The effects of a controller on the residual wavefront variance in an adaptive optics system can be represented by a
discrete-time system. Consequently, the controller design is optimized by the solution of a discrete-time Linear-
Quadratic-Gaussian (LQG) problem. This paper analyzes the structure of the LQG controller and the effects of varying
loop delay and actuator lag on the controller. The loop delay is represented as a delay of actuator commands to
emphasize the structure.
Specialized control structures can be used to reduce the computational burden of determining the control at each
frame. The parameters that define these controllers are chosen to maximize performance. The optimization of the
parameters is more efficient if gradient information is available. This paper presents the gradient calculation for an
arbitrarily parameterized controller of an adaptive optics system. The gradients are then specialized to modal gain and
proportional-plus-integral controllers.
Laser guide star (LGS) adaptive optics systems for extremely large telescopes must handle an important effect that is negligible for current generation telescopes. Wavefront errors, due to improperly focusing laser wavefront sensors (WFS) on the mesospheric sodium layer, are proportional to the square of the telescope diameter. The sodium layer, whose mean altitude is approximately 90 km, can move vertically at rates of up to a few metres per second; a few seconds lag in refocusing can substantially degrade delivered image quality (15 m of defocus can cause 120 nm residual wavefront error on a 30-m telescope.) As well, the range of temporal frequencies of sodium altitude focus, overlaps the temporal frequencies of focus caused by atmospheric turbulence. Only natural star wavefront sensors can disentangle this degeneracy. However, applying corrections with representative focus mechanisms having modest control bandwidths causes appreciable tracking errors. In principle, electronic offsets measured by natural guide star detectors could be rapidly applied to laser WFS measurements, but to provide useable sky coverage, integrating sufficient photons causes an unavoidable time delay, again resulting in potentially serious focus tracking errors. However, our analysis depends on extrapolating to temporal frequencies greater than 1 Hz from power spectra of sodium profile time series taken at 1-2 minute intervals. In principle, with a pulsed laser, (e.g. 3-μs pulses) and dynamic refocusing on a polar-coordinate CCD, this focus tracking error may be eliminated. This result is an additional benefit of dynamic refocusing beyond the commonly recognized amelioration of LGS WFS spot elongation.
KEYWORDS: Adaptive optics, Wavefronts, Feedback loops, Systems modeling, Analog electronics, Charge-coupled devices, Signal processing, Actuators, Lead, Process control
This paper presents an equivalent discrete-time model that combines the D-A converter, DM, and WFS. The
performance of the adaptive optics loop can then be evaluated in terms of the discrete-time (Z) closed-loop transfer
functions of the feedback loop. The closed-loop transfer functions using this discrete-time model are compared to those
obtained from an analog model. A simulation shows that the digital model produces accurate stability evaluations.
This paper presents a nonlinear modification of the standard linear adaptive optics controller that greatly reduces the startup lag due to saturation in pyramid wavefront sensors (or any wavefront sensor with 4-cell subapertures). Whenever the pyramid sensor is saturated (as determined by an internal model of the saturation in the controller), the deformable mirror signal is adjusted to quickly remove the saturation of the sensor. When the pyramid sensor is not saturated, a standard linear adaptive optics controller is used to generate the deformable mirror signal. The nonlinear controller is compared with a standard linear controller using a CAOS simulation. It is shown that the startup lag is significantly reduced, and that the steady-state performance is identical to the linear controller.
The W. M. Keck Observatory adaptive optics (AO) system uses the STRAP wavefront sensor to sense tip-tilt using a natural guidestar. The higher-order wavefront sensing can be done using light from either a laser guidestar (LGS) or a natural guidestar (NGS). The tip-tilt guidestar can be as bright as 10th or as faint as 19th magnitude. In both cases, as high a control bandwidth as possible is desired. Thus, it is of interest to determine the potential of various control algorithms over a wide range of signal-to-noise ratios (SNRs). This paper compares two control algorithms using a set of tip-tilt data taken with the STRAP wavefront sensor (a set of four avalanche diodes arranged as a quad cell). The two algorithms are the standard integral control and a minimum variance (LQG) control designed using the power spectral density (PSD) of the data. The bandwidths of the integral control and the minimum variance control are adjusted to produce the least RMS residual wavefront error. The controllers are compared for SNRs representative of the expected range of guidestars.
The performance of adaptive optics systems for existing as well as future giant telescopes heavily depends on the number of active wavefront compensating elements, the spatial, and the temporal sampling of the distorted incoming wavefront. In a phase-A study for an extreme adaptive optics system for the VLT (CHEOPS) as well as for LINC-NIRVANA a fizeau interferometer aboard LBT with a multi-conjugated adaptive optics system, we investigate how today's off-the-shelf computers compare in terms of floating point computing power, memory bandwidth, input/output bandwidth and real-time behavior. We address questions like how level three cache can impact the memory bandwidth, what matrix-vector multiplication performance is achievable, and what can we learn from standard benchmarks running on different architectures.
