Imaging through deep turbulence using single-shot digital holography data

This paper uses an experimental setup consisting of phase plates and a digital-holography receiver to validate the performance of an algorithm, referred to as multi-plane iterative reconstruction (MIR), for imaging through deep turbulence. In general, deep-turbulence conditions arise from aberrations being distributed along the propagation path. The resulting phase errors then cause a multifaceted problem with multiple empirically determined limitations. To address these limitations, the MIR algorithm works by sensing and correcting for the distributed-volume phase errors using single-shot digital holography data (i.e., one speckle measurement from the coherent illumination of an optically rough extended object). As such, we first show that our distributed-volume phase errors, created using the phase plates, follow path-integrated Kolmogorov statistics for weak-to-deep turbulence strengths. We then present results from two MIR algorithm configurations: a) where we have a priori knowledge of the placement of the phase plates, so that we sense and correct in the exact locations of the phase errors, and b) where we do not have a priori knowledge of the placement of the phase plates, so that we sense and correct in two fixed planes for all phase-error combinations. Given weak-to-deep turbulence strengths, the results show that the two MIR algorithm configurations perform comparably for the four imaging scenarios tested. Such results are promising for tactical applications, where one might not have a priori knowledge of the deep-turbulence conditions.