Super-resolution-enabled atmospheric tomography for astronomical multi-wavefront-sensor adaptive-optics systems

Recent work by Oberti et al, (Astron. Astrophys., 667, 48, 2022) argued and made a compelling case that classical astronomical adaptive optics (AO) tomography performance can be further enhanced by carefully designing and optically configuring the system to leverage inherent super-resolution (SR) capabilities. Our goal here is to further materialise the concept by providing the means to compute SR-enabling tomographic reconstructors for AO and showcase its broad uptake on soon every 10 m-class VIS/NIR telescopes and Giant Segmented Mirror Telescopes of up to 40 m in diameter. To that end we indicate the necessary tomography generalisations where we: (i) clarify how model-and-deploy is a generic methodological umbrella for linear minimum-mean-squared-error (LMMSE) tomographic reconstructors arising naturally from the solution of the tomographic inverse problem, thus unifying various solutions presented as distinct in the literature within a single framework, (ii) recall how such solutions are found as limiting cases of a model-based optimal control problem, thus elucidating how pseudo-open-loop control is a feature of the latter that allows LMMSE reconstructors to be adapted to closed-loop systems, (iii) review the two forms of the LMMSE tomographic reconstructors, highlighting the necessary adaptations to accommodate super-resolution, (iv) review the implementation in either dense-format vector-matrix-multiplication or sparse iterative forms and (v) discuss the implications for runtime and off-line real-time implementations, anticipating widespread adoption. We illustrate our examples with physical-optics numerical simulations for 10 m and 40 m-scale systems showing the performance benefits of super-resolution in the order of several tens of nm rms and the computational burden associated.