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Predictive Fourier control is a temporal power spectral density-based adaptive method for adaptive optics that predicts the atmosphere under the assumption of frozen flow. The predictive controller is based on Kalman filtering and a Fourier decomposition of atmospheric turbulence using the Fourier transform reconstructor. It provides a stable way to compensate for arbitrary numbers of atmospheric layers. For each Fourier mode, efficient and accurate algorithms estimate the necessary atmospheric parameters from closed-loop telemetry and determine the predictive filter, adjusting as conditions change. This prediction improves atmospheric rejection, leading to significant improvements in system performance. For a 48x48 actuator system operating at 2 kHz, five-layer prediction for all modes is achievable in under 2x10(9) floating-point operations/s.

Extensive results from the commissioning phase of PUEO, the adaptive optics instrument adaptor for the Canada-France-Hawaii telescope (CFHT), are presented and discussed. Analyses of more than 750 images recorded with a CCD and a near-IR camera on 16 nights in wavelengths from B to H are used to derive the properties of the compensated wavefront and images in a variety of conditions. The performance characteristics of the system are analyzed and presented in several ways, in terms of delivered Strehl ratios, full-width-half-maxima (FWHM), and quantities describing the improvements of both. A qualitative description is given of how the properties of the corrected images result from the structure function of the compensated phase. Under median seeing conditions, PUEO delivers essentially diffraction-limited images at H and K, images with FWHM∼0. ′′ 1 at J and I, and provides significant gains down to B, with guide stars as faint as R = 14. During good conditions, substantial gains were realized with guide stars as faint as R = 17. A simple user-interface and software which automatically and continuously optimizes the mode gains during observations makes the operational efficiency extremely high. A few astronomical examples are briefly discussed.

End-to-end simulation of adaptive optics (AO) systems allows high-fidelity modeling of system performance, but at the cost of long computation time. Analytical modeling, on the other hand, can provide much faster first-order performance estimates for a rapid exploration of the AO parameter space. In this paper, we present the foundations of a modeling method for the AO optical transfer function, based on an analytical description of the residual phase spatial power spectrum. The method has been implemented in an IDL-based code, PAOLA, and comparison with end-to-end simulations demonstrates the validity of the analytical approach.

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