In order to summarise the results of this study, we can consider three different types of requirements for the accuracy of photometry. First, not all photometric investigations require an accuracy higher than about 0.1 or 0.2 magnitude. For instance, Longmore et al. (1990) present a way of determining the distance to a globular cluster by magnitude measurement of RR Lyrae stars in the K band, where such uncertainties are acceptable. Other astronomical studies require a precision of 0.05 magnitudes or so. For example, the H-K colour of a star worked out with such a precision allows the determination of its spectral type (see Koorneef 1983). Last, some astronomical projects require uncertainties to be about 0.01 or 0.02 magnitude. This is for example the case when the age and metallicity of a globular cluster has to be inferred from its near-infrared colours (see Worthey 1994, for theoretical colours of simple stellar populations). We present the results of our study in Table 6 (click here) for these three types of required precision.


Required accuracy	0.1-0.2 mag	0.05 mag	0.01-0.02 mag
Uncrowded field	No problem	Problems if exposure	Might be impossible
	(except for very	time smaller than
	short exposures)	a few seconds
Anisoplanatism	No problem	FOV limited to	FOV limited to
	(aperture defined by	15'' in J, 17'' in H	10'' in J, 12'' in H
	second dark ring)	and 20'' in K	and 15'' in K
Flux of a faint	Down to	Down to	Only possible
companion	at 1''	at 1''	beyond 2'' and
	at 2''	at 2''	down to
Crowded field	Down to between	Impossible	Impossible
	and	except in
	typically	favourable cases
Anisoplanatism	FOV limited to	FOV limited to	Very limited FOV
	6'' in J, 8'' in H	3'' in J, 5'' in H
	and 10'' in K	and 7'' in K
Flux of a faint	Down to	Down to	Down to
companion after	further than 0.5''	further than 0.3''	further than 0.4''
deconvolution			Accurate PSF required

Table 6: The capabilities of photometry with adaptive optics for three different kinds of accuracy requirements. These results assume that sources of noise not linked with the use of adaptive optics are negligible. The correction is supposed to be fair (Strehl ratios between 0.15 and 0.3). Angular anisoplanatism effects assume a 4-meter telescope in good seeing conditions. Results for the detection of a companion, with or without deconvolution, apply to the K band, they also assume no artifacts near the objects studied. Deconvolution always requires a high signal-to-noise ratio for the companion's peak intensity, say between 10 and 50 depending on the object and the deconvolution method. FOV stands for field of view

All the results presented so far assume that only one measurement is carried out. Performing several measurements may improve the final accuracy. Repetition can reduce the errors due to seeing fluctuations, provided these are really random and that no systematic effect appears. In order to decrease the inaccuracies due to the mismatch between the point spread functions for the object studied and its calibrations stars, lots of suitable stars have to be found, which might be a major drawback. Our experience also suggests that performing several measurements will not affect most residual features and artifacts. Moreover, in most cases it will not allow a reduction of angular anisoplanatism effects. Finally, the quantitative accuracy of deconvolved images will probably not be increased because the effects are systematic rather than random. This shows that although performing several measurements will decrease errors linked to seeing fluctuations, this method will not be able to reduce the other sources of error. So, the only revision to Table 6 by repetition of observations will be in the case of an uncrowded field and maybe in the measurement of a faint companion.

Another possible way of improving the photometric accuracy might be to use a laser guide star rather then a natural one, but the improvement is likely to be very small. Using a laser guide star does not prevent seeing fluctuations from inducing global variations in the PSF shape. The halo of the PSF is going to be fainter as more modes can be corrected, and the problem of mismatched PSFs will disappear, but the halo will still fluctuate with time. Residual features and artifacts will not disappear. Neither will angular anisoplanatism, though its effects can be reduced since the guide star can be moved across the object studied. Finally, the accuracy of photometry on deconvolved images has no reason to improve. All these arguments show that the results presented in Table 6 apply in the case of a laser guide star adaptive optics system, with possible improvements in anisoplanatism problems and in the measurement of a faint companion. Multiple laser guide stars (solving the cone effect) and possibly turbulence layer multi-conjugate adaptive optics systems, giving very good Strehl ratios on large fields of view, may eventually alleviate some of the problems of obtaining good photometric accuracy.

The authors wish to thank M. Heydari-Malayeri and J.-L. Beuzit for providing them with data obtained during several runs on the Adonis system, and R. Wilson for his simulated point spread functions. They are grateful to H. Geoffray, P. Prado and E. Prieto for their assistance during the observations and to P. Léna for encouragement. They also thank the referee for helpful advice on improving the presentation of this work. O. Esslinger is supported by a PPARC PhD grant through the United Kingdom Adaptive Optics Programme.

8. Discussion and conclusion

8.1. Feasibility of astronomical programmes

8.2. Discussion