## 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 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 $\sim 60\text{\hspace{0.17em}}\mathrm{nm}$ 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 $\lambda /D$ separations ($\sim 1-5\lambda /D$) for a 0 magnitude star and reaching close to one order of magnitude for a 12 magnitude star.

© 2017 Optical Society of America

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