Effects of Shock Waves on Shack–Hartmann Wavefront Sensor Data

Abstract

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 [Formula: see text] caused by the shock is between 0 and approximately [Formula: see text]. However, when [Formula: see text], 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.

Branch-point detection using a Shack-Hartmann wavefront sensor

“…After creating a complex-optical field with an optical-vortex-phase function, the complex-optical field is applied to a SHWFS model, similar to the ones used in Refs. [27,32,40,41]. The resultant SHWFS image can be seen in the top-right plot of Fig.…”

Studies of local shock effects on Shack-Hartmann and digital holography wavefront sensors

“…16 However, when there is a discontinuity across the lenslet, the irradiance pattern bifurcates or smears, and C-tilt is no longer a good estimate of G-tilt. 7 Since the wavefront is constructed through a least-squares reconstructor, these contaminated tilt measurements affect the accuracy of the entire reconstructed wavefront.…”

“…[2][3][4][5] A large interest is in higher speed transonic and supersonic flow regimes, where shocks can form a sharp change in density, thereby affecting the index of refraction and having a significant effect on beam propagation. Kalensky et al 6,7 have shown that the presence of the shock will deteriorate the performance of SHWFS. As a reminder, SHWFS is comprised of an array of subaperture lenslets focused onto a camera sensor.…”

“…6 These slope estimates are traditionally used in a least-squares reconstructor to estimate the continuous wavefront aberration. 8 Recently, Kalensky et al 7 analytically showed how the density discontinuity of a shock crossing a subaperture lenslet leads to a distorted far-field irradiance pattern, resulting in "smeared" or bifurcated dots. This effect has also been shown to occur in experiments.…”

“…9,10 It was then shown through wave-optics simulation how these distorted dots affect wavefront reconstruction. 7 In Reference 11, Kalensky used second-moment to quantify the spatial spreads of the dots in a Shack-Hartmann irradiance pattern, which allowed him to find dots distorted by higher order aberration, and, in the case of that work, branch-points. In the work presented here, this approach is expanded to even higher order spatial statistics to study their ability to find the affected lenslets, and possibly provide additional information to aid in wavefront reconstruction.…”