Effects of Shock Waves on Shack-Hartmann Wavefront Sensor Data

Shock waves will form by turning supersonic or locally supersonic flow and result in an increase in the freestream density downstream of the shock. This increase leads to optical distortions that limit the effectiveness of aircraft mounted laser systems. In this paper, analytic expressions are developed to describe these optical distortions in terms of the optical-path difference (OPD). Pupil-plane disturbances imposed by the shock are studied for two cases: when the shock is parallel to the propagation direction and when the shock is on an angle relative to the propagation direction. Upon propagation from the pupil plane, the analysis shows that shock-induced phase discontinuities can sometimes cause the irradiance pattern in the image plane to bifurcate. Despite a large amount of tilt in the pupil plane, the bifurcated irradiance pattern does not map to a proportional shift in the image plane. The implications that these findings have on Shack-Hartmann wavefront sensor (SHWFS) data are also explored. The results show that least-squares reconstruction from the SHWFS data yield accurate estimates of the change in OPD across the shock when the magnitude of the phase difference delta phi caused by the shock is between 0 and approximately 0.5 pi [rad]. However, when vertical bar &Delta phi vertical bar > 0.5 pi [rad], the results show that least-squares reconstruction begins to severely underestimate the change in OPD across the shock. Such results will inform future efforts looking to develop aircraft-mounted laser systems.