The role of the Wigner distribution function in iterative ptychography

Ptychography employs a set of diffraction patterns that capture redundant information about an illuminated specimen as a localized beam is moved over the specimen. The robustness of this method comes from the redundancy of the dataset that in turn depends on the amount of oversampling and the form of the illumination. Although the role of oversampling in ptychography is fairly well understood, the same cannot be said of the illumination structure. This paper provides a vector space model of ptychography that accounts for the illumination structure in a way that highlights the role of the Wigner distribution function in iterative ptychography.