Interest in high resolution imaging techniques has recently multiplied due to their importance in bio-medical research. Quantitative phase measurements by holographic microscopy is an extraordinary tool to gain new understanding of transparent biological samples. The extremely high demand on resolution well beyond the diffraction limit, however, sets new benchmarks for imaging techniques. Digital Holographic Microscopy is an interferometric method providing access to the complex wave front. Its capacity to image amplitude and quantitative phase simultaneously makes it an attractive research tool in many fields of biological research. It is on the verge of becoming an appealing alternative to classical fluorescence microscopy. For intensity-based microscopy, however, super-resolution methods are well established. In this thesis, approaches to unleash resolution for phase imaging techniques are explored. Based on truncated inverse filtering, a theory for deconvolution of complex fields is developed. It is a post-processing method that does not require any additional optics in the holographic microscopy setup. Gain in resolution arises by accessing the object's complex field – containing the information encoded in the phase – and deconvolving it with the characteristic coherent transfer function (CTF). By efficient harvest of a diffraction limited bandpass, complex deconvolution is demonstrated to exceed the coherent resolution limit. A novel method, called a complex point source, serves to characterize the holographic microscopy system. It consists of a coherently illuminated nano-metric hole, located on a conventional microscope slide, most common in bio-microscopy. A thin opaque film is directly evaporated on the slide and the circular sub-wavelength structures are drilled with a focused ion beam. Theoretical as well as practical work on transmission properties of apertures confirms the advantageous signal-to-noise yield of proposed method. More abstractly, the thus gained experimental amplitude point spread function is demonstrated to be suitable for experimental CTF reconstruction. Herefrom, experimental parameters are extracted and introduced into scalar and vectorial Debye theory, called synthetic CTF, adaptable to realistic imaging conditions. Also, it allows to study the role of noise in the context of complex field deconvolution. The resolution power of holographic microscopy systems is systematically examined with pairs of nano-metric apertures separated by sub-resolution pitches. Theory of information content is elaborated depending on different experimental configurations. Resolution extends beyond classical Abbe's limit by introducing spatially a varying phase into the illumination beam of a phase imaging system. In a last step, the novel deconvolution method is generalized to three-dimensional image processing of complex fields. By combining scattering theory and signal processing, the method is demonstrated to yield the reconstruction of the scattering object field under non-design microscope objective imaging conditions. The suggested technique is best suited for an implementation in high-resolution diffraction tomography based on sample and/or illumination rotation.