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An analytical expression is given for the minimum of the time-delay induced wavefront error (also known as the servo-lag error) in Adaptive Optics systems under temporal prediction filtering. The analysis is based on the von K\'arm\'an…
We present the details of predicting atmospheric turbulence by mining Zernike moment data obtained from simulations as well as experiments. Temporally correlated optical wave-fronts were simulated such that they followed Kolmogorov phase…
For high contrast imaging systems, the time delay is one of the major limiting factors for the performance of the extreme adaptive optics (AO) sub-system and, in turn, the final contrast. The time delay is due to the finite time needed to…
We use telemetry data from the Gemini North ALTAIR adaptive optics system to investigate how well the commands for wavefront correction (both Tip/Tilt and high-order turbulence) can be forecasted in order to reduce lag error (due to…
Atmospheric wavefront prediction based on previous wavefront sensor measurements can greatly enhance the performance of adaptive optics systems. We propose an optimal linear approach based on the Empirical Orthogonal Functions (EOF)…
For extremely large telescopes, adaptive optics will be required to correct the Earth's turbulent atmosphere. The performance of tomographic adaptive optics is strongly dependent on the vertical distribution (profile) of this turbulence. An…
Nullifying the servo bandwidth errors improves the strehl ratio by a substantial quantity in adaptive optics systems. An effective method for predicting atmospheric turbulence to reduce servo bandwidth errors in real time closed loop…
Forecast of optical turbulence and atmospheric parameters relevant for ground-based astronomy is becoming an important goal for telescope planning and AO instruments optimization in several major telescope. Such detailed and accurate…
The controllability of advection-diffusion systems, subject to uncertain initial values and emission rates, is estimated, given sparse and error affected observations of prognostic state variables. In predictive geophysical model systems,…
Latency in the control loop of adaptive optics (AO) systems can severely limit performance. Under the frozen flow hypothesis linear predictive control techniques can overcome this, however identification and tracking of relevant turbulent…
Servo lag errors in adaptive optics lead to inaccurate compensation of wavefront distortions. An attempt has been made to predict future wavefronts using data mining on wavefronts of the immediate past to reduce these errors. Monte Carlo…
The least squares linear filter, also called the Wiener filter, is a popular tool to predict the next element(s) of time series by linear combination of time-delayed observations. We consider observation sequences of deterministic dynamics,…
We address the problem of prediction for extreme observations by proposing an extremal linear prediction method. We construct an inner product space of nonnegative random variables derived from transformed-linear combinations of independent…
Time-delay error is a significant error source in adaptive optics (AO) systems. It arises from the latency between sensing the wavefront and applying the correction. Predictive control algorithms reduce the time-delay error, providing…
We look at a stochastic time-varying optimization problem and we formulate online algorithms to find and track its optimizers in expectation. The algorithms are derived from the intuition that standard prediction and correction steps can be…
Seeing-limited resolution in large telescopes working over wide wavelength range depends substantially on the turbulence outer scale and cannot be adequately described by one "seeing" value. We attempt to clarify frequent confusions on this…
As we look to the next generation of adaptive optics systems, now is the time to develop and explore the technologies that will allow us to image rocky Earth-like planets; wavefront control algorithms are not only a crucial component of…
Kalman filter is a key tool for time-series forecasting and analysis. We show that the dependence of a prediction of Kalman filter on the past is decaying exponentially, whenever the process noise is non-degenerate. Therefore, Kalman filter…
We consider the problem of estimating the slope parameter in circular functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of 1-periodic, second order stationary random functions X1,...,Xn. We consider an…
In tomographic adaptive-optics (AO) systems, errors due to tomographic wave-front reconstruction limit the performance and angular size of the scientific field of view (FoV), where AO correction is effective. We propose a multi time-step…