Performance of the Gemini Planet Imager's adaptive optics system.

The Gemini Planet Imager's adaptive optics (AO) subsystem was designed specifically to facilitate high-contrast imaging. A definitive description of the system's algorithms and technologies as built is given. 564 AO telemetry measurements from the Gemini Planet Imager Exoplanet Survey campaign are analyzed. The modal gain optimizer tracks changes in atmospheric conditions. Science observations show that image quality can be improved with the use of both the spatially filtered wavefront sensor and linear-quadratic-Gaussian control of vibration. The error budget indicates that for all targets and atmospheric conditions AO bandwidth error is the largest term.

Spatio-angular minimum-variance tomographic controller for multi-object adaptive-optics systems.

Multi-object astronomical adaptive optics (MOAO) is now a mature wide-field observation mode to enlarge the adaptive-optics-corrected field in a few specific locations over tens of arcminutes. The work-scope provided by open-loop tomography and pupil conjugation is amenable to a spatio-angular linear-quadratic-Gaussian (SA-LQG) formulation aiming to provide enhanced correction across the field with improved performance over static reconstruction methods and less stringent computational complexity scaling laws. Starting from our previous work [J. Opt. Soc. Am. A31, 101 (2014)10.1364/JOSAA.31.000101JOAOD61084-7529], we use stochastic time-progression models coupled to approximate sparse measurement operators to outline a suitable SA-LQG formulation capable of delivering near optimal correction. Under the spatio-angular framework the wavefronts are never explicitly estimated in the volume, providing considerable computational savings on 10-m-class telescopes and beyond. We find that for Raven, a 10-m-class MOAO system with two science channels, the SA-LQG improves the limiting magnitude by two stellar magnitudes when both the Strehl ratio and the ensquared energy are used as figures of merit. The sky coverage is therefore improved by a factor of ~5.

Increased sky coverage with optimal correction of tilt and tilt-anisoplanatism modes in laser-guide-star multiconjugate adaptive optics.

Laser-guide-star multiconjugate adaptive optics (MCAO) systems require natural guide stars (NGS) to measure tilt and tilt-anisoplanatism modes. Making optimal use of the limited number of photons coming from such, generally dim, sources is mandatory to obtain reasonable sky coverage, i.e., the probability of finding asterisms amenable to NGS wavefront (WF) sensing for a predefined WF error budget. This paper presents a Strehl-optimal (minimum residual variance) spatiotemporal reconstructor merging principles of modal atmospheric tomography and optimal stochastic control theory. Simulations of NFIRAOS, the first light MCAO system for the thirty-meter telescope, using ~500 typical NGS asterisms, show that the minimum-variance (MV) controller delivers outstanding results, in particular for cases with relatively dim stars (down to magnitude 22 in the H-band), for which low-temporal frame rates (as low as 16 Hz) are required to integrate enough flux. Over all the cases tested ~21 nm rms median improvement in WF error can be achieved with the MV compared to the current baseline, a type-II controller based on a double integrator. This means that for a given level of tolerable residual WF error, the sky coverage is increased by roughly 10%, a quite significant figure. The improvement goes up to more than 20% when compared with a traditional single-integrator controller.

Simulation model based approach for long exposure atmospheric point spread function reconstruction for laser guide star multiconjugate adaptive optics.

This paper discusses an innovative simulation model based approach for long exposure atmospheric point spread function (PSF) reconstruction in the context of laser guide star (LGS) multiconjugate adaptive optics (MCAO). The approach is inspired from the classical scheme developed by Véran et al. [J. Opt. Soc. Am. A14, 3057 (1997)] and Flicker et al. [Astron. Astrophys.400, 1199 (2003)] and reconstructs the long exposure optical transfer function (OTF), i.e., the Fourier transformed PSF, as a product of separate long-exposure tip/tilt removed and tip/tilt OTFs, each estimated by postprocessing system and simulation telemetry data. Sample enclosed energy results assessing reconstruction accuracy are presented for the Thirty Meter Telescope LGS MCAO system currently under design and show that percent level absolute and differential photometry over a 30 arcsec diameter field of view are achievable provided the simulation model faithfully represents the real system.

Woofer-tweeter temporal correctors split in atmospheric adaptive optics.

