Sky coverage

The applicability of the Lucky Exposures method to faint astronomical targets depends on the limiting magnitude of reference star which can be used, and the size of the isoplanatic patch over which the technique will work. The results presented in Figure 5.19 indicate that reference stars as faint of $I=15.9$ can be used successfully for Lucky Exposures imaging. The results obtained on other nights (see e.g. Figure 5.12 and Chapter 5.5.5) were broadly consistent with these results from July 2001. Measurements of binaries presented in Figure 5.14 indicate that the technique works well up to $30$ $as$ from the reference star. These observations were taken on one night, and it has not been possible to confirm whether or not this isoplanatic angle is typical of the summer seeing conditions at the NOT.

From the limiting magnitude and isoplanatic angle measurements it is possible to calculate the fraction of the night sky which is close enough to a suitably bright reference star. Bahcall & Soneira (1984); Cox (2000) indicate that the mean density of stars brighter than $I=15.9$ is about $1300$ stars per square degree. Based on their models for the distribution of stars in galactic coordinates, the fraction of the night sky within range of a suitable reference star ranges from $10\%$ near the South Galactic pole to $25\%$ at $b=30$. In the galactic plane the probability can be much higher, particularly toward the galactic centre. This represents a very substantial improvement over the case of I-band natural guide star adaptive optics, where the sky coverage is typically less than $0.1\%$ for high resolution imaging. High resolution astronomical observations using I-band adaptive optics are limited predominantly to searches for faint companions around bright nearby stars. The small isoplanatic patch and bright reference stars mean that deep imaging observations often suffer from problems with scattered light from the reference star. In contrast, the Lucky Exposures method should be applicable to a much wider range of galactic and extra-galactic observing programs.