We develop a phase reconstruction algorithm for the Shack–Hartmann wavefront sensor (SHWFS) that is tolerant to phase discontinuities, such as the ones imposed by shock waves. In practice, this algorithm identifies SHWFS locations where the resultant tilt information is affected by the shock and improves the tilt information in these locations using the local SHWFS observation-plane irradiance patterns. The algorithm was shown to work well over the range of conditions tested with both simulated and experimental data. In turn, the reconstruction algorithm will enable robust wavefront sensing in transonic, supersonic, and hypersonic environments.
Current Shack-Hartmann Wavefront Sensor (SHWFS) reconstruction algorithms for aero-optical research underperform in the presence of flow features with strong density gradients, such as shockwaves in supersonic flow. The large density variations in shockwaves violate the key underlying assumption of SHWFS; that local changes in the wavefront within the lenslet subaperture manifest primarily as tip/tilt. In these cases, the image-plane irradiance pattern of individual lenslets can exhibit high-order aberrations, resulting in non-tip/tilt behaviors. Standard least-squares wavefront reconstruction methods fail to accurately recover the wavefront in the presence of a shock due to the least-squares estimator’s tendency to give too much “influence” to outliers present in the measured SHWFS data, resulting in an underprediction of the optical-path difference (OPD) across the shock. A new algorithm is described to overcome the limitations of the standard least-squares reconstruction method. Two weighting functions are investigated with the aim of using additional intensity information to quantify the degree to which each subaperture is aberrated. The least-squares estimator is replaced with a robust estimator to perform outlier handling and regularizing terms are then used to further constrain the spatial organization of the solution. The problem of wavefront reconstruction is cast as a global functional optimization problem where minimization is achieved iteratively. The algorithm is then evaluated on a sample of Mach 6 SHWFS dot patterns where oblique shocks produce flow discontinuities. The results show that the algorithm is capable of accurately targeting discontinuous flow features as outliers, and subsequently altering those outliers, increasing the OPD as well as the sharpness of the shockwave structure.
This paper develops a phase reconstruction algorithm for the Shack–Hartmann wavefront sensor that is tolerant to sharp phase gradients, such as the ones imposed by shock waves. The implications of this will enable robust wavefront sensing in transonic, supersonic, and hypersonic environments using a Shack–Hartmann wavefront sensor.
Shock waves are a commonly observed phenomenon in transonic and supersonic flow. These nearly discontinuous flow features form as a result of flow disturbances propagating faster than the local speed of sound. Across a shock wave, flow properties such as pressure, temperature, and density can change dramatically. In this paper, the effects of the near discontinuous change in density due to the shock wave on Shack–Hartmann wavefront sensor (SHWFS) measurements are studied experimentally. Experiments were conducted in the Mach 2 wind tunnel located in the Aero-Effects Laboratory at Kirtland, AFB. To generate the oblique shock wave, a wedge model was placed in the tunnel. Two dimensional, time-resolved wavefront measurements were collected simultaneously with a SHWFs and a digital holography wavefront sensor (DHWFS). In this manner, results from the two wavefront sensor techniques could be compared and contrasted. It is shown that the shock wave caused significant higher order distortion within the SHWFS lenslets. Significant lenslet beam spreading and bifurcation were observed in the raw SHWFS intensity images. When compared with the DHWFS measurements, the SHWFS measurements under predicted the phase distortion caused by the shock by up to approximately 1π.
