Phase retrieval with background compensation in 4f configuration:   advanced augmented Lagrangian technique for amplitude object
  Generally, wave field reconstructions obtained by phase-retrieval algorithms are noisy, blurred and corrupted by various artifacts such as irregular waves, spots, etc. These disturbances, arising due to many factors such as non-idealities of optical system (misalignment, focusing errors), dust on optical elements, reflections, vibration, are hard to be localized and specified. It is assumed that there is a generalized pupil function at the object plane which describes aberrations in the coherent imaging system manifested at the sensor plane. Here we propose a novel two steps phase-retrieval algorithm to compensate these distortions. We first estimate the cumulative disturbance, called background, using special calibration experiments. Then, we use this background for reconstruction of the object amplitude and phase. The second part of the algorithm is based on the maximum likelihood approach and, in this way, targeted on the optimal amplitude and phase reconstruction from noisy data. Numerical experiments demonstrate that the developed algorithm enables the compensation of various typical distortions of the optical track so sharp object imaging for a binary test-chart can be achieved. 
Artem Migukin, Mostafa Agour, and Vladimir Katkovnik
physics.optics