The Slope-Oriented Hadamard scheme for in-lab or on-sky interaction matrix calibration

The correct 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 E-ELT, for which on sky calibration procedures have to be considered. Here, we first build a tractable interaction matrix quality criterion. We then propose the Slope-Oriented Hadamard scheme which optimizes this quality criterion.We demonstrate that for a given level of quality, the calibration time needed using the Slope-Oriented Hadamard method is ten times less than with a classical Hadamard scheme. These analytical and simulation results are confirmed experimentally on the SPHERE XAO system (SAXO).