Ptychographic Imaging of Mixed States

Ptychography is a lens-less imaging technique which, by replacing the function of a lens with a computer algorithm, allows for aberration free, complex imaging, of all manner of specimens in a variety of situations. Compared to alternative methods, the technique has relatively loose requirements on the physical setup and has been demonstrated to operate across the visible light, x-ray, and electron regimes.
This thesis reviews progress in the field followed by four chapters of original work. The unique imaging process of ptychography is initially examined in theoretical terms and the conclusions that are drawn are subsequently applied in all three of the main imaging domains; visible light, x-ray, and electron. The development of several new algorithms is discussed, which alleviate many of the current experimental constraints. These include the processing of diffraction patterns that are sampled grossly below the conventional Nyquist limit, the automatic correction of detector imperfections, the imaging of mixed states through multiple wavelength illumination, and the reconstruction of partially coherent data in the STEM configuration through the deconvolution of an extended source.