Upgraded optical aberration correction techniques for Advanced Virgo plus: commissioning toward O4 and mitigation of non-axisymmetric optical defects

The absorption of laser power in the core optics of ground-based gravitational wave detectors induces thermoelastic deformations and changes of the optical path length that add up to mirror manufacturing defects causing deviations from the ideal optical configuration of the interferometer and worsening its performances. To mitigate these distortions a thermal compensation system (TCS) has been implemented in Advanced Virgo+. TCS is designed to deal with axisymmetric wavefront distortions that represent the main contribution to the aberration budget. One of the cornerstones of the thesis is the commissioning of the TCS in preparation for the fourth observing run O4. Preliminary characterizations performed on the TCS actuators in order to make them optimally settled to compensate the optical aberrations and cold defects are detailed. Tuning strategies developed to fully exploit the TCS resources are presented, highlighting the relevant results. In view of the input power increase foreseen in the observing run O5 an adaptive control of residual non-axisymmetric optical aberrations is known to be necessary. Deformable Mirrors (DM) have been proposed as static CO2 beam shapers to induce arbitrary compensation via thermooptic effect. The main advantage with respect to scanning beam actuators is that the DM correction does not introduce additional frequency-dependent noise. A Modified Gerchberg-Saxton (MoG-S) algorithm has been developed to extract the phase to be applied by the DM to obtain the heating pattern required for a complementary wavefront correction of the non-axisymmetric aberrations. In the last part of the thesis the MoG-S simulations of the DM-based system and the results of the experimental tests will be presented.