Phase retrieval in 4 f configuration : background compensation and sparse regularization of object with binary amplitude

1 Generally, wave field reconstructions obtained by phase-retrieval algorithms are noisy, blurred and corrupted by various artifacts such as irregular waves, spots, etc. These distortions, arising due to many factors such as non-idealities of optical system (misalignment, focusing errors), dust on optical elements, reflections, vibration, are hard to localize and specify. It is assumed that there is a cumulative disturbance called " background " , which describes mentioned distortions in the coherent imaging system manifested at the sensor plane. Here we propose a novel iterative phase-retrieval algorithm compensating for these distortions in the optical system. An estimate of this background is obtained via special calibration experiments, and then it is used for the object reconstruction. The algorithm is based on the maximum likelihood approach and, in this way, targeted on the optimal object reconstruction from noisy data. In this work we demonstrate the compensation of the distortions of the optical trace for a complex-valued object with a binary amplitude. The developed algorithm results in state-of-the-art filtering, and sharp reconstruction imaging of the object amplitude can be achieved.