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.
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.
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.
The separation principle of optimal adaptive optics control is derived, and definitions of controllability and observability are introduced. An exact finite dimensional state space representation of the control system dynamics is obtained without the need for truncation in modes such as Zernikes. The uncertainty of sensing uncontrollable modes confuses present adaptive optics controllers. This uncertainty can be modeled by a Kalman filter. Reducing this uncertainty permits increased gain, increasing the Strehl, which is done by an optimal control law derived here. A general model of the atmosphere is considered, including boiling.
A main objective of adaptive optics is to maximize closed-loop Strehl, or, equivalently, minimize the statistical mean-square wavefront residual. Most currently implemented AO wavefront reconstructors and closed-loop control laws do not take into account either the correlation of the Kolmogorov wavefronts over time or the modified statistics of the residual wavefront in closed loop. There have been a number of attempts in the past to generate "predictive" controllers, which utilize wind speed and Cn2 profiles and incorporate one or two previous time steps. We present here a general framework for a dynamic controller/reconstructor design where the goal is to maximize mean closed-loop Strehl ratio over time using all previous data and exploiting the spatial-temporal statistics of the Kolmogorov turbulence and measurement noise.