A laboratory demonstration of two novel tactical beam control methods for correcting the effects of strong turbulence
including Beacon Anisoplanatism, and the combined effects of Beacon Anisoplanatism and Thermal Blooming,
respectively, were performed in SAIC's Tactical Beam Control Test-Bed. Both systems were tested with ratio of
aperture diameter to Fried parameter, D/r0, of up to 7, and ratio of beam spot size at the target to isoplanatic angle, θB/θo,
of up to 10. The first method was implemented in a Wavefront-based Stochastic Parallel Gradient Decent (WSPGD)
adaptive optics (AO) system, which uses an off-axis wavefront sensor (WFS) to provide feedback for a multi-dithering
beam control algorithm. The second method was implemented in a Hybrid WSPGD AO system, which incorporates the
WSPGD AO system with a conventional Phase Conjugate (PC) AO system. The Hybrid system uses an on-axis WFS to
generate initial deformable mirror commands and an off-axis WFS to generate additional commands that account for the
high frequency phase components removed from the wavefront of a laser return by Beacon Anisoplanatism. We
developed a low speed PC-based WSPGD controller, implemented designs of the WSPGD and Hybrid WSPGD AO
systems in SAIC's Test-Bed, and tested both AO systems in static and dynamic turbulence over a wide range of
turbulence conditions. A target-plane tracker was used to stabilize the line-of-sight in the AO corrected beam. Test
results show that the WSPGD AO system efficiently compensates the effects of Beacon Anisoplanatism for both static
and dynamic turbulence, providing a mean performance gain of 1.8 averaged over multiple turbulent realizations. We
also found in testing that the Hybrid WSPGD system efficiently compensates for Beacon Anisoplanatism in the presence
of Thermal Blooming - providing improved compensation for both Thermal Blooming and turbulence. In the presence
of strong Beacon Anisoplanatism with θB/θo of up to 10, the maximum performance gain is 4.9 and the mean
performance gain for multiple turbulence realizations is 2.1.
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.
KEYWORDS: Actuators, Deformable mirrors, Data modeling, Finite element methods, Calibration, Sensors, Statistical modeling, Systems modeling, Error analysis, Data analysis
A calibration procedure is described for improved modeling of a continuous facesheet deformable mirror. A resistive force of each actuator as it attempts to move to its commanded position is modeled as a linear spring force. A force associated with the resistance of the facesheet to bending is modeled as a moment that exerts a force on the actuators. The resultant first order finite element model is parameterized by a gain on each actuator channel and a ratio relating the average actuator spring constant and the facesheet bending moment coefficient. Example experimental results are presented indicating that modeling accuracy is improved by use of the first order finite element model.
A noise analysis is presented for complex field estimation using a self-referencing interferometer wave front sensor with an amplified reference. The wave front sensor is constructed from a phase-shifting, point diffraction interferometer. The reference field is created by coupling a part of the incident wave front into a single mode fiber where it is optically amplified. The noise characteristics of this wave front sensor are examined in terms of the field estimation Strehl. The effects of several system parameters are examined\nobreak—shot noise, read noise, quantization noise, spontaneous emission from the amplifier, the relative intensities of the signal and reference fields, and temporal phase shifting.
A recently developed scheme for closed loop stable control of two deformable mirrors (DMs) for compensation of both amplitude and phase fluctuations is examined. An approximate model describing the two DM system is developed using the Rytov theory. This model is used to evaluate the impact of measurement noise on the performance of the two DM system. The model is also used to evaluate the impact of misregistration on the stability of the two DM system. Wave optical simulation results are used to validate the predictions obtained from the Rytov theory based model.
In many adaptive optical systems the standard wave front sensing and reconstruction process involves a conventional least squares reconstruction of gradient measurements obtained from a Shack-Hartman wave front sensor (WFS). This reconstruction algorithm assumes the WFS measurements are equal to the average phase gradient within each subaperture. However, this assumption does not account for the effects of scintillation in the wave front. As scintillation increases, intensity fluctuations in the wave front increase the disparity between the output of the WFS and what the reconstruction algorithm expects, which in turn causes a degradation in the performance of the reconstructor. We present an algorithm that attempts to mitigate the scintillation problem by reconstructing the real and imaginary components of the wave front using gradient and intensity information obtained from a Shack-Hartmann WFS. This algorithm estimates the wave front by inverting a more precise model of the WFS measurement process. Wave optics simulations over a variety of atmospheric conditions are used to compare the performance of our algorithm against a least squares reconstructor and a complex exponential reconstructor.
The weighted parallel generalized projection algorithm is applied in two steps to the control of two deformable mirrors using multiple wavefront sensing beacons to simultaneously increase the compensated field of view while maximizing point spread function uniformity. Wave optical simulation results are presented that indicate that, even in strong scintillation, not only can the size of the compensated field of view be increased, but also the uniformity of the point spread function over the compensated field of view can be improved by augmentation of constraints enforcing point spread function uniformity.
A method for determining the registration of an adaptive optical system is presented. Three deformable mirror actuators are sinusoidally driven at a high rate and the resulting gradients are measured using a Hartmann sensor. The gradient measurements are used to determine the translational, rotational, and magnificational registration of the deformable mirror relative to the Hartmann wavefront sensor. Two configurations are presented. The first is not effected by the compensation system but requires the use of auxiliary beams outside the clear aperture of the adaptive optical system. In the second configuration, the dithering actuators are within the clear aperture of the adaptive optical system. Simulation results are presented that show that the method can be used reliably in either configuration. In the second configuration, the method can be used reliably even in the presence of residual amplitude and phase aberrations.
