Luke C. Johnson

Performance of MEMS-based visible-light adaptive optics at Lick Observatory: Closed- and open-loop control

At the University of Californias Lick Observatory, we have implemented an on-sky testbed for next-generation adaptive optics (AO) technologies. The Visible-Light Laser Guidestar Experiments instrument (ViLLaGEs) includes visible-light AO, a micro-electro-mechanical-systems (MEMS) deformable mirror, and open-loop control of said MEMS on the 1-meter Nickel telescope at Mt. Hamilton. (Open-loop in this sense refers to the MEMS being separated optically from the wavefront sensing path; the MEMS is still included in the control loop.) Future upgrades include predictive control with wind estimation and pyramid wavefront sensing. Our unique optical layout allows the wavefronts along the open- and closed-loop paths to be measured simultaneously, facilitating comparison between the two control methods. In this paper we evaluate the performance of ViLLaGEs in openand closed-loop control, finding that both control methods give equivalent Strehl ratios of up to ~ 7% in I-band and similar rejection of temporal power. Therefore, we find that open-loop control of MEMS on-sky is as effective as closed-loop control. Furthermore, after operating the system for three years, we find MEMS technology to function well in the observatory environment. We construct an error budget for the system, accounting for 130 nm of wavefront error out of 190 nm error in the science-camera PSFs. We find that the dominant known term is internal static error, and that the known contributions to the error budget from open-loop control (MEMS model, position repeatability, hysteresis, and WFS linearity) are negligible.

Bulk wind estimation and prediction for adaptive optics control systems

We present a wind-predictive controller for astronomical adaptive optics (AO) systems that is able to predict the motion of a single windblown layer in the presence of other, more slowly varying phase aberrations. This controller relies on fast, gradient-based optical flow estimation to identify the velocity of the translating layer and a recursive mean estimator to account for turbulence that varies on a time scale much slower than the operating speed of the AO loop. We derive the Cramer-Rao lower bound for the wind estimation problem and show that the proposed estimator is very close to achieving theoretical minimum-variance performance. We also present simulations using on-sky data that show significant Strehl increases from using this controller in realistic atmospheric conditions.

Wind estimation and prediction for adaptive optics control systems

Performance of adaptive optics (AO) systems is limited by the tradeoff between photon noise at the wavefront sensor and temporal error from the duty cycle of the controller. Optimal control studies have shown that this temporal error can be reduced by predicting the turbulence evolution during the control cycle. We formulate a wind model that divides the wind into two components: a quasi-static layer and a wind-driven frozen-flow layer. Using this internal wind model, we design a computationally efficient controller that is able to estimate and predict the dynamics of a single windblown layer and simulate this controller using on-sky data from the Palomar Adaptive Optics system. We also present results from a laboratory implementation of multi-conjugate AO (MCAO) with multi-layer wind estimation in conjunction with tomographic reconstruction. The tomography engine breaks the atmosphere into discrete layers, each with its own wind estimator. The resulting MCAO control algorithm is able to track and predict the motion of multiple wind layers with wind estimates that update at every controller cycle. Once the wind velocities of each layer are known, the deformable mirror update speed is no longer limited by the wavefront sensor exposure time so it is possible to send multiple correction updates to the deformable mirror each control cycle in order to dynamically track wind layers across the telescope aperture. The result is better dynamics in the feedback control system that enables higher closed-loop bandwidth for a given wavefront sensor frame rate.

A Fix-Up for the EKF Parameter Estimator

Abstract We have reduced recursive parameter estimation to Kalman filtering, with a few added fixes. By incorporating projections in the parameter gain updates and parameter variance estimates, the recursive maximum likelihood method asymptotically becomes a reformulation and fix-up of the extended Kalman filter used as a parameter estimator (EKFPE), except that an additional n x n linear symmetric matrix must also be updated for each parameter estimate. Estimates for both the process and measurement noise variances, as well as for structural parameters, have been proven globally convergent to a local maximum of the likelihood function. This obviates the usual guesswork in finding noise variances when fitting data using the EKFPE, and assures the existence of the innovations representation for the recursive maximum likelihood method. Slightly non-linear and also slightly unstable linear, as well as drastically time-varying stable linear, system parameters can be estimated even in severe noise environments On average, the rate of convergence of parameter estimates appears to be faster than other methods if no projection limit is hit.

