Experimental Setup for Single-Pixel Imaging of Turbulent Wavefronts and Speckle-Based Phase Retrieval

The mitigation of atmospheric effects is an essential component of any high-throughput optical satellite downlink. In this work, as part of the High-throughput and Secure Networks Challenge Program, we apply computational imaging approaches to turbulent wavefront estimation by capturing single pixel images of the speckle pattern from a simulated turbulence-corrupted wavefront. In particular, Hadamard patterns are sequentially displayed on a digital micromirror device (DMD) and used to reconstruct the turbulent speckle pattern. This speckle pattern can be used as an input to a phase-retrieval algorithm to estimate the wavefront phase that produced the speckle. We present the concepts of computational turbulent speckle imaging along with an experimental setup to demonstrate this approach. A spatial light modulator (SLM) is used to simulate turbulence-degraded wavefronts. These are then imaged onto a computational imaging system implemented with a DMD and balanced detection using two photodiodes. The experimental setup is described along with the image reconstruction algorithm. Preliminary computational speckle images are presented and compared with the predicted image obtained by numerically simulating the beam propagation through the optical system showing close agreement.