Many adaptive optics applications require wavefront corrections with a high stroke, and at a high bandwidth. Often, these two requirements cannot be met by a single wavefront corrector, and, instead, the combination of a low-bandwidth, high-stroke woofer and a high-bandwidth low-stroke tweeter is used in a so-called woofer-tweeter architecture. The optimal (minimum residual phase variance) way to split the correction between the woofer and the tweeter in the context of a linear-quadratic-Gaussian (LQG) controller has been addressed previously. However, the necessity to fold the temporal characteristics of the woofer and tweeter into the LQG controller significantly increases its complexity. In this Letter, this optimal strategy is compared to a simpler, ad hoc approach, which consists in optimizing the LQG controller as if it were controlling a high-bandwidth, high-stroke corrector and splitting the correction using first-order high- and low-pass temporal filters. In the case of tilt correction for NFIRAOS on the Thirty Meter Telescope, it is found that the ad hoc approach, which is already used or planned for several systems, holds the same overall correction performance compared to the optimal strategy.

Advanced vibration suppression algorithms in adaptive optics systems.

Vibration suppression in astronomical adaptive optics (AO) systems has gathered great attention in the context of next-generation instrumentation for current telescopes and future Extremely Large Telescopes. Laser tomographic AO systems require natural guide stars to measure the low-order modes such as tip-tilt (TT) and TT-anisoplanatism. To increase the sky coverage, the guide stars are often faint, thus requiring lower temporal sampling frequencies to work on a more favorable signal-to-noise regime. Such sampling frequencies can be of the order of, or even lower than, the range of frequencies where vibrations are likely to appear. Ideally, vibrations affecting the low-order modes could be corrected at the higher laser loop frame rate using an upsampling procedure. This paper compares the most relevant solutions proposed hitherto to a novel multirate algorithm using the linear-quadratic-Gaussian (LQG) approach capable of upsampling the correction to further reduce the impact of vibrations. Results from numerical Monte Carlo simulations span a large range of parameters from pure sinusoids to relatively broad peak vibrations, covering the likely-to-be signals in a realistic AO system. The improvement is shown at sampling frequencies from 20 to 800 Hz, including below the vibration itself, in the example of 29.5 Hz on a Thirty Meter Telescope-like scenario. The multirate LQG ensures the least residual for both faint and bright stars for all the peak widths considered based on telemetry from the Keck Observatory.

Kalman filtering to suppress spurious signals in adaptive optics control.

In many scenarios, an adaptive optics (AO) control system operates in the presence of temporally non-white noise. We use a Kalman filter with a state space formulation that allows suppression of this colored noise, hence improving residual error over the case where the noise is assumed to be white. We demonstrate the effectiveness of this new filter in the case of the estimated Gemini Planet Imager tip-tilt environment, where there are both common-path and non-common-path vibrations. We discuss how this same framework can also be used to suppress spatial aliasing during predictive wavefront control assuming frozen flow in a low-order AO system without a spatially filtered wavefront sensor, and present experimental measurements from Altair that clearly reveal these aliased components.

High fidelity sky coverage analysis via time domain adaptive optics simulations.

We describe a high fidelity simulation method for estimating the sky coverage of multiconjugate adaptive optics systems; this method is based upon the split tomography control architecture, and employs an AO simulation postprocessing technique to evaluate system performance with hundreds of randomly generated natural guide star (NGS) asterisms. A novel technique to model the impact of quadratic wavefront aberrations upon the NGS point spread functions is described; this is used to model the variations in system performance with different asterisms, and is crucial for obtaining accurate results with the postprocessing technique. Several design and algorithm improvements help to reduce the residual wavefront error in the tip/tilt and plate scale modes that are controlled using the NGS asterism. These improvements include choosing the right wavefront sensor (WFS) pixel size, optimal pixel weights, and type II control of the plate scale modes.

Experimental verification of the frozen flow atmospheric turbulence assumption with use of astronomical adaptive optics telemetry.

We use closed-loop deformable mirror telemetry from Altair and Keck adaptive optics (AO) to determine whether atmospheric turbulence follows the frozen flow hypothesis. Using telemetry from AO systems, our algorithms (based on the predictive Fourier control framework) detect frozen flow >94% of the time. Usually one to three layers are detected. Between 20% and 40% of the total controllable phase power is due to frozen flow. Velocity vector RMS variability is less than 0.5 m/s (per axis) on 10-s intervals, indicating that the atmosphere is stable enough for predictive control to measure and adapt to prevailing atmospheric conditions before they change.

Calibration and testing with real turbulence of a pyramid sensor employing static modulation.

