Improved wavefront reconstruction for Shack–Hartmann wavefront sensor in the presence of shock-related distortions

Previous research has demonstrated that large density gradients, such as those produced by supersonic shockwaves, adversely affect the wavefront reconstruction of Shack–Hartmann wavefront sensors (SHWFS). Shocks cause non-diffraction-limited irradiance patterns, leading to incorrect local tilt measurements by SHWFS, and, as a consequence, degraded reconstructed wavefront accuracy. To study the effect of shocks on the reconstruction accuracy of SHWFS, experimental wavefront measurements were performed, when the interrogating laser beam was propagated along a local shock formed in transonic flow over a partial cylinder. The resulting wavefronts were simultaneously measured by a SHWFS and a digital holography wavefront sensor (DHWFS) and then compared, treating the DHWFS as the ”ground truth.” Significant error was found in the SHWFS measurements, with the error increasing nonlinearly with shock strength. Three metrics, specifically standard deviation, kurtosis, and slope discrepancy, were evaluated for their effectiveness in identifying the dots, distorted by the local shock. Excluding points that exceeded a set threshold significantly improved wavefront accuracy. A complete SHWFS wavefront was then recovered by filling in the excluded points with a spline interpolation. This algorithm decreased the root mean squared error of the SHWFS wavefront by around 30% on average. These findings contribute to the advancement of shock-wave-tolerant phase reconstruction algorithms and introduce a method for more accurate wavefront recovery in the case where a shock partially crosses the aperture.