Jeffrey D. Barchers

Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics

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.

Closed-loop stable control of two deformable mirrors for compensation of amplitude and phase fluctuations

A method for closed-loop stable control of two deformable mirrors for compensation of both amplitude and phase fluctuations is described. A generic implementation is described as well as an implementation that integrates the concept behind a point diffraction interferometer with a two-deformable-mirror system. The relationship of the closed-loop control algorithm to previously developed open-loop iterative algorithms is described. Simulation results are presented that indicate that the system is stable and provides superior performance over that of a single-deformable-mirror system. The impact of finite servo bandwidth on control of two deformable mirrors is evaluated by means of wave optical simulation, and it is found that to achieve a performance improvement attributable to compensation of amplitude fluctuations, the bandwidth of the two-deformable-mirror system must be at least twice the Greenwood frequency.

Improved compensation of turbulence-induced amplitude and phase distortions by means of multiple near-field phase adjustments.

An approach for compensation of turbulence-induced amplitude and phase distortions is described. Two deformable mirrors are placed optically conjugate to the collecting aperture and to a finite range from this aperture. Two control algorithms are presented. The first is a sequential generalized projection algorithm (SGPA) that is similar to the Gerchberg-Saxton phase retrieval algorithm. The second is a parallel generalized projection algorithm (PGPA) that introduces constraints that minimize the number of branch points in the control commands for the deformable mirrors. These approaches are compared with the approach of placing the second deformable mirror conjugate to the far field of the collecting aperture and using the Gerchberg-Saxton algorithm to determine the optimal mirror commands. Simulation results show that placing the second deformable mirror at a finite range can achieve near-unity Strehl ratio regardless of the strength of the scintillation induced by propagation through extended paths, while the maximum Strehl ratio of the far-field approach drops off with increasing scintillation. The feasibility of the solutions is evaluated by counting the branch points contained in the deformable mirror commands. There are large numbers of branch points contained in the control commands that are generated by the Gerchberg-Saxton SGPA-based algorithms, irrespective of where the second deformable mirror is located. However, the control commands generated by the PGPA with branch point constraints achieves excellent Strehl ratio and minimizes the number of branch points.

Application of the parallel generalized projection algorithm to the control of two finite-resolution deformable mirrors for scintillation compensation

A modification of the parallel generalized projection algorithm is presented that allows for the use of projections in a weighted norm. Convergence properties of the modified algorithm, denoted the weighted parallel generalized projection algorithm, are developed. The weighted parallel generalized projection algorithm is applied to the control of two finite-resolution deformable mirrors to compensate for both the amplitude and the phase fluctuations that result from propagation through a turbulent medium. Numerical results are shown that indicate that a two-deformable-mirror system can provide improved performance over that of a single-deformable-mirror system.

Supersampling multiframe blind deconvolution resolution enhancement of adaptive optics compensated imagery of low earth orbit satellites

We describe a postprocessing methodology for reconstructing undersampled image sequences with randomly varying blur that can provide image enhancement beyond the sampling resolution of the sensor. This method is demonstrated on simulated imagery and on adaptive- optics-(AO)-compensated imagery taken by the Starfire Optical Range 3.5-m 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 that include a representation of spatial sampling by the focal plane array elements based on a forward stochastic model. This generalization enables the random shifts and shape of the AO-compensated point spread function (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 that occurs when imaging in wide-field-of-view (FOV) modes.

Evaluation of the impact of finite-resolution effects on scintillation compensation using two deformable mirrors

The impact of finite-resolution deformable mirrors and wave-front sensors is evaluated as it applies to fullwave conjugation using two deformable mirrors. The first deformable mirror is fixed conjugate to the pupil, while the second deformable mirror is at a finite range. The control algorithm to determine the mirror commands for the two deformable mirrors is based on a modification of the sequential generalized projection algorithm. The modification of the algorithm allows the incorporation of Gaussian spatial filters into the optimization process to limit the spatial-frequency content applied to the two deformable mirrors. Simulation results are presented for imaging and energy projection scenarios that establish that the optimal spatial filter waist to be applied is equal to the subaperture side length in strong turbulence. The effect of varying the subaperture side length is examined, and it is found that to effect a significant degree of scintillation compensation, the subapertures, and corresponding spacing between actuators, must be much smaller than the coherence length of the input field.

Linear analysis of thermal blooming compensation instabilities in laser propagation

Thermal blooming compensation instabilities are examined. The linearized system of thermal blooming compensation (TBC) equations is studied to develop parameters that characterize the stability of phase-only and full-wave (amplitude and phase) compensation for the effects of thermal blooming. The stabilizing effects of microscale wind shear are included in the analysis to provide a mechanism to stabilize the TBC equations. Stability is equated to existence of bounded solutions of the linear TBC equations, and appropriate dimensionless parameters are developed that ensure existence and uniqueness of bounded solutions to the TBC equations. Parameters characterizing stability are expressed in forms analogous to conventional scaling laws.

Convergence rates for iterative vector space projection methods for control of two deformable mirrors for compensation of both amplitude and phase fluctuations

The control of two deformable mirrors for compensation of time-varying fluctuations in the complex field that results from wave propagation through a turbulent medium is considered. Iterative vector space projection methods are utilized to determine the control commands to be applied to the two deformable mirrors. Convergence of the iterative algorithm is accelerated when the algorithm is initialized, at each measurement period, with the values for the phase commands obtained from the previous measurement period. Furthermore, it is found that, if the sample frequency is sufficiently greater than the Greenwood frequency, then only a single iterative step at each measurement period is required to obtain good compensation of both amplitude and phase fluctuations.

Complex field reconstruction using gradient and intensity measurements from a Shack-Hartmann wave front sensor

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.

Supersampling multiframe blind deconvolution resolution enhancement of adaptive-optics-compensated imagery of LEO satellites

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.