Impact of local turbulence on high-order adaptive optics

We present an experiment set to address a standard specification aiming at avoiding local turbulence inside the Coud\'e train of telescopes. Namely, every optical surface should be kept within a 1.5$^\circ$ range around ambient temperature. Such a specification represents an important concern and constraint when developing optical systems for astronomy. Our aim was to test its criticality in the context of the development of the VLTI/NAOMI and VLTI/GRAVITY+ adaptive optics. This experiment has been conducted using the hardware of the future Corrective Optics (CO) of GRAVITY+. Optical measurements were performed in order to observe the evolution of turbulence in front of a flat mirror for which the surface temperature was controlled in a range of $22^\circ$ above ambient temperature. A time-dependent analysis of the turbulence was led along with a spatial analysis. This experiment shows no influence of temperature on local turbulence. It should be noted however that this result is only applicable to the very specific geometry described in this paper, which is representative of an adaptive optics (AO) system located inside the Coud\'e train (facing-down mirror heated on its backface).