| Phase aberrations due to atmospheric turbulence, experimental conditions or the imaging system itself can severely limit the resolution of an image. Phase aberrations can be spatially dependent, meaning that a linear, space-invariant transfer function cannot fully correct for all the phase errors across the field-of-view. One can use digital holography to access the complex-valued optical field from a laser-illuminated object after detecting the intensity interference between object and reference beams. Then one can digitally apply phase corrections to the field and propagate that field to the object plane to form an image. In this work, we developed image sharpening approaches to the correction of phase aberrations in digital holography. Image sharpening algorithms employ a nonlinear optimization routine to sense and compensate the phase aberrations to form a fine-resolution reconstructed image. In this thesis, we examined phase correction for two specific applications: imaging through multiple phase screens and synthetic-aperture digital holography. In both cases, our work concentrated on numerical simulation, algorithm development, and implementation of laboratory experiments.;For imaging through phase screens, we developed a modified sharpness metric which preserves the space-bandwidth product upon propagation to prevent oversharpening the image. We successfully demonstrated successful image reconstructions through multiple phase screens in numerical simulation for two and three phase screens and in a laboratory experiment for two phase screens, simulating space-variant aberrating media such as volume atmospheric turbulence.;Synthetic aperture digital holography (SADH) takes a collection of individual translated holographic frames and mosaics them to form a larger aperture. This increased aperture size results in greatly increased resolution (if not degraded by phase aberrations). We developed multiple approaches to aberration correction in SADH. We demonstrated the use of slope measurements between hologram sub-apertures with a non-iterative modal reconstructor to correct lower-order phase errors. Using an angular spectrum propagation technique with an image sharpening approach, we have demonstrated higher-order aberration correction and diffraction-limited resolution for a 12,000 by 18,000 pixel synthetic aperture. Finally, using an approximate Fresnel-like propagator in combination with an image sharpening algorithm, we demonstrated high-resolution, nonparaxial imaging over a region-of-interest for a 32,768 by 32,768 pixel (full gigapixel) synthetic aperture. |
