Fast guiding and small telescopes in the 8-m era

Fast guiding may improve the images delivered by telescopes. It may be implemented fairly cheaply and offers an upgrade path to smaller telescopes, which will make them more useful in the 8-m era. However, the detailed performance of a fast guiding system must depend on many parameters and this makes it difficult to assess its precise scientific benefits. This paper provides a comprehensive mathematical framework for calculating the performance of fast guiding systems. A range of models has been calculated that illustrates the benefits for telescopes of various sizes in various wavelength ranges. Three measures of performance have been examined: FWHM, 50 per cent encircled energy diameter and energy concentration in a 0.35-arcsec aperture. Typical gains over natural seeing are found to be in the 20 to 40 per cent range at useful levels of sky coverage. Other things being equal, small telescopes do not benefit as much as large ones from fast guiding. The sensitivity of these benefits to assumptions has also been examined, and this highlights the need to operate in the correct wavelength range for the aperture in question. The largest perturbations to ideal models are likely to be the result of telescope windshake and the outer scale of turbulence. If there is appreciable windshake, fast guiding will yield larger benefits than expected from the natural seeing. A short outer scale (a few hundred metres) will, however, lose most of the gains.