  Small inner working angle coronagraphs, like the vortex phase mask, are
essential to exploit the full potential of ground-based telescopes in the
context of exoplanet detection and characterization. However, the drawback of
this attractive feature is a high sensitivity to pointing errors, which
degrades the performance of the coronagraph. We propose a tip-tilt retrieval
technique based on the analysis of the final coronagraphic image, hereafter
called Quadrant Analysis of Coronagraphic Images for Tip-tilt Sensing (QACITS).
Under the assumption of small phase aberrations, we show that the behaviour of
the vortex phase mask can be simply described from the entrance pupil to the
Lyot stop plane by Zernike polynomials. This convenient formalism is used to
establish the theoretical basis of the QACITS technique. Simulations have been
performed to demonstrate the validity and limits of the technique, including
the case of a centrally obstructed pupil. The QACITS technique principle is
further validated by experimental results in the case of an unobstructed
circular aperture. The typical configuration of the Keck telescope (24% central
obstruction) has been simulated with additional high order aberrations. In
these conditions, our simulations show that the QACITS technique is still
adapted to centrally obstructed pupils and performs tip-tilt retrieval with a
precision of $5 \times 10^{-2}$ {\lambda}/D when wavefront errors amount to
{\lambda}/14 rms and $10^{-2}$ {\lambda}/D for {\lambda}/70 rms errors (with
{\lambda} the wavelength and D the pupil diameter). The implementation of the
QACITS technique is based on the analysis of the scientific image and does not
require any modification of the original setup. Current facilities equipped
with a vortex phase mask can thus directly benefit from this technique to
improve the contrast performance close to the axis.
