The Laser guide Star Sensor Integrated Extreme adaptive optics (LASSIE) project seeks to improve extreme adaptive optics (ExAO) performance for dim objects using a laser guide star (LGS) AO system to correct for higher spatial frequency phase aberrations minimizing the flux required for the NGS wavefront measurement. As part of that effort, the LASSIE program is exploring avenues for improving LGS AO performance through pre-compensation of the uplink beam and improved wavefront sensor design. Various systems designs are explored to estimate performance improvement that may be obtained with a pre-compensated LGS AO system and an optimized wavefront sensor design relative to a standard ExAO system.
We use wave-optics simulations to investigate branch-point density (i.e., the number of branch points within the pupil-phase function) in terms of the grid sampling. The goal for these wave-optics simulations is to model plane-wave propagation through homogeneous turbulence, both with and without the effects of a finite inner scale modeled using a Hill spectrum. In practice, the grid sampling provides a gauge for the amount of branch-point resolution within the wave-optics simulations, whereas the Rytov number, Fried coherence diameter, and isoplanatic angle provide parameters to setup and explore the associated deep-turbulence conditions. Via Monte Carlo averaging, the results show that without the effects of a finite inner scale, the branch-point density grows without bound with adequate grid sampling. However, the results also show that as the inner-scale size increases, this unbounded growth (1) significantly decreases as the Rytov number, Fried coherence diameter, and isoplanatic angle increase in strength and (2) saturates with adequate grid sampling. These findings imply that future developments need to include the effects of a finite inner scale to accurately model the multifaceted nature of the branch-point problem in adaptive optics.
We report on a test bed to compare the performance of three different wavefront sensors, the Shack-Hartmann Wavefront Sensor (SHWFS), the Pyramid Wavefront Sensor (PWFS), and the non-linear Curvature Wavefront Sensor (nlCWFS). No single wavefront sensor easily allows for sensing all aspects of atmospheric turbulence. For instance the SHWFS has a large dynamic range and a linear response to input phase aberrations but is not sensitive to low order modes. The PWFS uses the full spatial resolution of the pupil which gives it increased sensitivity to low order modes, however it still treads the line between achieving high dynamic range and high sensitivity. The nlCWFS is the only wavefront sensor designed to sense low and high, spatial frequencies, however this leads to a complex algorithm. We discuss the reconstruction algorithm for each WFS along with simulated comparisons, we present the optical design for the WFS comparison tes tbed, and outline the adaptive optics controls system.
This study uses traditional wave-optics techniques, such as the split-step beam propagation method with angular-spectrum propagation, to explore the number of branch points as a function of the numerical grid size (i.e., the branch-point density) with increasing strengths of turbulence. To help quantify the strength of the turbulence, the analysis makes use of the log-amplitude variance for a spherical wave. Given a point-source beacon and horizontal-propagation paths, this parameter gives a straightforward gauge for the amount of scintillation, and therefore the number of branch points in the phase function. As such, the goal throughout is to investigate the branch-point density in terms of a two-step process. The first step is to increase the numerical grid size to have an ever increasing number of grid points for a given instance of turbulence; particularly, with a log-amplitude variance for a spherical wave above 0.25, because this is where branch points start to arise in the phase function. In turn, the second step is to utilize a Monte-Carlo averaging scheme with the resultant branch-point density for many instances of turbulence and turbulence strengths. Using this two-step process, the initial results show that the branch-point density grows without bound. Such results seem unphysical and could have direct implications for wave-optics studies that involve wavefront sensing in the presence of deep turbulence.
Adaptive-optics (AO) systems correct the distortions caused by atmospheric turbulence for imaging and laser transmission applications. Given an extended, uncooperative object, the AO system must create a reference wave for wavefront measurement. It does so by focusing a laser beam onto the object; therefore, creating a beacon. Unfortunately, the extended size of the beacon after propagation gives rise to speckle, causing noise in the wavefront measurements which degrades the AO system’s correction of the turbulence effects. In this paper, we use polychromatic illumination to create the reference wave, which results in an associated reduction in the speckle noise. To quantify the benefits, we use split-step wave-optics simulations with the spectral-slicing method for polychromatic light. We assume that the AO system uses a Shack Hartmann wavefront sensor. Furthermore, we assume that the speckle decorrelates over short periods of time corresponding to reasonable object motions. We consider a range of conditions for the object size (i.e. the object Fresnel number), object motion, and illuminator coherence length. The results show a reduction in the speckle-induced error with polychromatic light, especially when the object is large. This finding indicates that polychromatic illumination can improve the performance of AO systems when the object is both uncooperative and extended.
In this study we use a series of computational-wave-optics experiments to look at the statistics associated with speckle fields resulting from a tilted flat plate (i.e. one that is optically rough compared to the wavelength of plane-wave illumination). To help quantify the strength of the simulated speckle, we make use of the target Fresnel number. This parameter gives a gauge for the number of speckles across the receiver. The goal throughout is to show that, frame to frame, the analysis can appropriately simulate correlated speckle fields in terms of the magnitude of the complex degree of coherence as a function of tilt. The results show that the simulated speckle fields are properly correlated from frame to frame, and this outcome leads to the ability to perform closed-loop-phase-compensation studies in the presence of extended beacons. Such studies are becoming increasingly important for applications that involve imaging through turbulence.
