Numerical and experimental aspect of coherent lensless imaging

This thesis is devoted to the understanding, application, and extension of coherent lensless imaging methods for microscopy purposes. Particular attention is given to the Fourier transform holography and coherent diffractive imaging methods.These two methods share several properties such as the ability for singleshot imaging and their experimental geometries, but differ greatly in their reconstruction approach. Holographic approaches use reference waves to encode phase information into the measurements which means the reconstruction quality is controlled, to a large extent, by the characteristics of the reference wave. In contrast, coherent diffractive imaging utilizes prior knowledge to iteratively recover the phase information; this has the effect that the reconstruction quality is independent of any optics or references, but relies heavily on the performance of iterative numerical algorithms. The complex nature of the phase retrieval problem raises questions regarding the existence and uniqueness of a solution which makes understanding the numerical and mathematical aspects of the problem of central importance.

The main topics in this thesis include: the extension of coherent diffractive imaging to multi-wavelength diffraction data, effects related to optically thick references in Fourier transform holography and an alternative numerical approach to phase retrieval which is based on non-rigid image registration. Along the way, various topics are covered which form the foundations of these techniques, or could be useful to a practioner in the field.