This work presents a comprehensive characterization of a benchtop optical-turbulence simulator system using a Shack—Hartmann (SH) wavefront sensor, an off-axis digital holography (DH) wavefront sensor, and a far-field imaging camera. The system employs two spatial-light modulators (SLMs) to impose turbulent phase screens with prescribed statistics onto a laser beam, simulating atmospheric turbulence. We conduct tests to compare the system’s performance against wave-optics simulations by varying turbulence strength, varying the modeled propagation distance, and using both SLMs to model beam propagation. The results show that the DH wavefront measurements have a root mean square error (RMSE) of 0.02–0.03 µm compared to the simulated wavefronts, while the SH measurements have a RMSE of 0.02–0.05 µm compared to the DH wavefront measurements. We also assess the system’s ability to model beam propagation. Here, we find that the extent of phase disagreement increases with increasing propagation distances. Overall, the results of a Monte–Carlo simulation that models a 25 cm beam along a 1 km path reveal that DH measurements closely match the known turbulence parameters whereas the SH measurements generally underestimate turbulence strength. At large, this work informs system designers of how different wavefront sensors perform in varying optical-turbulence conditions.
This paper explores the efficacy of employing machine learning, specifically an encoder-style convolutional neural network, to estimate the magnitude of an optical-phase discontinuity (|Δϕ|) that results in an aberrated, farfield irradiance pattern. The model receives a single 32×32 normalized irradiance pattern image and returns the estimated |Δϕ|. We train and validate the model using simulated data with varying values of Δϕ (from 0 to 2π radians), discontinuity locations within the aperture of the simulated system, and strengths of background noise. In exploring this trade space, we calculate the mean absolute errors of the model to be between 0.0603 and 0.475 radians. We also explore the model’s versatility using varying spot sizes to augment the transfer of this model across various systems where the focal length, aperture diameter, or light wavelength may differ, thereby influencing the number of pixels holding information across each irradiance pattern. Finally, this model is tested on experimentally collected data using a spatial light modulator, resulting in a mean absolute error of 0.909 radians. This research supports the development of a shock-wave-tolerant phase reconstruction algorithm for the Shack–Hartmann wavefront sensor. At large, robust shock-wave-tolerant phase reconstruction algorithms will improve wavefront sensing efforts where shock waves are present.
This work presents preliminary results on aero-mechanical jitter of a hemispherical optical turret. A simplified geometry with a hemispherical shell and optics-holding canister was designed to reduce degrees of freedom and provide better insight into fundamental physics. Modal analysis of the turret and mounting plate to the wind tunnel, performed using finite element analysis (FEA), revealed significant plate displacements in the lowest frequency modes. Three mounting plate thicknesses (1/4”, 1/2”, and 1”) were tested. Wind tunnel tests at the University of Notre Dame’s White Field Mach 0.6 wind tunnel assessed turret vibrations at speeds from Mach 0.2 to 0.5, using accelerometers and Shack-Hartmann tilt sensors. Two scenarios were tested: one with the turret inside the tunnel exposed to the flow, and another with the turret attached outside of the wind tunnel so that it is only excited by the base motion of the wind tunnel. The 1/4” plate showed tilt measurements ranging from 30 to 190 microradians when exposed to flow, compared to 10 to 50 microradians in the baseline case. The 1/2” and 1” plates exhibited lower tilts and less distinction between flow and baseline conditions. Overall, the simplified turret only had about three vibration modes affecting tilt, with strong spatial agreement between experimental and FEA modal patterns.
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.
Standard methods of Shack-Hartmann wavefront reconstruction rely on solving a system of linear equations, extracting wavefront estimates from measured wavefront slopes, which are calculated by retrieving centroids from a Shack-Hartmann Wavefront Sensor (SHWFS). As the dimensions of a micro-lens array in the SHWFS increase, the computational cost of processing wavefronts can become increasingly expensive. For applications that require rapid and accurate computations, such as closed-loop adaptive-optic systems, traditional centroiding and the least-squares reconstruction becomes the main bottleneck limiting performance. In this work, we apply a convolutional neural network (CNN) approach to directly reconstruct wavefronts from raw SHWFS measurements, circumventing both bottlenecks. The CNN model utilizes the ResU-Net framework to perform a zonal wavefront reconstruction, and a method for preprocessing the raw data was investigated with the prospect of enhancing the accuracy of this model specifically for the zonal approach to wavefront reconstruction.
At supersonic speeds, shock waves create steep gradients in the density of the flow field. These large gradients have been shown to adversely affect the accuracy of Shack-Hartmann Wavefront Sensor (SHWFS) during wavefront reconstruction. This is caused by higher-order beam distortions within the lenslet. In the presented work, the wavefront of a collimated beam propagating through a local shock region over a partially protruding cylinder body was measured using SHWFS and off-axis Digital Holography Wavefront Sensor (DHWFS). These measurements were taken simultaneously allowing for direct comparison. Further study was done on computational and post-processing methods of handling the higher order aberrations caused by the shock, as well as studying their effects on the resulting wavefront. By varying the incoming transonic Mach numbers, the shock strength and spatial extent could be adjusted, thus providing multiple scenarios for comparison. The experimental data presented in this work provides valuable insight into shock-induced effects on the resulting wavefront. These results help to further support the development of new methods for mitigating the adverse effects of shocks on well-established measurement methods such as SHWFS and off-axis DHWFS in similar applications.
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.
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.
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.
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