Optical characterization of the Advanced Virgo gravitational wave detector for the O4 observing run

The Advanced Virgo Plus detector, an upgrade of the Advanced Virgo Detector, is a dual-recycled Fabry--Perot Michelson interferometer characterized by 3\&\#x00A0;km long arm cavities. The main upgrades in view of the fourth observing run (O4) were the implementation of the signal recycling cavity and the installation of the frequency-dependent squeezing system. Another upgrade was the increasing of the laser power at the input of the detector, which could lead to more severe thermal aberrations impacting the achievement of the interferometer optimal working point. Therefore, the fine-tuning of the thermal compensation system, optimized with respect to the one implemented for the O3 run, was also challenging. In order to achieve the best performance of such a sophisticated optical system, having a clear knowledge of all its optical parameters is crucial. The optical characterization of the detector in different working conditions could help in understanding its behavior and optimizing the global control system. Moreover, the characterization in different thermal conditions, i.e.,\&\#x00A0;different values of the input laser power or different configurations of the thermal compensation system, could provide significant guidance for the optimization of the thermal tuning. In this paper, we will describe all the methodologies adopted for the optical characterization activities performed in Advanced Virgo Plus, presenting the experimental results for all the relevant parameters obtained during the preparation of the O4 run.