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The accurate calibration of the interaction matrix affects the performance of an adaptive optics system. In the case of high-order systems, when the number of mirror modes is worth a few thousands, the calibration strategy is critical to reach the maximum interaction matrix quality in the minimum time. This is all the more true for the future European Extremely Large Telescope. Here, we propose a novel calibration scheme, the Slope-Oriented Hadamard strategy. We then build a tractable interaction matrix quality criterion, and show that our method tends to optimize it. We demonstrate that for a given level of quality, the calibration time needed using the Slope-Oriented Hadamard method is seven times less than with a classical Hadamard scheme. These analytic and simulation results are confirmed experimentally on the SPHERE XAO system (SAXO).

Optimized calibration strategy for high order adaptive optics systems in closed-loop: the slope-oriented Hadamard actuation