Static and predictive tomographic reconstruction for wide-field multi-object adaptive optics systems

Abstract

Multi-object adaptive optics (MOAO) systems are still in their infancy: their complex optical designs for tomographic, wide-field wavefront sensing, coupled with open-loop (OL) correction, make their calibration a challenge. The correction of a discrete number of specific directions in the field allows for streamlined application of a general class of spatio-angular algorithms, initially proposed in Whiteley et al. [J. Opt. Soc. Am. A15, 2097 (1998)], which is compatible with partial on-line calibration. The recent Learn & Apply algorithm from Vidal et al. [J. Opt. Soc. Am. A27, A253 (2010)] can then be reinterpreted in a broader framework of tomographic algorithms and is shown to be a special case that exploits the particulars of OL and aperture-plane phase conjugation. An extension to embed a temporal prediction step to tackle sky-coverage limitations is discussed. The trade-off between lengthening the camera integration period, therefore increasing system lag error, and the resulting improvement in SNR can be shifted to higher guide-star magnitudes by introducing temporal prediction. The derivation of the optimal predictor and a comparison to suboptimal autoregressive models is provided using temporal structure functions. It is shown using end-to-end simulations of Raven, the MOAO science, and technology demonstrator for the 8 m Subaru telescope that prediction allows by itself the use of 1-magnitude-fainter guide stars.

Multi time-step wavefront reconstruction for tomographic adaptive-optics systems

“…where ϕ is a column vector of distorted phase values on a discrete grid of points on the telescope aperture, φ i (t) is a column vector of a phase distortion on a discrete grid on the i-th turbulence layers at time t, φ(t) = [φ T 1 (t) · · · φ T N l (t)] T , P i θ is a raytracing submatrix which extracts a phase distortion within a footprint of a GS optical path in the direction θ on the i-th atmospheric turbulence by using a bilinear interpolation, and P θ is a concatenation of all submatrices P i θ . In MOAO systems, a tomographic reconstructor is determined to minimize the aperture-plane phase variance for each science direction θ k [10],…”

“…The idea to use wind information for the WFAO control is studied for predictive control, which reduces the lag error resulting from the change of the atmospheric turbulence during the exposure time of the WFS and the computation time for AO corrections [10,11]. These predictive controllers allow the use of longer integration times of the WFS and/or real-time processing, and therefore result in an increased limiting magnitude of GSs and improved sky-coverage.…”

Natural guide-star processing for wide-field laser-assisted AO systems

“…To estimate the tilt in the science direction of interest we consider the following options 1. Tilt tomography with spatio-angular reconstruction 2,16 Since for LTAO only pupil-plane tilt is required (no fitting on multiple DMs) we use a simplified measurement model involving the pupil-plane turbulence only…”

Fast iterative tomographic wavefront estimation with recursive Toeplitz reconstructor structure for large-scale systems

“…More recently, for some classes of AO systems not requiring multi-conjugation, it has been noted that the MMSE reconstruction can be further simplified if we skip the explicit estimation of the 3D wave-front profiles to estimate instead the pupil-plane wave-front in the directions of interest only [7][8][9][10] (hereinafter, referred to as spatio-angular WFR), which is suitable for multiobject AO (MOAO), laser-tomography AO (LTAO) and optionally ground-layer AO (GLAO) systems. The spatio-angular WFR doesn't require any approximation and thus can provide more accurate estimation than the sparse reconstructor.…”