Focal plane $C_n^2(h)$ profiling based on single conjugate adaptive optics compensated images

Abstract: Knowledge of the atmospheric turbulence in the telescope line-of-sight is crucial for wide-field observations assisted by adaptive optics (AO), for which the Point Spread Function (PSF) becomes strongly elongated due to the anisoplanatism effect. This one must be modelled accurately to extrapolate the PSF anywhere across the Field of view (FOV) and improve the science exploitation. However, anisoplanatism is a function of the Cn2(h) profile, that is not directly accessible from single conjugate AO telemetry. One may rely on external profilers, but recent studies have highlighted more than 10% of discrepancies with AO internal measurements, while we aim better than 1% of accuracy for PSF modelling. To tackle this existing limitation, we present the Focal plane profiling (FPP), as a $C_n^2(h)$ profiling method that relies on post-AO focal plane images. We demonstrate such an approach complies with a 1%-level of accuracy on the $C_n^2(h)$ estimation and establish how this accuracy varies regarding the calibration stars magnitudes and positions in the field. We highlight that photometry and astrometry errors due to PSF mis-modelling reaches respectively 1% and 50{\mu}as using FPP on a Keck baseline, with a preliminary calibration using a star of magnitude H=14 at 20". We also validate this concept using Canadas NRC-Herzberg HENOS testbed images in comparing FPP retrieval with alternative $C_n^2(h)$ measurements on HeNOS. The FPP approach allows to profile the $C_n^2(h)$ using the SCAO systems and improve significantly the PSF characterisation. Such a methodology is also ELT-size compliant and will be extrapolated to tomographic systems in a near future.