Wind tunnel experiments were conducted to measure the unsteady surface pressure field of a hemisphere-on-cylinder turret in subsonic flow. These measurements were obtained using pressure transducers coupled with fast response pressure sensitive paint. The surface pressure field data resulting from Mach 0.5 flow (ReD ≈ 2 × 106 ) over three different turret protrusion distances were analyzed. Previously, dominant surface pressure modes on the turret were found using proper orthogonal decomposition. The results of which showed that greater turret protrusion into the freestream flow increased the prevalence of spanwise anti-symmetric surface pressure field fluctuations. These anti-symmetric pressure fluctuations are caused by anti-symmetrical vortex shedding. However, when a partially submerged hemispherical turret geometry is used, it was shown that this anti-symmetric mode was of much lower relative energy. This suggests that there is a transition in flow field phenomena as protrusion is changed from partially submerged to a full hemisphere configuration. Further investigation into this so-called “mode switching” is the emphasis of the work presented here. This research heavily relied on modal analysis to identify correlations between turret and wake surface pressure fields. The fluctuations in the surface pressure field around the partial hemisphere were found to be mostly dominated by the wake with little influence from fluidic structures on the turret itself. For the hemisphere and hemisphere-on-cylinder configurations, both symmetric and anti-symmetric unsteady separation grew to be the largest influence and was coupled with the wake fluctuations.
Shock waves result from turning supersonic or locally supersonic flow and result in a large change in gas properties downstream of the shock. This change in gas properties, namely, the large increase in freestream density can affect the wavefront of a laser beam propagating through the shock. In this paper, analytic expressions are developed to describe the effects of these shock waves on the wavefront a laser beam propagating through the shock both parallel and on an angle relative to the shock direction. Furthermore, these near-field disturbances are then brought to a focus at the image-plane using a thin lens transmittance function with the Fresnel diffraction integral. The effects of the near-field disturbances imposed by the shock on the image-plane irradiance patterns are investigated and the implications of these image-plane irradiance patterns on Shack-Hartmann wavefront sensor measurements are also discussed.
In the typical analysis of aero-optical wavefront data, the three lowest order spatial modes are removed from the experimental data. These three spatial modes (tip, tilt, and piston) are commonly corrupted by mechanical disturbances. In this work an algorithm was developed that takes advantage of the advective nature of aberrations to compensate for the tip, tilt, and piston removal common in experiment. The algorithm is able to recover the aero-optical component of the jitter and provide time series of global tilt free of mechanical disturbances. This algorithm is called the stitching method. Experiments were conducted in Notre Dame’s Tri-sonic Wind Tunnel (TWT) Facility. Optical wavefront measurements were conducted on a Mach 0.6/0.1 shear layer. Voice coil actuators were placed on the shear layer splitter plate to regularize the shear layer. The predicted results for the RMS of the aero-optical jitter from the stitching method matched well with modeled results. Since the stitching method produces full time series of global tilt, energy spectra were also computed and presented. This information can be used by systems designers to benchmark fast steering mirrors for use in airborne directed energy systems.
Optical measurements of a hemispherical turret were conducted in both a wind tunnel and airborne testing environment to measure aero-mechanical jitter imposed onto a laser beam. A hemispherical turret was positioned in the freestream flow at various protrusion distances, Mach numbers, and azimuthal angles. Lasers and accelerometers were used to quantify the mechanical contamination imposed onto the beam due to the fluid-structure interaction of the incoming freestream flow and the protruding turret body. The results from wind tunnel and in-flight testing were compared. It was shown that the wind tunnel and in-flight tests yielded different results both quantitatively and qualitatively. The possible reasons for the discrepancies between these testing campaigns were also discussed.
Surface pressure measurements were taken on a hemisphere-on-cylinder turret in a wind tunnel using pressure sensitive paint and fast response pressure transducers. Four different turret protrusion distances were tested to study the characteristics of the unsteady pressure field on the backside and wake of the turret. Proper orthogonal decomposition was used to identify the dominant spatial surface pressure modes acting on the turret in this parametric study. It was found that the further the turret protruded into the freestream flow, the more the surface pressure field became dominated by spanwise antisymmetric surface pressure distributions resulting from anti-symmetrical vortex shedding at a normalized frequency of approximately StD=0.2. For the case of the partial hemisphere, this anti-symmetrical vortex shedding was essentially absent, insinuating that at some protrusion distance, the surface pressure environment on the turret fundamentally changes. The normalized net force rms was calculated on the turret for each configuration. It was found that the greater the turret protrusion, the greater the net force acting in the spanwise direction.