Laboratory demonstration of the prediction of wind-blown turbulence by adaptive optics at 8 kHz with use of LQG control.

The low-latency adaptive optical mirror system (LLAMAS) is designed to push the limits on achievable latencies and frame rates. It has 21 subapertures across its pupil. A reformulated version of the linear quadratic Gaussian (LQG) method predictive Fourier control is implemented in LLAMAS; for all modes, it takes just 30 µs to compute. In the testbed, a turbulator mixes hot and ambient air to produce wind-blown turbulence. Wind prediction clearly improves correction when compared to an integral controller. Closed-loop telemetry shows that wind-predictive LQG removes the characteristic "butterfly" and reduces temporal error power by up to a factor of three for mid-spatial frequency modes. Strehl changes seen in focal plane images are consistent with telemetry and the system error budget.

Wavefront shaping with a Hadamard basis for scattering soil imaging.

Soil is a scattering medium that inhibits imaging of plant-microbial-mineral interactions that are essential to plant health and soil carbon sequestration. However, optical imaging in the complex medium of soil has been stymied by the seemingly intractable problems of scattering and contrast. Here, we develop a wavefront shaping method based on adaptive stochastic parallel gradient descent optimization with a Hadamard basis to focus light through soil mineral samples. Our approach allows a sparse representation of the wavefront with reduced dimensionality for the optimization. We further divide the used Hadamard basis set into subsets and optimize a certain subset at once. Simulation and experimental optimization results demonstrate our method has an approximately seven times higher convergence rate and overall better performance compared to that with optimizing all pixels at once. The proposed method can benefit other high-dimensional optimization problems in adaptive optics and wavefront shaping.

X-ray metrology and performance of a 45-cm long x-ray deformable mirror.

We describe experiments with a 45-cm long x-ray deformable mirror (XDM) that have been conducted in End Station 2, Beamline 5.3.1 at the Advanced Light Source. A detailed description of the hardware implementation is provided. We explain our one-dimensional Fresnel propagation code that correctly handles grazing incidence and includes a model of the XDM. This code is used to simulate and verify experimental results. Initial long trace profiler metrology of the XDM at 7.5 keV is presented. The ability to measure a large (150-nm amplitude) height change on the XDM is demonstrated. The results agree well with the simulated experiment at an error level of 1 µrad RMS. Direct imaging of the x-ray beam also shows the expected change in intensity profile at the detector.

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.

Computationally efficient autoregressive method for generating phase screens with frozen flow and turbulence in optical simulations.

We present a sample-based, autoregressive (AR) method for the generation and time evolution of atmospheric phase screens that is computationally efficient and uses a single parameter per Fourier mode to vary the power contained in the frozen flow and stochastic components. We address limitations of Fourier-based methods such as screen periodicity and low spatial frequency power content. Comparisons of adaptive optics (AO) simulator performance when fed AR phase screens and translating phase screens reveal significantly elevated residual closed-loop temporal power for small increases in added stochastic content at each time step, thus displaying the importance of properly modeling atmospheric "boiling". We present preliminary evidence that our model fits to AO telemetry are better reflections of real conditions than the pure frozen flow assumption.

Sub-nanometer flattening of 45 cm long, 45 actuator x-ray deformable mirror.

We have built a 45 cm long x-ray deformable mirror (XDM) of super-polished single-crystal silicon that has 45 actuators along the tangential axis. After assembly, the surface height error was 19 nm rms. With use of high-precision visible-light metrology and precise control algorithms, we have actuated the XDM and flattened its entire surface to 0.7 nm rms controllable figure error. This is, to our knowledge, the first sub-nanometer active flattening of a substrate longer than 15 cm.

Computer vision applications for coronagraphic optical alignment and image processing.

Modern coronagraphic systems require very precise alignment between optical components and can benefit greatly from automated image processing. We discuss three techniques commonly employed in the fields of computer vision and image analysis as applied to the Gemini Planet Imager, a new facility instrument for the Gemini South Observatory. We describe how feature extraction and clustering methods can be used to aid in automated system alignment tasks, and also present a search algorithm for finding regular features in science images used for calibration and data processing. Along with discussions of each technique, we present our specific implementation and show results of each one in operation.

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.

Laboratory demonstration of accurate and efficient nanometer-level wavefront control for extreme adaptive optics.

A 32 x 32 microelectricalmechanical systems mirror is controlled in a closed-loop adaptive optics test bed with a spatially filtered wavefront sensor (WFS), Fourier transform wavefront reconstruction, and calibration of references with a high-precision interferometer. When correcting the inherent aberration of the mirror, 0.7 nm rms phase error in the controllable band is achieved. When correcting an etched phase plate with atmospheric statistics, a dark hole 10(3) deeper than the uncontrollable phase is produced in the phase power spectral density. Compensation of the mirror's influence function is done with a Fourier filter, which results in improved loop convergence. Use of the spatial filter is shown to reduce the gain variability of the WFS in a quadcell configuration.

