Coded aperture ptychography: uniqueness and reconstruction

Abstract

Uniqueness of solution is proved for any ptychographic scheme with a random mask under a minimum overlap condition and local geometric convergence analysis is given for the alternating projection (AP) and Douglas–Rachford (DR) algorithms. DR is shown to possess a unique fixed point in the object domain and for AP a simple criterion for distinguishing the true solution among possibly many fixed points is given.A minimalist scheme, where the adjacent masks overlap 50% of the area and each pixel of the object is illuminated by exactly four illuminations, is conveniently parametrized by the number q of shifted masks in each direction. The lower bound 1 − C/q2 is proved for the geometric convergence rate of the minimalist scheme, predicting a poor performance with large q which is confirmed by numerical experiments. The twin-image ambiguity is shown to arise for certain Fresnel masks and degrade the performance of reconstruction.Extensive numerical experiments are performed to explore the general features of a well-performing mask, the optimal value of q and the robustness with respect to measurement noise.