This study evaluates the effects of beacon-wavelength mismatch on phase-compensation performance. In general,
beacon-wavelength mismatch occurs at the system level because the beacon-illuminator laser (BIL) and high-energy
laser (HEL) are often at different wavelengths. Such is the case, for example, when using an aperture sharing element to
isolate the beam-control sensor suite from the blinding nature of the HEL. With that said, this study uses the WavePlex
Toolbox in MATLAB® to model ideal spherical wave propagation through various atmospheric-turbulence conditions.
To quantify phase-compensation performance, we also model a nominal adaptive-optics (AO) system. We achieve
correction from a Shack-Hartmann wavefront sensor and continuous-face-sheet deformable mirror using a least-squares
phase reconstruction algorithm in the Fried geometry and a leaky integrator control law. To this end, we plot the power
in the bucket metric as a function of BIL-HEL wavelength difference. Our initial results show that positive BIL-HEL
wavelength differences achieve better phase compensation performance compared to negative BIL-HEL wavelength
differences (i.e., red BILs outperform blue BILs). This outcome is consistent with past results.
Theory presented in the companion paper [1] reveals that for paraxial propagation of scalar waves transverse linear momentum (TLM) and orbital angular momentum (OAM) of beam waves are simply related to the wave coherence function, and that the TLM and OAM densities can be measured by a conventional Shack-Hartman sensor, which is typically used for the phase measurements. Here we present the extension of this theory to the case of the OAM fluctuations of a spherical wave intercepted by a finite aperture. We report the OAM measurements derived from the data obtained by the Hartman Turbulence Sensor (HTS) during the field measurement campaign in 2009-10 and data produced by wave optics simulation of the HTS. We examine the statistics of the total OAM intercepted by the wave front sensor aperture and compare it to theoretical results. Modeling data supports the conservation of the mean OAM and relatively slow development of the OAM fluctuations predicted by the theory.
The presence of distributed-volume atmospheric aberrations or “deep turbulence” presents unique challenges for beam-control applications which look to sense and correct for disturbances found along the laser-propagation path. This paper explores the potential for branch-point-tolerant reconstruction algorithms and tiled-aperture architectures to correct for the branch cuts contained in the phase function due to deep-turbulence conditions. Using wave-optics simulations, the analysis aims to parameterize the fitting-error performance of tiled-aperture architectures operating in a null-seeking control loop with piston, tip, and tilt compensation of the individual optical beamlet trains. To evaluate fitting-error performance, the analysis plots normalized power in the bucket as a function of the Fried coherence diameter, the log-amplitude variance, and the number of subapertures for comparison purposes. Initial results show that tiled-aperture architectures with a large number of subapertures outperform filled-aperture architectures with continuous-face-sheet deformable mirrors.
The Airborne Aero-Optical Laboratory has produced a large database of aero-optical measurements with a high-speed, high-resolution Shack Hartmann wavefront sensor. The data have been collected over a wide range of flight conditions. An analysis of the statistical characteristics of the subsonic and early transonic data is performed to assess the adequacy of the spatial and temporal resolution of the data. Sample rate requirements for a minimum variance phase estimator are also explored. The techniques employed are validated by application to measurements of optical atmospheric turbulence where results can be anticipated based on established Kolmogorov statistics.
The Air Force Research Laboratory (AFRL) is developing and extending a model of the boundary layer that takes, as input,
common atmospheric measurements and ground condition parameters, and predicts key parameters of optical turbulence
such as strength and inner scale. In order to anchor the model, a field campaign is also being conducted. The campaign will
include co-located meteorological instruments and an open loop Hartmann wavefront sensor. Here, a portion of the
boundary layer model is discussed: that relevant for the daytime surface layer. A sensitivity analysis of input parameters is
presented.
In the field of optical propagation through the atmosphere a knowledge of optical turbulence strength and
other key statistical parameters is crucial for performance prediction and system design. This work presents
techniques for reliably estimating the most essential parameters of optical turbulence, namely r0, the Fried
coherence length, fG, the Greenwood frequency, and l0, the inner scale of turbulence from Shack-Hartmann
wavefront sensor measurements. The earliest approaches for estimating r0 were based on MTF measurements.1
The MTF approach requires accurate calibration and stability of the system MTF which is often problematic.
Astronomers have used differential motion and scintillation to measure seeing conditions.2-5 Others have used
the slope structure function estimated from a Hartmann wavefront sensor principally for r0 estimation.6
We have shown that the slope discrepancy7 or rotational component of the slopes can be used effectively in
turbulence estimates.8 The techniques we describe here can be used to estimate r0, fG, and l0. The inner scale
estimate is based on the assumption of the Hill spectrum for refractive index fluctuations.9-11 A high resolution,
high frame rate, mobile sensor has been developed to utilize these estimation techniques. Section 2 describes the
estimation techniques. Results from field measurement campaigns will be presented in Section 3.
