Model-Based Digital Holographic Imaging using Mulit-Shot Data

Imaging through deep-atmospheric turbulence is a challenging and unsolved problem. However, digital holography (DH) has recently demonstrated the potential for sensing and digitally correcting moderate turbulence. DH uses coherent illumination and coherent detection to sense the amplitude and phase of light reflected off of an object. By obtaining the phase information, we can digitally propagate the measured field to points along an optical path in order to estimate and correct for the distributed-volume aberrations. This so-called multi-plane correction is critical for overcoming the limitations posed by moderate and deep atmospheric turbulence. Here we loosely define deep turbulence conditions to be those with Rytov numbers greater than 0.75 and isoplanatic angles near the diffraction limited viewing angle. Furthermore, we define moderate turbulence conditions to be those with Rytov numbers between 0.1 and 0.75 and with isoplanatic angles at least a few times larger than the diffraction-limited viewing angle. Recently, we developed a model-based iterative reconstruction (MBIR) algorithm for sensing and correcting atmospheric turbulence using single-shot DH data (i.e., a single holographic measurement). This approach uniquely demonstrated the ability to correct distributed-volume turbulence in the moderate turbulence regime using only single-shot data. While the DH-MBIR algorithm pushed the performance limits for single-shot data, it fails in deep turbulence conditions. In this work, we modify the DH-MBIR algorithm for use with multi-shot data and explore how increasing the number of measurements extends our capability to sense and correct imagery in deep turbulence conditions.