Blind Ptychography via Blind Deconvolution

Ptychography involves a sample being illuminated by a coherent, localised probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the probe or sample is shifted laterally in space to illuminate a new area of the sample while ensuring there is sufficient overlap. Far-field Ptychography occurs when there is a large enough distance (when the Fresnel number is much greater than 1) to obtain magnitude-square Fourier transform measurements. In an attempt to remove ambiguities, masks are utilized to ensure unique outputs to any recovery algorithm are unique up to a global phase. In this paper, we assume that both the sample and the mask are unknown, and we apply blind deconvolutional techniques to solve for both. Numerical experiments demonstrate that the technique works well in practice, and is robust under noise.