High SNR measurement of interaction matrix on-sky and in lab

The fundamental task of AO system calibration is the acquisition of the Interaction Matrix (IM). This task is usually performed in a laboratory or at the telescope using a reference fiber illuminating both deformable mirror and wavefront sensor. The problem of measuring the IM on a bright reference star has been attacked by some authors. The principal problem of this measurement is to achieve a high SNR when atmospheric turbulence is present. This is very difficult if sensor signals are simply time averaged to get rid of the turbulence effects. The paper presents a new technique to perform an on sky measurement of the IM with high SNR and reducing the overall measurement time by an order of magnitude. This technique can be very useful for AO systems using large size DMs like MMT, LBT and possibly VLT and OWL. In these cases fiber-based IM measurements require challenging optical set-up that in some cases, like for OWL, are unpractical to build. The technique is still relevant for classical small DM AO systems that could be calibrated on sky avoiding misregistration errors. Finally this technique is valuable for laboratory measurements when the IM of an AO system has to be measured with great accuracy against external disturbances like bench vibrations, local turbulence effects and so on. Again IM measurement SNR is increased and the overall measurement time can be significantly reduced. The paper will introduce and detail the technique physical principle and quantify with numerical simulations the SNR improvement achieved using this technique. Finally laboratory results obtained during the test of the LBT AO system prototype are given and compared to simulations.