Extension of the matched-filter algorithm to multiple guide star Shack-Hartmann wavefront sensor.

The adaptive optics (AO) systems with multiple laser guide stars (LGSs) may significantly benefit in terms of hardware simplification from merging several LGS optical channels into one with a single wavefront sensor. As Shack-Hartmann sensors typically suffer from incomplete filling of the camera area, there exists an opportunity to overlay several Hartmann spot patterns densely within a compact composite one, resulting in very frugal use of the camera pixels. We show that such a pattern with only slight spot overlap can be composed even in the quite extreme case of the Giant Magellan Telescope laser tomography AO system employing six highly elongated side-launched laser beacons. The problem of disentangling the overlapped spots is efficiently solvable by a generalization of the matched-filter (MF) algorithm, which is the main focus of this work. Dynamic calibration by star dithering in the case of extended MF is still possible, albeit more complicated. Computational complexity increase and performance degradation in comparison to classical MF can be minimized to acceptable values by careful system parameter tuning.

Shack-Hartmann mask/pupil registration algorithm for wavefront sensing in segmented mirror telescopes.

Shack-Hartmann wavefront sensing in general requires careful registration of the reimaged telescope primary mirror to the Shack-Hartmann mask or lenslet array. The registration requirements are particularly demanding for applications in which segmented mirrors are phased using a physical optics generalization of the Shack-Hartmann test. In such cases the registration tolerances are less than 0.1% of the diameter of the primary mirror. We present a pupil registration algorithm suitable for such high accuracy applications that is based on the one used successfully for phasing the segments of the Keck telescopes. The pupil is aligned in four degrees of freedom (translations, rotation, and magnification) by balancing the intensities of subimages formed by small subapertures that straddle the periphery of the mirror. We describe the algorithm in general terms and then in the specific context of two very different geometries: the 492 segment Thirty Meter Telescope, and the seven "segment" Giant Magellan Telescope. Through detailed simulations we explore the accuracy of the algorithm and its sensitivity to such effects as cross talk, noise/counting statistics, atmospheric scintillation, and segment reflectivity variations.

Projection approach to complexity reduction in tomographic alignment of extremely large telescopes.

We describe a complexity reduction approach intended to solve the tomographic alignment problem for the Thirty Meter Telescope by means of its alignment and phasing system (APS) with little loss of information. This approach is computationally efficient enough to perform detailed Monte-Carlo simulations of the APS on a standard PC. We present sample simulations to model error propagation through the system and to build a preliminary APS alignment error budget.

Tomographic alignment algorithm for an extremely large three-mirror telescope: invisible modes.

We analyze the optical effects due to distortions of a three-mirror telescope that is sufficiently large that all three mirrors must be actively controlled. Numerical experiments on telescopes with both monolithic and segmented primary mirrors reveal the existence of telescope misalignment configurations (modes) that are invisible to a fixed focal station wavefront sensor, even for highly redundant multidirectional tomographic measurement schemes. We describe these modes and give a theoretical explanation for them.

Bootstrap beacon creation for overcoming the effects of beacon anisoplanatism in a laser beam projection system.

We address the problem of using adaptive optics to deliver power from an airborne laser platform to a ground target through atmospheric turbulence under conditions of strong scintillation and anisoplanatism. We explore three options for creating a beacon for use in adaptive optics beam control: scattering laser energy from the target, using a single uncompensated Rayleigh beacon, and using a series of compensated Rayleigh beacons. We demonstrate that using a series of compensated Rayleigh beacons distributed along the path provides the best beam compensation.

Beaconless stochastic parallel gradient descent laser beam control: numerical experiments.

We apply a target-in-the-loop strategy to the case of adaptive optics beam control in the presence of strong atmospheric turbulence for air-to-ground directed energy laser applications. Using numerical simulations we show that in the absence of a cooperative beacon to probe the atmosphere it is possible to extract information suitable for effective beam control from images of the speckled and strongly turbulence degraded intensity distribution of the laser energy at the target. We use a closed-loop, single-deformable-mirror adaptive optics system driven by a target-in-the-loop stochastic parallel gradient descent optimization algorithm minimizing a mean-radius performance metric defined on the image of the laser beam intensity distribution formed at the receiver. We show that a relatively low order 25-channel zonal adaptive optical beam control system controlled in this way is capable of achieving a high degree of turbulence compensation with respect to energy concentration if the tilt can be corrected separately.

Performance study of Kalman filter controller for multiconjugate adaptive optics.

We compare the performance of the Kalman filter (KF)-based and the minimum variance (MV) control algorithms for a zonal adaptive optics with a phase temporal prediction step included for effective compensation of the errors attributable to latencies in the system. The main goal is to evaluate the performance achievable by the computationally more expensive KF approach, which explicitly accounts for the atmospheric turbulence temporal behavior through a first-order autoregressive evolution model, and the simpler MV algorithm, with and without temporal prediction. For a representative example, the Gemini-South 8 m telescope multiconjugate adaptive optics system performance of the KF and the MV controllers has been compared with respect to their turbulence compensation capability. We show that the KF algorithm, as expected, shows superior performance to that of the MV algorithm, especially for extremely low sampling rates and large control latencies. We also show that for moderate control latencies the MV algorithm with a temporal prediction step added to it approaches the performance of the KF technique.

Robustness study of the pseudo open-loop controller for multiconjugate adaptive optics.

Robustness of the recently proposed "pseudo open-loop control" algorithm against various system errors has been investigated for the representative example of the Gemini-South 8-m telescope multiconjugate adaptive-optics system. The existing model to represent the adaptive-optics system with pseudo open-loop control has been modified to account for misalignments, noise and calibration errors in deformable mirrors, and wave-front sensors. Comparison with the conventional least-squares control model has been done. We show with the aid of both transfer-function pole-placement analysis and Monte Carlo simulations that POLC remains remarkably stable and robust against very large levels of system errors and outperforms in this respect least-squares control. Approximate stability margins as well as performance metrics such as Strehl ratios and rms wave-front residuals averaged over a 1-arc min field of view have been computed for different types and levels of system errors to quantify the expected performance degradation.