Solar adaptive optics with the DKIST: status report

The DKIST wavefront correction system will be an integral part of the telescope, providing active alignment control, wavefront correction, and jitter compensation to all DKIST instruments. The wavefront correction system will operate in four observing modes, diffraction-limited, seeing-limited on-disk, seeing-limited coronal, and limb occulting with image stabilization. Wavefront correction for DKIST includes two major components: active optics to correct low-order wavefront and alignment errors, and adaptive optics to correct wavefront errors and high-frequency jitter caused by atmospheric turbulence. The adaptive optics system is built around a fast tip-tilt mirror and a 1600 actuator deformable mirror, both of which are controlled by an FPGA-based real-time system running at 2 kHz. It is designed to achieve on-axis Strehl of 0.3 at 500 nm in median seeing (r0 = 7 cm) and Strehl of 0.6 at 630 nm in excellent seeing (r0 = 20 cm). We present the current status of the DKIST high-order adaptive optics, focusing on system design, hardware procurements, and error budget management.

Evidence that wind prediction with multiple guide stars reduces tomographic errors and expands MOAO field of regard

We explore the extension of predictive control techniques to multi-guide star, multi-layer tomographic wavefront measurement systems using a shift-and-average correction scheme that incorporates wind velocity and direction. In addition to reducing temporal error budget terms, there are potentially additional benefits for tomographic AO systems; the combination of wind velocity information and phase height information from multiple guide stars breaks inherent degeneracies in volumetric tomographic reconstruction, producing a reduction in the geometric tomographic error. In a tomographic simulation of an 8-meter telescope with 3 laser guide stars over 2 arcminute diameter, we find that tracking organized wind motion as it flows into metapupil regions sampled by only one guide star improves layer estimates beyond the guide star radius, allowing for an expansion of the field of view. For this case, we demonstrate improvement of layer phase estimates of 3% to 12%, translating into potential gains in the MOAO field of regard area of up to 40%. The majority of the benefits occur in regions of the metapupil sampled by only 1-2 LGSs downwind at high altitudes.

Adaptive optics control of wind blown turbulence via translation and prediction

In the case where wind blown turbulence is mostly adhering to frozen flow conditions the use of the Kalman Filter in an adaptive optics controller is of interest because it incorporates prior the time history of wavefront measurements as additional information to be combined with the immediate measurement of the wavefront. In prior work we have shown that indeed there is a signal to noise advantage, however the extra real-time overhead of the Kalman Filter computations can become prohibitive for larger aperture systems. In this paper we investigate a Fourier domain implementation that might approximate, and gain the advantages of, the Kalman Filter while being feasible to implement in real time control computers. Most of the advantage of using the Kalman Filter comes from its ability to predict the wind blown turbulence for the next measurement step. For the photonic and instrumentation noise levels commonly found in astronomical AO systems, we find that most of the Strehl gain is achieved by simply translating the wavefront estimate the incremental distance.

