On the sampling requirements for ptychography

We investigate how the distance between probe positions and the resolution of measured diffraction patterns affects iterative ptychographic reconstruction. The ptychographic phase retrieval problem where both the object and probe are reconstructed is analyzed theoretically, by introducing a 4D object to describe the 4D ptychopgraphical data set. This is similar to introducing the 3D Ewald sphere to describe the field in a 3D focal volume. Conclusions drawn on the basis of the theoretical analysis are verified using simulations with a simplified 2D ptychographic problem where the probe and object are 1D. Though the 2D problem is a simplification compared to the typical 4D ptychography problem of lensless imaging, it still has practical applications for pulse reconstruction.