Scientific exploitation in ground-based astronomy is improved thanks to adaptive optics (AO) that restore diffraction-limit angular resolution. Besides, the ultimate data interpretation is delivered by post-processing techniques that usually relies on a Point spread function (PSF) model. Nevertheless, existing methods to constrain this model based on standard pipeline encounter the spatial and time variations of the AO PSF. In order to improve accuracy on key science observables, such as photometry and astrometry, alternative methods are investigated, such as PSF reconstruction (PSF-R), designed to estimate the PSF from AO control-loop data and key atmosphere and system parameters. We aim in this paper at retrieving directly these relevant inputs we need to reconstruct the PSF using an hybrid approach, that couples AO telemetry with focal plane images, named as Focal plane profiling and reconstruction (FPPR). It adjusts atmosphere parameters (the C2n (h) profile) and optical gains in the system. We describe the FPPR method that is applied to on-sky Keck images in engineering mode operated with either natural or laser guide star and show we get 1% of accuracy on respectively the Strehl-ratio and the PSF FWHM reconstruction.