Multiple plane phase retrieval-inpainting with the saturated noisy data

In the present work, we investigate the multiple plane phase retrieval (MPPR) algorithm which addresses the issue of missing center in diffraction patterns, which results from saturation due to the use of a detection system with a limited dynamic range. Using an extrapolation technique in saturated areas, we algorithmically overcome this hardware constraint associated with the restricted dynamic range of the detection system. The validation of the proposed phase retrieval method is conducted on a dataset captured in the terahertz (THz) region, which contains overexposed areas. We compared the reconstructed amplitude and phase distributions obtained from incomplete data with reference images obtained using a conventional algorithm when processing a high dynamic range (HDR) dataset. The algorithm’s convergence was examined when processing datasets with different levels of noise and saturation. Phase retrieval is shown to be possible even if 90−94% of the total energy of the beam is compromised by saturation in recordings, and at a low signal-to-noise ratio (SNR) near 6. Our proposed method effectively addresses the limitation associated with the insufficient dynamic range of the receiver, significantly simplifying data acquisition compared to HDR registration. For the first time, we demonstrate the application of MPPR to address the issue of data saturation and show the feasibility of retrieving the wavefront using only information from the high-frequency diffraction components while extrapolating the missing center information.