7 Conclusions

The AO correction of an image theorically allows to reach the diffraction limit of ground based telescope. Unfortunately this correction is always partial and the image is still blurred by the residual PSF.

In this article, we have presented a myopic deconvolution method for stellar fields based on the a priori knowledge we have of the object and the PSF. The object knowledge leads us to reparametrize our object model. The structure and variability of the PSF given by the WFS measurements are introduced as first (mean) and second (PSD) order moments in an a priori probability law.

We have shown on simulations that this technique allows a good restoration of the object (position and photometry) and of the PSF. Experimental data have been also successfully processed.

Future work should implement other probability statistics. Non-stationary Gaussian or Poisson plus Gaussian statistics should be used in order to provide a better noise model.

A current limitation of our method is that it does not include a systematic detection of stars. Up to now, the number of star is first estimated on the image then the residual of the deconvolution is checked for missed stars. A Bernouilli-Gaussian or P-Gaussian statistic should permit the inclusion of an automatic star detection in the algorithm.

Also, the estimation of a theorical error calculation on the star parameters should be added to better quantify the precision of the estimations.

Lastly, in the case of a field larger than the isoplanatic path, a space variant PSF could be introduced to take into account anisoplanatic effects. The advantage of our multiple-star object model in addition with a myopic approach is that one can easily incorporate one PSF for each star as additional unkowns. In that case, another regularization term should be added to account for the angular correlation of the PSF in the field.

Acknowledgements

The authors wish to thank V. Michau and G. Rousset for fruitful discussions and helpful comments.