Modelling astronomical adaptive optics performance with temporally-filtered Wiener reconstruction of slope data

Abstract

We build on a long-standing tradition in astronomical adaptive optics (AO) of specifying performance metrics and error budgets using linear systems modeling in the spatial-frequency domain. Our goal is to provide a comprehensive tool for the calculation of error budgets in terms of residual temporally filtered phase power spectral densities and variances. In addition, the fast simulation of AO-corrected point spread functions (PSFs) provided by this method can be used as inputs for simulations of science observations with next-generation instruments and telescopes, in particular to predict post-coronagraphic contrast improvements for planet finder systems. We extend the previous results and propose the synthesis of a distributed Kalman filter to mitigate both aniso-servo-lag and aliasing errors whilst minimizing the overall residual variance. We discuss applications to (i) analytic AO-corrected PSF modeling in the spatial-frequency domain, (ii) post-coronagraphic contrast enhancement, (iii) filter optimization for real-time wavefront reconstruction, and (iv) PSF reconstruction from system telemetry. Under perfect knowledge of wind velocities, we show that $\sim$60 nm rms error reduction can be achieved with the distributed Kalman filter embodying anti- aliasing reconstructors on 10 m class high-order AO systems, leading to contrast improvement factors of up to three orders of magnitude at few $\lambda /D$ separations ($\sim 1-5\lambda /D$) for a 0 magnitude star and reaching close to one order of magnitude for a 12 magnitude star.

15 pages, 8 figures

References in corpus (3)

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• Spatiotemporal statistics of the turbulent piston-removed phase and Zernike coefficients for two distinct beams
• The Mysterious Lives Of Speckles. I. Residual atmospheric speckle lifetimes in ground-based coronagraphs
• PEPITO: atmospheric Profiling from short-Exposure focalPlane Images in seeing-limiTed mOde
• LUVOIR-ECLIPS closed-loop adaptive optics performance and contrast predictions