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 presented in Correia and Teixeira [J. Opt. Soc. Am. A 31, 2763 (2014) [CrossRef] ] to the closed-loop case with predictive controllers and generalize the analytical modeling of Rigaut et al. [Proc. SPIE 3353, 1038 (1998) [CrossRef] ], Flicker [Technical Report (W. M. Keck Observatory, 2007)], and Jolissaint [J. Eur. Opt. Soc. 5, 10055 (2010) [CrossRef] ]. We follow closely the developments of Ellerbroek [J. Opt. Soc. Am. A 22, 310 (2005) [CrossRef] ] and propose the synthesis of a distributed Kalman filter to mitigate both aniso-servo-lag and aliasing errors while 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 rms error reduction can be achieved with the distributed Kalman filter embodying antialiasing reconstructors on 10 m class high-order AO systems, leading to contrast improvement factors of up to three orders of magnitude at few separations () for a 0 magnitude star and reaching close to one order of magnitude for a 12 magnitude star.
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