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

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. A31, 2763 (2014)JOAOD60740-323210.1364/JOSAA.31.002763] to the closed-loop case with predictive controllers and generalize the analytical modeling of Rigaut et al. [Proc. SPIE3353, 1038 (1998)PSISDG0277-786X10.1117/12.321649], Flicker [Technical Report (W. M. Keck Observatory, 2007)], and Jolissaint [J. Eur. Opt. Soc.5, 10055 (2010)1990-257310.2971/jeos.2010.10055]. We follow closely the developments of Ellerbroek [J. Opt. Soc. Am. A22, 310 (2005)JOAOD60740-323210.1364/JOSAA.22.000310] 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 ∼60  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 λ/D separations (∼1-5λ/D) for a 0 magnitude star and reaching close to one order of magnitude for a 12 magnitude star.