Anti-aliasing Wiener filtering for wave-front reconstruction in the spatial-frequency domain for high-order astronomical adaptive-optics systems

摘要

Computationally-efficient wave-front reconstruction techniques forastronomical adaptive optics systems have seen a great development in the pastdecade. Algorithms developed in the spatial-frequency (Fourier) domain havegathered large attention specially for high-contrast imaging systems. In this paper we present the Wiener filter (resulting in the maximization ofthe Strehl-ratio) and further develop formulae for the anti-aliasing Wienerfilter that optimally takes into account high-order wave-front terms foldedin-band during the sensing (i.e. discrete sampling) process. We employ a continuous spatial-frequency representation for the forwardmeasurement operators and derive the Wiener filter when aliasing is explicitlytaken into account. We further investigate and compare to classical estimatesusing least-squares filters the reconstructed wave-front, measurement noise andaliasing propagation coefficients as a function of the system order. Regardinghigh-contrast systems, we provide achievable performance results as a functionof an ensemble of for ward models for the Shack-Hartmann wave-front sensor(using sparse and non-sparse representations) and compute point-spread functionraw intensities. We find that for a 32x32 single-conjugated adaptive optics system thealiasing propagation coefficient is roughly 60% of the least-squares filterswhereas the noise propagation is around 80%. Contrast improvements of factorsof up to 2 are achievable across the field in H-band. For current and nextgeneration high-contrast imagers, despite better aliasing mitigation,anti-aliasing Wiener filtering cannot be used as a stand-alone method and musttherefore be used in combination with optical spatial filters deployed beforeimage formation takes actual place.