Comprehensive error analysis framework for Shack–Hartmann wavefront measurements in aero-optical applications

Shack–Hartmann wavefront sensor (SHWFS) is an essential device for experimental aero-optics. However, quantifying the wavefront measurement errors with turbulent flows is not trivial. This paper proposes a comprehensive error analysis framework for SHWFS measurements on turbulent flows of variable density based on high-fidelity nonlinear ray tracing. The evolution of wavefront distortions during the light propagation can be clarified by extracting the wavefront at several planes along the optical path, with and without the target flows allocated. The results show that high-precision wavefront measurements based on SHWFS can only be achieved with a nominal incoming wavefront for well-controlled SHWFS aero-optical measurements. Once the multi-scale turbulent flows are involved, the SHWFS measurement error increases considerably, and the associated dominating error source is elucidated. The dependence of the degraded dot images on the magnitude of the flow density gradients is also explored. The proposed error analysis framework can facilitate understanding the behaviors of degraded dotted images and evaluating SHWFS measurement errors in advance for aero-optical applications.