Branch-point identification using second-moment Shack-Hartmann wavefront sensor statistics

In this paper, an approach for detecting branch points using a Shack-Hartmann wavefront sensor (SHWFS) is introduced. Simulated data are created using Monte Carlo wave-optics simulations of varying turbulence strengths. It is assumed that the presence of a branch point in the SHWFS subaperture lenslet pupils causes appreciable beam spreading in the image plane. Therefore, second-moment statistics are used to quantify beam spread for each sub-aperture image-plane irradiance pattern. Thresholding is then employed to dictate what degree of beam spreading is sufficient to determine the presence of a branch point. Three different thresholds are imposed: liberal, moder-ate, and conservative. Furthermore, the collected SHWFS signal is treated as analog, digitized, and digitized with three levels of additive noise: low, moderate, and high. Monte Carlo simulations are conducted for 20 different spherical-wave Rytov numbers (RSW) ranging from 0.1 to 2.0. It was found that when conservative thresholds were employed, for the analog signal, digitized signal with no noise, and digitized signal with low noise, the percent of detections mostly comprised actual branch points, and false-positive detections were largely minimized. For the liberal thresholding cases, many false-positives were detected for all SHWFS signal types; however, significantly more branch points were also detected. The results presented in this paper are encouraging, and such results will inform efforts to develop branch-point tolerant least-squares reconstructors or use a SHWFS for optical-turbulence characterization in high-RSW environments.& COPY; 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement