, ptychography is perfectly suited to be combined with tomographic routines to resolve three-dimensional structures.Nevertheless, ptychography is still a challenging method. The mechanical hardware of a ptychographic microscope must provide a stability similar to the achieved spatial resolution. Instabilities cause a blurring of the reconstructed object and reduce the reconstruction quality.The ptychographic data evaluation is computationally expensive and mostly done offline, which means the data acquisition and evaluation are subsequent steps. If the sample is positioned out of the field of view, this is only noticed once the data is reconstructed, leading to a waste of valuable measurement time at synchrotron radiation sources. The computational effort of the ptychographic data evaluation is enormous. The evaluation software has to be optimized to cope with the amount of data. Fourth generation synchrotron radiation sources such as PETRA IV will acquire ptychographic datasets at even higher data rates.In this thesis, three projects are presented that address the current challenges of ptychography. First, an algorithmic approach is introduced that corrects for the vibrations that occur during the ptychographic data acquisition. The algorithm decreases the spatial resolution by a factor 2 for a dataset that is significantly disturbed by vibrations. Second, a structure and implementation for online ptychography has been developed, that performs the data evaluation while the data is still acquired. This enables a real time feedback during the experiment. Third, an optimized software for direct 3D ptychography has been implemented, that yields a performance high enough to catch up with the high acquisition rate of fourth generation synchrotron sources. The implementation is about a factor 3000 faster than the before version.