Accurate measurement of laser light phase after propagation through underwater optical turbulence is crucial for defense and commercial applications like underwater communications and sensing. Traditional phase-measuring methods, like Shack-Hartmann wavefront sensors, have limited effectiveness in strong optical turbulence. The Gerchberg-Saxton (GS) method utilizes synchronized intensity images in the image and Fourier planes and retrieves the phase through an iterative algorithm. We evaluate the Gerchberg-Saxton algorithm's accuracy for laser light propagation through simulated Kolmogorov turbulence and experimentally generated Rayleigh-Bénard (RB) natural convection. The results of the phase retrieved from the experimental data recorded in pupil and focal planes are compared with the phase measurements from a Shack-Hartmann sensor. We tested the efficacy of the Gerchberg-Saxton algorithm to estimate the phase of laser light upon propagation through underwater optical turbulence.
Experimental Shack–Hartmann wavefront sensor (SHWFS) measurements were collected for a laser beam that propagated through a weakly compressible shear layer. Complementary computational fluid dynamics (CFD) was also conducted to match the experiment. The path-integrated CFD results were then applied to a SHWFS model such that the experimental and CFD results could be compared. Using both the experimental and CFD wavefront results, it was found that, although the CFD results slightly overestimated the resultant wavefront error, the CFD and experimental results revealed extremely similar wavefront topology. In order to further examine the aberrations imposed onto the laser beam in both datasets, the SHWFS image-plane irradiance patterns and circulation of phase gradients were studied. Similar to the overall wavefront topology, these data reduction approaches revealed similar phenomena in both the experimental and CFD-modeled results. Specifically, appreciable circulation and beam spread of the SHWFS image-plane irradiance patterns were exhibited throughout the shear layer’s braid region. Both of these findings suggest that sharp phase gradients exist in the weakly compressible shear layer and both (1) the SHWFS resolution and (2) the continuous nature of the phase estimate obtained using SHWFS data in a least-squares reconstruction algorithm make these phase gradients challenging to resolve. The findings presented here inform efforts looking to experimentally or computationally study aero-optical environments.
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.
Two methods for identifying branch points from Shack–Hartmann wavefront sensor (SHWFS) measurements were studied: the circulation of phase gradients approach and the beam-spread approach. These approaches were tested using a simple optical-vortex model, with wave-optics simulations, and with experimental data. It was found that these two approaches are synergistic regarding their abilities to detect branch points. Specifically, the beam-spread approach works best when the branch point is located toward the center of the SHWFS’s lenslet pupil, whereas the circulation of phase gradients approach works best when the branch point is located toward the edge of the SHWFS’s lenslet pupil. These behaviors were observed studying the simple optical-vortex model; however, they were further corroborated with the wave-optics and experimental results. The developments presented support researchers studying high scintillation optical-turbulence environments and inform efforts in developing branch-point tolerant reconstruction algorithms.
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.
Experimental Shack–Hartmann Wavefront Sensor (SHWFS) measurements were collected and examined to further understand image-plane irradiance pattern behavior in the presence of potentially sharp thermodynamic gradients. An analysis of path-integrated phase and image-plane irradiance pattern spreading discovered regions within a weakly compressible shear layer where sharp gradients were previously not observed. This paper describes the analysis process and shows results which suggest that Shack-Hartmann wavefront sensors are not adequately resolving sharp thermodynamic gradients in aberrating flows.
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.
In this paper, two methods for identifying branch points from Shack–Hartmann wavefront sensor (SHWFS) measurements were studied; the circulation of phase gradients approach and the beam-spread approach. These approaches were tested using a simple optical-vortex model, wave-optics simulations, and with experimental data. It was found that these two approaches are synergistic regarding their abilities to detect branch points. Specifically, the beam-spread approach works best when the branch point is located towards the center of the SHWFS’s lenslet pupil, while the circulation of phase gradients approach works best when the branch point is located towards the edge of the SHWFS’s lenslet pupil. These behavior were observed studying the simple optical-vortex model; however, they were further corroborated with the wave-optics and experimental results. The developments presented within support researchers looking to study high scintillation optical-turbulence environments as well as will inform efforts looking to develop branch-point tolerant reconstruction algorithms.
Beam propagation systems are often used in a wide range of atmospheric environments. Therefore, it is important to be able to characterize those environments in order to appropriately assess performance and inform design decisions. In this paper, a variety of methods for measuring atmospheric coherence length, r0, were analyzed including a Shack–Hartmann-based differential image motion monitor (DIMM), gradient-tilt variance, slope discrepancy variance, and phase variance methods, as well as using the modulation transfer function (MTF). These methods were tested on varying turbulence strength environments with known atmospheric coherence lengths, first using a single modified von Kármán phase screen, then using full wave-optics simulations with 20 phase screens. The Shack–Hartmann based approaches were shown to greatly increase in error for d/r0 > 1 due to discrepancies between gradient tilt and the centroid tilt measured from the SHWFS’ image-plane irradiance patterns. An atmospheric data collection system was built and experimental results were taken for a beam propagating 2.4 km through a littoral environment over a 24 hour period.
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.
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.
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.
High speed time-resolved wavefront and imaging measurements were taken synchronously in-flight through both boundary layer and shear layer environments around the Airborne Aero-Optical Laboratory for Beam Control. Instantaneous modulation transfer functions and point spread functions (PSFs), which characterize image degradation, were generated using wavefront data. Instantaneous power-in-bucket ratios were extracted from both the image data and computed from the wavefront data, and the ratios were found to correlate well with each other. The lower power-in-bucket values and related increased blurring that occurred predominantly in the streamwise direction were associated with large-scale, large-amplitude wavefront spatial variations due to large organized vortical structures present in the shear layer. The boundary layer did not create any significant image blurring due to the low level of aero-optical distortions. Finally, spatial autocorrelation functions were extracted from the wavefront data using the stitching method and were used to compute time-averaged PSFs for different aperture diameters.
High speed time-resolved wavefront and imaging measurements were taken synchronously in-flight through the boundary layer and the shear layer environments around the Airborne Aero-Optical Laboratory for Beam Control (AAOL-BC). Instantaneous point spread functions were generated using wavefront data which enabled a relationship between largescale structures present in turbulent flows and resultant instantaneous image degradation to be identified. In this manner, image blurring patterns can be related to specific flow structures which begins to abridge the knowledge gap between treating quantitative wavefront properties and the resultant blurred images.
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