To compensate for large phase errors at high bandwidth, a dual deformable mirror (DM) architecture is
introduced. One DM (the tweeter) handles the high spatial resolution errors with a small stroke, high bandwidth,
capability while the other DM (the woofer) corrects the larger but more slowly varying phase errors with a larger
stroke capability. An offload control architecture is shown to be very effective with the Kolmogorov turbulence
spectrum. The architecture is also shown to be effective when used with a self-referencing interferomenter (SRI)
wavefront sensor and an exponential control law for phase unwrapping. Performance is verified in simulation
and in an advanced wavefront control testbed facility at the Air Force Research Laboratory.
A new approach, for estimating r0 and the Greenwood frequency from wavefront sensor measurements, is introduced. Unlike other techniques, which use phase statistics calculated from reconstructed wavefront sensor measurements, this approach makes use of the slope discrepancy, the component of the measurement that is not reconstructed by a least squares reconstructor. It is shown that the r0 estimator based on the slope discrepancy is a high degree-of-freedom estimator with a much smaller estimation variance than estimates based on the phase variance. An new temporal atmospheric sample rate, f0(ε2), is introduced in this work. This quantity is calculated from the slope discrepancy structure function and sets the minimum required sampling rate to maintain the residual wavefront error below ε2/K for a system dependent gain, K. For Kolmogorov turbulence statistics it is shown that the Greenwood frequency is related to f0 by fG=f0(K(2π/20)2)/40. In non-Kolmogorov turbulence, f0 continues to be a legitimate specification of sampling requirements. These results are all illustrated with wave optics simulations.
The estimation accuracy of wavefront sensors in strong scintillation is examined. Wave optical simulation is used to characterize the performance of several wavefront sensors in the absence of measurement noise. The estimation accuracy of a Schack-Hartmann sensor is shown to be poor in strong scintillation due primarily to the presence of branch points in the phase function. The estimation accuracy of a unit-shear, shearing interferometer is found to be significantly better than that of a Hartmann sensor in strong scintillation. The estimation accuracy of a phase shifting point diffraction interferometer is shown to be invariant with scintillation.
A phase reconstructor for an adaptive optics system depends on a model of the response of commands to the deformable mirror in the gradient sensor. Errors in this model may be due to actuator/sensor misregistration. The level of misregistration which produces closed loop instability is calculated for several systems (2 X 2, 4 X 4, and 15 X 15 subapertures). Depending on the servo law, the 15 X 15 system may be stable for misregistration up to 17% of a subaperture but loses 30 degrees of phase margin at 5%. The effects of system size, servo bandwidth, latency, and actuator slaving are illustrated. It is also shown that spatially filtering the reconstructed phase can dramatically reduce the sensitivity to misregistration.
The ABL Lockheed Martin has prepared and validated a highly versatile adaptive optics testbed to simulate in an accurately scaled fashion all aspects of ABL laser beam propagation, including atmospheric compensation and pointing and tracking in selected atmospheres. This system allows repetitive, highly controlled, and well diagnosed experiments to be carried out that are generally impossible to do in field test where the user has little control over atmospheric and other test conditions. Testing of beam control hardware including components, assemblies, control loops and software, as well as development of methodology such as alignment and sensor techniques, determinations of system operational robustness, and finally, measurement of overall system performance under various atmospheric or other propagation and seeing conditions are routinely done. This presentation will discuss 1) the system scaling chosen to preserve diffraction, turbulence and temporal fidelity to ABL, 2) agreement of experiment results to those of other laser propagation experiments and wave optic code simulations, and 3) experiments that have demonstrated ABL beam control system robustness, compensation for jitter and turbulence, and overall performance when operating in atmospheric turbulence that emulates that measured in the real-world theater.
This paper describes the differential phase experiment (DPE) which formed a major part of the ABLE ACE suite of experiments conducted by the Air Force. The work described covers the rationale for the experiment, the basic experimental concept, the analysis of the differential phase, the optical and software design analysis, a discussion of the polarization scrambling characteristics of the optics, calibration of the equipment and a presentation of some of the major results of the data reduction effort to date. The DPE was a propagation experiment conducted between two aircraft flying at an altitude of 40,000 feet whose purpose was to measure the phase difference between two beams propagating at slightly different angels through the atmosphere. A four bin polarization interferometer was used to measure the differential phase. Due to the high level of scintillation that was presented branch points were present in the phase function. Rytov theory, wave optics simulation and the experimental measurements are in general agreement. Self consistency checks that were performed on the data indicate a high level of confidence in the results. Values of Cn2 that are consistent with the measurements of the differential phase agree with simultaneous scintillometer measurement taken long the same path in levels of turbulence where the scintillometer is not saturated. These differential phase based Cn2 estimates do not appear to saturate as is typical of scintillometer measurements and appear to extend the range over which high levels of Cn2 can be estimated. In addition the differential phase and anisoplanatic Strehl computed from the data is consistent with Rytov theory and wave optics simulations.
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