Beyond the diffraction limits: Inverse numerical imaging based on transform-domain sparse modeling for phase and amplitude

Abstract

We consider the following basic wave field reconstruction problem. A wave field at an object plane is modeled as complex-valued with arbitrary phase and amplitude. The forward wave field propagation from the object to a parallel image/sensor plane is defined by the Rayleigh-Sommerfeld diffraction integral. The problem is to reconstruct the object plane distribution for both the phase and the amplitude from complex-valued observations at the sensor plane.