Status of the DKIST system for solar adaptive optics

When the Daniel K. Inouye Solar Telescope (DKIST) achieves first light in 2019, it will deliver the highest spatial resolution images of the solar atmosphere ever recorded. Additionally, the DKIST will observe the Sun with unprecedented polarimetric sensitivity and spectral resolution, spurring a leap forward in our understanding of the physical processes occurring on the Sun. The DKIST wavefront correction system will provide active alignment control and jitter compensation for all six of the DKIST science instruments. Five of the instruments will also be fed by a conventional adaptive optics (AO) system, which corrects for high frequency jitter and atmospheric wavefront disturbances. The AO system is built around an extended-source correlating Shack-Hartmann wavefront sensor, a Physik Instrumente fast tip-tilt mirror (FTTM) and a Xinetics 1600-actuator deformable mirror (DM), which are controlled by an FPGA-based real-time system running at 1975 Hz. It is designed to achieve on-axis Strehl of 0.3 at 500 nm in median seeing (r0 = 7 cm) and Strehl of 0.6 at 630 nm in excellent seeing (r0 = 20 cm). The DKIST wavefront correction team has completed the design phase and is well into the fabrication phase. The FTTM and DM have both been delivered to the DKIST laboratory in Boulder, CO. The real-time controller has been completed and is able to read out the camera and deliver commands to the DM with a total latency of approximately 750 μs. All optics and optomechanics, including many high-precision custom optics, mounts, and stages, are completed or nearing the end of the fabrication process and will soon undergo rigorous acceptance testing. Before installing the wavefront correction system at the telescope, it will be assembled as a testbed in the laboratory. In the lab, performance tests beginning with component-level testing and continuing to full system testing will ensure that the wavefront correction system meets all performance requirements. Further work in the lab will focus on fine-tuning our alignment and calibration procedures so that installation and alignment on the summit will proceed as efficiently as possible.

Online wind estimation and prediction for a two-layer frozen flow atmosphere

We present a method for online estimation and prediction of wavefront distortions caused by two independent layers of frozen flow turbulence. The key to this algorithm is a fast, gradient-based estimator that uses optical flow techniques to extract the bulk velocity vectors of the two wind layers from three consecutive measurements of their combined wavefront. Once these velocity vectors are known, the phase aberrations resulting from the two-layer atmosphere can be predicted at any future time using a linear combination of shifted wavefronts. This allows calculation of a deformable mirror correction that compensates for the time delay errors in the control loop. Predictive control will be especially beneficial for visible light and high-contrast astronomical adaptive optics as well as for any adaptive optics system whose performance suffers due to time delay errors. A multilayer approach to predictive control is necessary since most observing sites have multi-layer atmospheres. The spatial domain method that we present is attractive because it uses all spatial frequency components of the wavefront simultaneously to find a global wind model. Its ability to update the wind velocity estimate at each control cycle makes it sensitive to changes in the wind on the order of tens of milliseconds. Our simulations show a potential Strehl increase from 0.45 to 0.65 for visible-light adaptive optics in low-noise, moderate-wind conditions with two frozen-flow wind layers and a strong static layer.

Laboratory integration of the DKIST wavefront correction system

The Wavefront Correction (WFC) system for the Daniel K. Inouye Solar Telescope (DKIST) is in its final stages of laboratory integration. All optical, mechanical, and software components have been unit tested and installed and aligned in our laboratory testbed in Boulder, CO. We will verify all aspects of WFC system performance in the laboratory before disassembling and shipping it to Maui for final integration with the DKIST in early 2019. The DKIST Adaptive Optics (AO) system contains a 1600-actuator deformable mirror, a correlating Shack- Hartmann wavefront sensor, a fast tip-tilt mirror, and an FPGA-based control system. Running at a nominal rate of 1975 Hz, the AO system will deliver diffraction-limited images to five of the DKIST science instruments simultaneously. The DKIST AO system is designed to achieve the diffraction limit (on-axis Strehl > 0.3) at wavelengths up to 500 nm in median daytime seeing (r0 = 7 cm). In addition to AO for diffraction-limited observing, the DKIST WFC system has a low-order wavefront sensor for sensing quasi-static wavefront errors, a context viewer for telescope pointing and image quality assessment, and an active optics engine. The active optics engine uses inputs from the low-order wavefront sensor and the AO system to actively correct for telescope misalignment. All routine alignment and calibration procedures are automated via motorized stages that can be controlled from Python scripts. We present the current state of the WFC system as we prepare for final integration with the DKIST, including verification test design, system performance metrics, and laboratory test data.