1 Introduction

Atmospheric turbulence severely limits the angular resolution of ground based telescopes. Adaptive Optics (AO) [Rousset et al.1990,Roddier1999] is a powerful technique to overcome this limitation and to reach the diffraction limit of large telescopes. AO compensates, in real-time, for the random fluctuation of the wavefront induced by the turbulent atmosphere. The turbulent wavefront is measured by a wavefront sensor (WFS) and optically corrected by a deformable mirror. This compensation allows to record high spatial resolution long exposure images. However, even if the object spatial frequencies are preserved up to the diffraction limit of the telescope, they are often severely attenuated since AO correction is only partial. A degraded point spread function (PSF) still blurs the object. It is therefore necessary to use image processing techniques to improve the quality of the recovered object [Lucy1994,Thiébaut & Conan1995,Christou et al.1997,Conan et al.1998b]. Nevertheless, all these techniques are based on the assumption that the field of view (FOV) of interest is smaller than the so-called isoplanatic patch [Fried1982]. Wavefronts, coming from angularly separated points, do not cross the same part of the atmosphere and are not identically disturbed. In the visible, the isoplanatic patch is about a few arcseconds [Fried1982]. If the FOV is greater than this field, the AO correction, which is optimal on the optical axis, is degraded as a function of angle [Chassat1989,Sasiela1995,Molodij & Rousset1997]. The residual PSF is no longer space invariant: this fundamentally limits the performance of all the deconvolution techniques.

We present here a simple and analytical expression of this PSF degradation in the FOV and an application to a posteriori processing of wide FOV images.

After a short presentation of the image formation in a wide FOV, a theoretical calculation of the PSF angular dependence is presented in Sect. 2. The results are validated on simulations in Sect. 3 and on experimental data in Sect. 4. In Sect. 5, an example of application is proposed: post processing of an AO corrected image of a stellar field. A deconvolution algorithm, presented in [Fusco et al.1999b], is modified to include the theoretical expression of the PSF spatial variation, in order to obtain accurate photometric and astrometric estimations for wide FOV images. This algorithm is then tested on simulated and experimental data.