4 Conclusions

The theoretical analysis presented in the paper has shown that the off-axis adaptive optics correction produces the elongation in the science objects' PSFs. This elongation is directed towards the guide star and has a variable magnitude depending on the angular separation between the science object and the guide star, the telescope diameter, the Fried parameter and the Cn2 profile. This elongation effect has recently been found in the experimental observations made with the AO system at the CFHT in Mauna Kea (Close 1998).

In order to concentrate on the essential features of the anisotropic imaging, two main simplifications have been made through this paper.

First, we have considered the case of adaptive system with the perfect correction. This assumption has permitted us to stress out the physics of anisotropic imaging leaving aside engineering details related to the partial correction. However, in real off-axis AO systems the residual distortion arising due to the partial correction is an additional source of degradation of the PSF which contributes to its widening but keeps it symmetric. This widening obscures partially the effect of elongation, especially for those systems with the low-order AO correction. The rapid developing of AO technology, however, makes us expect that the AO systems will approach the perfect ones that is the case considered here.

Second, the calculations have been made making use of the conventional Kolmogorov model that assumes an infinite outer scale of the turbulence. In reality, the outer scale is finite, with a magnitude dependent on the observation place and atmospheric conditions, and it may vary from several meters to several hundred meters. According to our preliminary estimations, the finite outer scale affects mainly the asymptotic behavior of the elongation, and its influence is pronounced when the outer scale magnitude is small. As an example let us consider how this effect will change the graphs in Fig. 1. For the Kolmogorov model the elongation tends asymptotically to the unity, but at a very slow rate. However, if the outer scale effect is taken into account, the graphs will approach the unity faster. From the experimental point of view it means that the smaller is the outer scale, the quicker the elongation will disappear with the increase of star separations.

A quantitative comparison of theoretical predictions with the real observation data is also of interest. In order to perform such a comparison, the simplified model used in the paper can be easily extended for the case of partial correction AO correction and finite outer scale, once the additional information is available. Along with the observation data, this information has to include the parameters of the AO system, the Cn2 profile, and, maybe, the outer scale magnitude which have to be measured during the observations. Such measurements can be performed in a quasi-real time applying for example G-SCIDAR (Avila et al. 1997).

Acknowledgements

This work was supported by Ministerio de Educacion y Cultura, Spain, Ref.: SAB1995-0729 and by Sistema Nacional de Investigadores, Mexico.