Low-wind-effect impact on Shack-Hartmann-based adaptive optics. Partial control solution in the context of SPHERE and GRAVITY+

Context. The low wind effect (LWE) occurs at the aperture of 8-meter class telescopes when the spiders holding the secondary mirror get significantly cooler than the air. The effect creates phase discontinuities in the incoming wavefront at the location of the spiders. Under the LWE, the wavefront residuals after correction of the adaptive optics (AO) are dominated by low-order aberrations, pistons, and tip-tilts, contained in the pupil quadrants separated by the spiders. Those aberrations, called petal modes, degrade the AO performances during the best atmospheric turbulence conditions. Ultimately, the LWE is an obstacle for high-contrast exoplanet observations at a small angular separation from the host star. Aims. We aim to understand why extreme AO with a Shack-Hartmann (SH) wavefront sensor fails to correct for the petal tip and tilt modes, while these modes imprint a measurable signal in the SH slopes. We explore if the petal tip and tilt content of the LWE can be controlled and mitigated without an additional wavefront sensor. Methods. We simulated the sensitivity of a single subaperture of a SH wavefront sensor in the presence of a phase discontinuity across this subaperture. We explored the effect of the most important parameters: the amplitude of the discontinuity, the spider thickness, and the field of view. We then performed end-to-end simulations to reproduce and explain the behavior of extreme AO systems based on a SH in the presence of the LWE. We then evaluated the efficiency of a new mitigation strategy by running simulations, including atmosphere and realistic LWE phase perturbations. Results. For realistic parameters (i.e. a spider thickness at 25% of a SH subaperture, and a field of view of 3.5 lambda/d), we find that the sensitivity of the SH to a phase discontinuity is dramatically reduced, or even reversed. Under the LWE, a nonzero curl path is created in the measured slopes, which transforms into vortex-structures in the residuals when the loop is closed. While these vortexes are easily seen in the residual wavefront and slopes, they cannot be controlled by the system. We used this understanding to propose a strategy for controlling the petal tip and tilt modes of the LWE by using the measurements from the SH, but excluding the faulty subapertures. Conclusions. The proposed mitigation strategy may be of use in all extreme AO systems based on SH for which the LWE is an issue, such as SPHERE and GRAVITY+.