Performance of ground-based high resolution imaging techniques

Ground-based high resolution imaging techniques can be broadly classified into two types:

1. Passive observations - techniques which make astronomical measurements on time- scales comparable to the atmospheric coherence time. Measurements are usually repeated many times in order to increase the signal to noise ratio. Typical examples include speckle interferometry, the shift-and-add method, Lucky Exposures and observations of visibilities and closure phases at long baseline interferometers such as COAST and SUSI.
2. Active correction - designed to remove atmospheric perturbations in optical wavefronts in real time before they enter an imaging instrument. Adaptive optics (including tip-tilt correction) and fringe tracking at long baseline interferometers such as NPOI represent active correction.

The Lucky Exposures method is passive, relying on a high frame-rate camera in the image plane of a telescope to record the speckle patterns. In the past the poor signal-to-noise performance of high frame-rate cameras has often limited observations like this to relatively bright targets. It should be noted that the recent development of high frame-rate CCD cameras with extremely low readout noise will allow many of the active and passive imaging methods to be used on much fainter astronomical sources.

All of the techniques require measurements of the perturbations introduced by the atmosphere using light from a reference source. This reference source may either be a component of the astronomical target (e.g. the bright core of an active galaxy) or another source nearby in the sky such as a star. For most of the methods described here the reference source must be small enough that it is not significantly resolved by the observations. For adaptive optics slightly larger reference sources may be used. The abundance of stars in the night sky mean that they are the most common form of reference source used for high-resolution imaging through the atmosphere.

Each of the imaging techniques can only be applied in a small field around each reference source - this field is usually called the isoplanatic patch. Only those astronomical objects which are close enough to a suitably bright reference source can be imaged. Under the same observing conditions passive imaging approaches can typically use fainter reference stars than active techniques, which require a servo-loop operating at a fast rate.

The range of astronomical sources to which each technique can be applied is thus dependent on how faint a reference source can be used. The fraction of the sky which is within range of a suitable reference star is termed the sky coverage of the imaging technique. For most of the techniques described here the sky coverage is relatively small, seriously limiting their applicability in scientific observations. This thesis will concentrate on imaging at wavelengths shorter than $1\mu m$. For these wavelengths the small sky coverage available is the principle limitation on the scientific output of all these techniques, making this the most important issue to address here. Some aspects of the discussion presented below would be less relevant for observations at longer wavelengths.

In comparing the methods I will discuss four aspects of the techniques:

1. The limiting magnitude of reference star which can be used;
2. The isoplanatic patch;
3. The sensitivity to faint objects; and
4. The cost and complexity of implementation.