Accurate photometry with adaptive optics in the presence of anisoplanatic effects with a sparsely sampled PSF The Galactic center as an example of a challenging target for accurate AO photometry

Context. Anisoplanatic effects can cause significant systematic photometric uncertainty in the analysis of dense stellar fields observed with adaptive optics. Program packages have been developed for a spatially variable PSF, but they require that a sufficient number of bright, isolated stars in the image are present to adequately sample the PSF. Aims. Imaging the Galactic center is particularly challenging. We present two ways of dealing with spatially variable PSFs when only one or very few suitable PSF reference stars are present in the field. Methods. Local PSF fitting with the StarFinder algorithm is applied to the data. Satisfying results can be found in two ways: (a) creating local PSFs by merging locally extracted PSF cores with the PSF wings estimated from the brightest star in the field; (b) Wiener deconvolution of the image with the PSF estimated from the brightest star in the field and subsequent estimation of local PSFs on the deconvolved image. The methodology is tested on real, and on artificial images. Results. The method involving Wiener deconvolution of the image prior to local PSF extraction and fitting gives excellent results. It limits systematic effects to similar to 2-5% in point source photometry and similar to 10% in diffuse emission on fields-of-view as large as 28 '' x 28 '' and observed through the H-band filter. Particular attention is given to how deconvolution changes the noise properties of the image. It is shown that mean positions and fluxes of the stars are conserved by the deconvolution. However, the estimated uncertainties of the PSF fitting algorithm are too small if the presence of covariances is ignored in the PSF fitting as has been done here. An appropriate scaling factor can, however, be determined from simulated images or by comparing measurements on independent data sets. Conclusions. We present ways of obtaining reliable photometry and astrometry from images with a spatially variable, but poorly sampled PSF, where standard techniques may not work.