Linear prediction of atmospheric wave-fronts for tomographic adaptive optics systems: modelling and robustness assessment

Abstract

We use a theoretical frame-work to analytically assess temporal prediction error functions on von-Kármán turbulence when a zonal representation of wave-fronts is assumed. Linear prediction models analysed include auto-regressive of order up to three, bilinear interpolation functions and a minimum mean square error predictor.This is an extension of the authors' previously published work [2] in which the efficacy of various temporal prediction models was established. Here we examine the tolerance of these algorithms to specific forms of model errors, thus defining the expected change in behaviour of the previous results under less ideal conditions. Results show that ±100% wind-speed error and ±50 deg are tolerable before the best linear predictor delivers poorer performance than the no-prediction case. Temporal prediction of the atmosphere is a much debated topic. The purpose of prediction is to reduce the error due to servo lag since the turbulence profile changes rapidly (on timescales of a few milliseconds) during the time that it takes to gather sensor information and to compute corrections.Unlike single-conjugated AO systems, in tomographic AO direct access to an estimate of the layered wavefront (WF) is provided at the end of the tomographic step. With turbulence estimated in a discrete number of layers, the frozen-flow approximation can now be called upon with a higher degree of fidelity [1].Temporal prediction is useful for both MultiConjugate AO (MCAO) and Multi-Object AO (MOAO) as a means to increase the sky-coverage [2, 3]. Allowing for greater integration times whilst compensating for the lag error by applying a predictive algorithm enables the system to guide on fainter sources [2]. Provided information on the dynamics of the atmospheric turbulence is available or can be construed, one should be able to obtain a more accurate estimate of the WF at the time a set of commands is applied to the deformable mirror (DM) and therefore improve performance. Lag errors are also considered a serious limitation in high-contrast imaging systems where the broadening of the PSF along * Corresponding author: katjac@uvic.ca the main axis of wind-blown turbulence severely limits contrast at small separations [4].In this letter we discuss alternatives for timeprogressing the atmospheric wave-fronts namely a nearMarkovian model, auto-regressive models and spatial shifting under frozen-flow [2, 5, 6]. The main goal of our work is to provide insight into the accuracy and robustness bounds of such models in view of a contemporary application to the Raven science and technology demonstrator installed on the Subaru Telescope [7].Under the hypothesis that the turbulent atmosphere is a sum of L thin layers located at a discrete number of different altitudes h l , the aperture-plane phase φ(ρ, θ, t) indexed by the bi-dimensional spatial coordinate vectorwhere ϕ l (ρ, t) is the l th -layer wave-front, ω l is the l th layer strength and H θ is a propagation operator in the near-field approximation that relates the aperture-plane ...

Speckle statistics in adaptive optics images at visible wavelengths

“…See for instance Refs. [17][18][19]. Very recently, the validity of this approach was demonstrated on sky.…”

Impact of time-variant turbulence behavior on prediction for adaptive optics systems

“…Predictive control to mitigate the effect of time delays in AO systems has been worked on for many years. Outside of HCI, predictive control has been studied to improve the performance of flux-limited laser guide star AO, increase sky coverage for natural guide stars [8], as well as many other AO applications. Linear prediction has been very successful for tip-tilt compensation, especially when induced by structural vibrations [9], using Linear Quadratic Gaussian control (LQG).…”

Speckle statistics in adaptive optics images at visible wavelengths

“…See for instance Refs. 17,18,19, to mention a few. Very recently, the validity of this approach has been demonstrated on-sky.…”