Auto-calibration and performance monitoring of GRAVITY+ Adaptive Optics system with physics-based methods and inverse problem approaches

In 2024/2025, the GRAVITY+ Adaptive Optics (GPAO) project installed four extreme AO systems on the

8-meter UTs of the Very Large Telescope: 43x43 deformable mirrors (DM, 1432 actuators), 40x40 visible and

30x30 laser guide star Shack-Hartmann wavefront sensors (SH-WFS) with 9x9 infrared or 2x2 visible SH-WFSs

for low order sensing. These subsystems are distributed across the entire infrastructure (pupil in M2 rotating

with elevation ; DM in Coud´e train wobbling and rotating with azimuth ; WFSs fixed on the ground ; science

focal plane in the interferometric laboratory 150 meters away). GPAO’s complexity prefigures that of the AO

systems of future giant telescopes: numerous modes, many moving components, and the need to operate robustly

in a broad range of magnitudes and turbulence conditions. GPAO successfully achieved these goals thanks to a

complete re-design of the tools available in the Standard Platform for Adaptive optics Real Time Applications

(SPARTA, from ESO) and the development of new, versatile methods based on physical modelling and inverse

problem approaches. In this work we present the five main modules and their on-sky performances: (i) the Pseudo

Synthetic Interaction Matrix (PSIM) module, in charge to numerically (and quickly) compensate the system

rotation, which includes a physical model of the ALPAO DM influence functions, (ii) the innovative estimators

of WFS/DM lateral mis-registrations for the instrument bootstrapping through the turbulence in open loop

and its auto-alignment in closed loop, (iii) a robust spot monitor for faint star detection and centering during

the automatic acquisition sequence and for the update of the weighted center of gravity in closed loop, (iv) the

atmospheric and performance monitor made versatile to the different GPAO modes and augmented with an

innovative multi-layer profiler for wind estimation, and (v) a pupil monitor that offers a fine positioning of the

photometric pupil, its orientation and magnification.