The calibration process for an adaptive optics system using modal control computes the reconstructor matrix in terms of a matrix whose columns are the measurements from a wavefront sensor. Each column of wavefront sensor measurements corresponds to a mode that is applied to the mirror. Since the measured gradients are corrupted by errors, the accuracy of the computed reconstructor is degraded by large condition numbers of the gradient matrix. A common method used to limit the condition number of this matrix is to reject all higher order modes when the condition number reaches the maximum desired value. However, it is possible (even likely) that one or a few modes are responsible for much of the increase in the condition number. By rejecting only those modes, an increased number of modes could be controlled. Unfortunately, computing the condition number of the gradient matrix for all possible combinations of modes is prohibitive.
This paper uses a genetic optimization algorithm to increase the number of modes that are retained for control. The genetic algorithm maximizes the number of modes retained. A bound on the condition number of the gradient matrix is imposed. The paper applies this method to both the ALFA adaptive optics system on Calar Alto (with 37 subapertures), and a proposed CHEOPS adaptive optics system with 1652 subapertures.
Adaptive optics systems that use a single guide star can only accomplish their best atmospheric correction over a small area. Layer oriented MCAO has been proposed for extremely large telescopes as a method to achieve adaptive optics correction over a larger field of view. Diolaiti et al have analyzed the stability and steady-state performance properties of layer oriented MCAO system with a number of (reasonable) simplifying assumptions: no loop delay; no mirror dynamics; continuous and position-independent control action; significantly faster adaptive optics loop than turbulence; and performance assessed by the static response of the closed loop system. This paper will use dynamic analyses to investigate the effects of these assumptions on the overall system performance and stability.
The Max-Planck institutes for astronomy and for extraterrestrial physics run a high order adaptive optics system with a laser guide star facility at the Calar Alto 3.5- m telescope in southern Spain. This system, called ALFA, saw first light in September 1996. Today, ALFA can compensate for atmospheric turbulences with natural guide stars as faint as 13.5th magnitude in R-band. ALFA recently succeeded in overcoming this limiting magnitude with the deployment of its laser guide star. This paper briefly reviews the ALFA project and its progress over the last 3 years. We further discuss the impact of sodium-layer laser guide stars on wavefront sensing and present results obtained with both kinds of guide stars.
The MPIA/MPE adaptive optics with a laser guide star system ALFA works excellent with natural guide stars up to 13th magnitude in R-band. Using fainter natural guide stars or the extended laser guide star, ALFA's performance does not entirely satisfy our expectations. We describe our efforts in optimizing the wavefront estimation process. Starting with a detailed system analysis, this paper will show how to construct a modal basis set which efficiently uses Shack- Hartmann measurements while keeping a certain number of low order modes close to analytical basis sets like Zernikes or Karhunen-Loeve functions. We will also introduce various phase estimators (least squares, weighted least squares, maximum a posteriori) and show how these can be applied to the ALFA AO. A first test done at the Calar Alto 3.5-m-telescope will be discussed.
Atmospheric turbulence over long horizontal paths perturbs phase in the pupil of an optical communications receiver, and also can cause severe intensity scintillations. We describe a real time wavefront compensation system using PC technology to perform all wavefront control tasks. This system uses a modal correction scheme, and we report the first measurements of residual wavefront taken approximately 1 meter above ground level at 1 km range. The effects of turbulence, scintillations and control bandwidth on the correction are all examined.
The Max-Planck-Institutes for Astronomy and for Extraterrestrial Physics (MPE) have recently installed a laser guide star (LGS) adaptive optics (AO) system at the 3.5m telescope on Calar Alto in Spain. The AO system consists of a Shack-Hartmann sensor, a deformable mirror with 97 actuators, and a wave-front processor that allows closed loop operations of up to 1200 Hz. As a first step we closed the high order AO loop on bright natural guide stars. As a second step we closed the AO loop ALFA's design, operation, and upgrade plans.
In this paper we characterize and illustrate Adaptive Optics Control system errors associated with sensor misregistration and present an approach to minimize them by employing nonlinear adaptive control methodologies. Furthermore, through the use of the Extended Kalman Filter methods, we determine if it is feasible that experimental data can be used to drive a complete multi-input multi-output dynamic model of the closed-loop adaptive optics system to estimate parameters directly related to stability margins. Finally, we review some results from an experimental verification of these theories. A closed loop adaptive optics breadboard is used to compare the observed effects of misregistration and other systematic error sources with the predictions of the models described above.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.