Blind Ptychography by Douglas-Rachford Splitting

Blind ptychography is the scanning version of coherent diffractive imaging which seeks to recover both the object and the probe simultaneously. Based on alternating minimization by Douglas-Rachford splitting, AMDRS is a blind ptychographic algorithm informed by the uniqueness theory, the Poisson noise model and the stability analysis. Enhanced by the initialization method and the use of a randomly phased mask, AMDRS converges globally and geometrically. Three boundary conditions are considered in the simulations: periodic, dark-field and bright-field boundary conditions. The dark-field boundary condition is suited for isolated objects while the bright-field boundary condition is for non-isolated objects. The periodic boundary condition is a mathematically convenient reference point. Depending on the avail- ability of the boundary prior the dark-field and the bright-field boundary conditions may or may not be enforced in the reconstruction. Not surprisingly, enforcing the boundary condition improves the rate of convergence, sometimes in a significant way. Enforcing the bright-field condition in the reconstruction can also remove the linear phase ambiguity.