The pyramid sensor (PS) is an interesting alternative to the Shack-Hartmann wavefront sensor (SH WFS) for astronomical Adaptive Optics (AO) because of its potential advantages in sensitivity and applicability to novel wavefront sensing schemes. The PS uses a pyramidal prism to perform a knife-edge test in two dimensions simultaneously and relies on modulating the position of the prism to increase the linear dynamic range. It has been suggested that this could also be accomplished by a static diffusing element. We test this idea and show that the diffuser produces a modulation effect. We compare the results of our PS to a SH WFS measuring spatial and temporal properties of real turbulence produced in the lab with a hot-air turbulence generator.

Woofer-tweeter control in an adaptive optics system using a Fourier reconstructor.

Future adaptive optics systems seeking a higher degree of correction may need to split the command between two deformable mirrors (DMs), the woofer and the tweeter. We first present a method to specify the order of correction of the woofer DM for a given tweeter stroke requirement using an analytical and Monte Carlo approach. We then develop a computationally efficient algorithm to split the command between the two DMs in the case where a Fourier reconstructor is used. We find that the computational efficiency can be dramatically improved by splitting the command in Fourier space and by sending to the woofer only the modes it can reproduce accurately.

Predictive wavefront control for adaptive optics with arbitrary control loop delays.

We present a modification of the closed-loop state space model for adaptive optics control that allows delays that are a noninteger multiple of the system frame rate. We derive the new forms of the predictive Fourier control Kalman filters for arbitrary delays and show that they are linear combinations of the whole-frame delay terms. This structure of the controller is independent of the delay. System stability margins and residual error variance both transition gracefully between integer-frame delays.

Fourier transform wavefront control with adaptive prediction of the atmosphere.

Predictive Fourier control is a temporal power spectral density-based adaptive method for adaptive optics that predicts the atmosphere under the assumption of frozen flow. The predictive controller is based on Kalman filtering and a Fourier decomposition of atmospheric turbulence using the Fourier transform reconstructor. It provides a stable way to compensate for arbitrary numbers of atmospheric layers. For each Fourier mode, efficient and accurate algorithms estimate the necessary atmospheric parameters from closed-loop telemetry and determine the predictive filter, adjusting as conditions change. This prediction improves atmospheric rejection, leading to significant improvements in system performance. For a 48x48 actuator system operating at 2 kHz, five-layer prediction for all modes is achievable in under 2x10(9) floating-point operations/s.

Adaptive optics sky coverage modeling for extremely large telescopes.

A Monte Carlo sky coverage model for laser guide star adaptive optics systems was proposed by Clare and Ellerbroek [J. Opt. Soc. Am. A 23, 418 (2006)]. We refine the model to include (i) natural guide star (NGS) statistics using published star count models, (ii) noise on the NGS measurements, (iii) the effect of telescope wind shake, (iv) a model for how the Strehl and hence NGS wavefront sensor measurement noise varies across the field, (v) the focus error due to imperfectly tracking the range to the sodium layer, (vi) the mechanical bandwidths of the tip-tilt (TT) stage and deformable mirror actuators, and (vii) temporal filtering of the NGS measurements to balance errors due to noise and servo lag. From this model, we are able to generate a TT error budget for the Thirty Meter Telescope facility narrow-field infrared adaptive optics system (NFIRAOS) and perform several design trade studies. With the current NFIRAOS design, the median TT error at the galactic pole with median seeing is calculated to be 65 nm or 1.8 mas rms.

Analytical modeling of adaptive optics: foundations of the phase spatial power spectrum approach.

End-to-end simulation of adaptive optics (AO) systems allows high-fidelity modeling of system performance, but at the cost of long computation time. Analytical modeling, on the other hand, can provide much faster first-order performance estimates for a rapid exploration of the AO parameter space. In this paper, we present the foundations of a modeling method for the AO optical transfer function, based on an analytical description of the residual phase spatial power spectrum. The method has been implemented in an IDL-based code, PAOLA, and comparison with end-to-end simulations demonstrates the validity of the analytical approach.

Optimal modal fourier-transform wavefront control.

Optimal modal Fourier-transform wavefront control combines the speed of Fourier-transform reconstruction (FTR) with real-time optimization of modal gains to form a fast, adaptive wavefront control scheme. Our modal basis is the real Fourier basis, which allows direct control of specific regions of the point-spread function. We formulate FTR as modal control and show how to measure custom filters. Because the Fourier basis is a tight frame, we can use it on a circular aperture for modal control even though it is not an orthonormal basis. The modal coefficients are available during reconstruction, greatly reducing computational overhead for gain optimization. Simulation results show significant improvements in performance in low-signal-to-noise-ratio situations compared with nonadaptive control. This scheme is computationally efficient enough to be implemented with off-the-shelf technology for a 2.5 kHz, 64 x 64 adaptive optics system.