Although several papers have dealt with the image quality of an adaptive optics system (see e.g. Wilson & Jenkins (1996) for theoretical performance and Tessier (1997) for real results), none has focused specifically on the quality of photometry possible with these images. Since the accuracy of photometry is often crucial in the astrophysical conclusions drawn from observations, we attempt to give a guide for the average observer of the performance and limitations that can be expected when an adaptive optics system is used. Most of the examples given here use Strehl ratios between 0.15 and 0.3, which is typical of fair correction currently achievable in H and K wavelength bands, and have been obtained with the ADONIS system at the 3.6-metre ESO telescope. We do not try to estimate performances in a complete set of atmospheric conditions, since such a complete error analysis would really only be appropriate to a particular adaptive optics system, and our intention is to provide "rule-of-thumb" estimates rather than investigating the ultimate accuracy achievable under special circumstances. Table 6 at the end of this paper gives a brief summary of typical achievable accuracies for near-infrared photometry in a range of astronomical programmes.
Using adaptive optics introduces problems which are not usually encountered in normal photometry: global variations of the PSF with time, fluctuations in the large halo surrounding the core of the PSF, the presence of features in the PSF due to residual aberrations and variations of the PSF with the position in the image (due to the dependence of phase perturbations on position in the sky, called angular anisoplanatism). The influence of these problems on photometric performance is considered in several cases: uncrowded fields, faint structures around unresolved bright objects, and crowded fields. These examples should give a useful guide to performance in most astronomical photometric programmes that might be tackled using adaptive optics. We also study the effect on photometry of image deconvolution. This article looks at errors directly linked to the use of adaptive optics, and therefore most of the time ignores issues such as the presence of noise (sky background, photon or readout noise) or other problems with which the astronomer is used to dealing (for instance, flat fielding).
Section 2 introduces photometry with arrays and reviews the particular problems introduced by the use of an adaptive optics system. It also describes the observational data which is a vital input to our estimates. In Sect. 3, the potential advantages of using adaptive optics for photometry are illustrated by two examples. Section 4 then studies the impact of the limitations of adaptive optics in the simple case of an uncrowded field. Section 5 assesses their influence in the more complex case of a crowded field. This includes the detection of a faint companion or complex structure around a bright object, and the case of a field containing a large number of objects. The effects of deconvolution on photometry are considered in Sect. 6. Conclusions are drawn in Sect. 7, including a brief discussion of the implications of the use of laser guide stars, and simple advice on estimating photometric errors.