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.

Experimental demonstration of phase correction with a 32 x 32 microelectromechanical systems mirror and a spatially filtered wavefront sensor.

A 32 x 32 microelectromechanical systems deformable mirror is controlled in closed loop with a spatially filtered Shack-Hartmann wavefront sensor and a Fourier-transform wavefront reconstruction algorithm. A phase plate based on atmospheric turbulence statistics is used to generate a 1 microm peak-valley static phase aberration. Far-field images and direct phase measurements of the residual are used to compare performance with and without the spatial filter. Use of the spatial filter reduces error in the controllable band from 20 to 6 nm rms. Residual phase power is reduced by more than a factor of 5 for all spatial frequencies up to 0.85 x 1/2d, with a maximum attenuation factor of 37.

Optimal Fourier control performance and speckle behavior in high-contrast imaging with adaptive optics.

High-contrast imaging with adaptive optics (AO) for planet detection requires a sophisticated AO control system to provide the best possible performance. We evaluate the performance improvements in terms of residual error and point-spread function intensity provided by optimal Fourier control using detailed end-to-end simulation. Intensity, however, is not the final measure of system performance. We explore image contrast through analysis and simulation results, showing that speckles caused by atmospheric errors behave very differently in a temporal fashion from speckles caused by wavefront sensor noise errors.

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.

Spatially filtered wave-front sensor for high-order adaptive optics.

Adaptive optics (AO) systems take sampled measurements of the wave-front phase. Because in the general case the spatial-frequency content of the phase aberration is not band limited, aliasing will occur. This aliasing will cause increased residual error and increased scattered light in the point-spread function (PSF). The spatially filtered wave-front sensor (SFWFS) mitigates this phenomenon by using a field stop at a focal plane before the wave-front sensor. This stop acts as a low-pass filter on the phase, significantly reducing the high-spatial-frequency content phase seen by the wave-front sensor at moderate to high Strehl ratios. We study the properties and performance of the SFWFS for open- and closed-loop correction of atmospheric turbulence, segmented-primary-mirror errors, and sensing with broadband light. In closed loop the filter reduces high-spatial-frequency phase power by a factor of 10(3) to 10(8). In a full AO-system simulation, this translates to a reduction by up to 625 times in the residual error power due to aliasing over a specific spatial frequency range. The final PSF (generated with apodization of the pupil) has up to a 100 times reduction in intensity out to lambda/2d.

Scene-based Shack-Hartmann wave-front sensing: analysis and simulation.

In many situations it is not possible for an adaptive optics system to use a point source to measure the phase derivative, such as imaging along slant paths through the atmosphere and observation of the earth from space with a lightweight optic. Instead, small subimages of the observed scene can be used in a scene-based wave-front sensing technique. This study presents three important advances in the understanding of this technique. Rigorous analysis shows how slope estimation performance depends precisely on scene content and illumination. Scaling laws for changes in illumination are derived. The technique, when applied to point sources, is more robust to detect size changes and background levels than current methods.

Experimental validation of Fourier-transform wave-front reconstruction at the Palomar Observatory.

Wave-front reconstruction with use of the Fourier transform has been validated through theory and simulation. This method provides a dramatic reduction in computational costs for large adaptive (AO) systems. Because such a reconstructor can be expressed as a matrix, it can be used as an alternative in a matrix-based AO control system. This was done with the Palomar Observatory AO system on the 200-in. Hale telescope. Results of these tests indicate that Fourier-transform wave-front reconstruction works in a real system. For both bright and dim stars, a Hudgin-geometry Fourier-transform method produced performance comparable to that of the Palomar Adaptive Optics least squares. The Fried-geometry method had a noticeable Strehl ratio performance degradation of 0.043 in the K band (165-nm rms wave-front error added in quadrature) on a dim star.

Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform.

Wave-front reconstruction with the use of the fast Fourier transform (FFT) and spatial filtering is shown to be computationally tractable and sufficiently accurate for use in large Shack-Hartmann-based adaptive optics systems (up to at least 10,000 actuators). This method is significantly faster than, and can have noise propagation comparable with that of, traditional vector-matrix-multiply reconstructors. The boundary problem that prevented the accurate reconstruction of phase in circular apertures by means of square-grid Fourier transforms (FTs) is identified and solved. The methods are adapted for use on the Fried geometry. Detailed performance analysis of mean squared error and noise propagation for FT methods is presented with the use of both theory and simulation.