  Atmospheric profiling is a requirement for controlling wide-field Adaptive
Optics (AO) instruments, analyzing the AO performance with respect to the
observing conditions and predicting the Point Spread Function (PSF) spatial
variations. We present PEPITO, a new concept for profiling atmospheric
turbulence from {\em post~facto} tip-tilt (TT) corrected short-exposure images.
PEPITO utilizes the anisokinetism effect in the images between several stars
separated from a reference star, and then produces the profile estimation using
a model-fitting methodology, by fitting to the long exposure TT-corrected PSF.
PEPITO has a high sensitivity to both $C_n^2(h)$ and $L_0(h)$ by relying on the
full telescope aperture and a large field of view. It then obtains a high
vertical resolution (1\,m-400\,m) configurable by the camera pixel scale,
taking advantage of fast statistical convergence (of order of tens of seconds).
With only a short exposure-capable large format detector and a numerical
complexity independent of the telescope diameter, PEPITO perfectly suits
accurate profiling for night optical turbulence site characterization or
adaptive optics instruments operations. We demonstrate, in simulation, that the
$C_n^2(h)$ and $L_0(h)$ can be estimated to better than 1\% accuracy, from
fitted PSFs of magnitude V=11 on a D=0.5\,m telescope with a 10 arcmin field of
view.

Instrumentation and Methods for Astrophysics