A post-processing methodology for reconstructing undersampled image sequences with randomly varying blur is described which can provide image enhancement beyond the sampling resolution of the sensor. This method is demonstrated on simulated imagery and on adaptive optics compensated imagery taken by the Starfire Optical Range 3.5 meter telescope that has been artificially undersampled. Also shown are the results of multiframe blind deconvolution of some of the highest quality optical imagery of low earth orbit satellites collected with a ground based telescope to date. The algorithm used is a generalization of multiframe blind deconvolution techniques which includes a representation of spatial sampling by the focal plane array elements in the forward stochastic model of the imaging system. This generalization enables the random shifts and shape of the adaptive compensated PSF to be used to partially eliminate the aliasing effects associated with sub- Nyquist sampling of the image by the focal plane array. The method could be used to reduce resolution loss which occurs when imaging in wide FOV modes.
Mellin transform techniques are applied to develop power series formulas to efficiently evaluate covariances for zernike representations of turbulence-induced phase distortions along a pair of ray paths through the atmosphere from one or several sources at finite or infinite range. The formulas also apply when the phase distortions are temporally filtered by a closed loop adaptive optics system. The power series formulas are developed using an automated computer logic algorithm designed to solve multiple contour integrals in multiple complex planes resulting from the application of Mellin transform techniques. Results are presented for the von Karman turbulence spectrum with a finite outer scale. Amplitude scintillation effects are neglected. The Taylor hypothesis is assumed to model the temporal behavior of the turbulence using either a fixed or random wind profile. The resulting formulas are weighted integrals of the refractive index structure constant Cn2(z), where the weighting functions are power series in from one to six indices depending on the beacons used and the choices made regarding the atmospheric turbulence spectrum and the direction of the wind.
The optimal track loop controller in an adaptive optics system is a function of the steering mirror dynamics, the temporal statistics of the input disturbance signal, measurement noise, and the sensor gain. The atmospheric input statistics and the sensor gain of a quadrant detector are slowly time-varying on a scale of minutes. If all parameters are known a prior, the analytical optimal controller is found by augmenting the dynamics of the input disturbance spectra and solving an H2 optimization problem. Near optimal control is achieved by augmenting the mount jitter dynamics and a first order approximation of the atmosphere dynamics and finding the LQG/LTR controller. The optimal bandwidth to compensate for time-varying atmospheric disturbance and noise levels is found by optimizing the loop gain. Recursive least squares is used to estimate the sensor gain and optimize the bandwidth in real time. The only measurements necessary for optimization are the residual track errors from a high frame rate, low noise quad cell algorithm and from a low frame rate dense ccd array using a centroid algorithm. Provided the temporal variations in the sensor gain are slow, closed loop robust stability is guaranteed by constraining the optimization algorithm via projection. Simulation results are presented which verify that the constrained optimal controller is achieved under a variety of conditions.
We report preliminary results of wavefront tilt measurements for the star Polaris at the Starfire Optical Range 3.5 m telescope at Kirtland AFB in Albuquerque, NM. We measured full aperture gradient tilt by using five pupil masks representing aperture diameters from 0.1m to 3.5m. Two optical configurations were exploited. In the first configuration, five images of Polaris were recorded simultaneously on one camera frame. The telescope was operated in its normal sidereal pointing mode. In the second configuration, pupil masks were changed sequentially. Additional measurements were collected with the telescope bolted to attempt to mitigate the effects of mont jitter. The coordinate system of the tilt measurement was rotated so that the cross-correlation coefficient between X- and Y-axis tilt components is equal to zero. Several interesting results were obtained. We observed anisotropy of the statistics of wavefront tilt. The observed one-axis tilt variances are unequal and the horizontal tilt variance is consistently greater than the vertical one. We believe these effects dare due to anisotropy of the large evidence of the effects of non-Kolmogorov turbulence on wavefront tilt. The measured tilt variance vs. aperture diameter curve has a knee beyond which the tilt variance no longer decreases for larger diameters. In the low and high frequency range the tilt power spectra obey the f-2/3 and f-11/3 power law, respectively. The tilt temporal correlation scale for the 3.5m aperture is on the order of 0.4 sec.
The adaptive optical system for the Starfire Optical Range 3.5-meter telescope includes a SHack-Hartmann wavefront sensor (WFS) with 30 by 30 subapertures and a continuous facesheet deformable mirror (DM) with 31 by 31 actuators within the telescope aperture. Time histories of turbulence- induced phase distortions have been estimated from WFS gradient measurements and DM actuator commands acquired simulators with the adaptive optics loop closed. The statistics of these phase distortion profiles have been characterized in terms of spatial structure functions, Zernike coefficient statistics, and temporal power spectral densities. The results obtained are in good agreement with predictions based upon Kolmogorov theory.
Feedback control theory offers several useful tools for analysis of adaptive optics systems. The basic tools of single-input-single-output analysis are applied to design first order and optimal filters for a specific loop bandwidth or gain margin as a function of latency and sample rate. Optimizing filter loop band-width as a function of temporal disturbance and noise statistics is addressed with respect to the internal model principles. Latency, due to camera readout and processing time, is shown to be the primary design driver for optical AO system performance. The effects of wavefront sensor saturation are discussed and simulation and experimental results are presented.
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