Angular resolution: how much is enough?

                       

The first step is to determine the range of angular resolution that is appropriate for the project. You should think about both the minimum and maximum values of .
The lowest resolution (maximum value of the synthesized beam width ) will be set by your need to separate, or to resolve, astrophysically important features of the region being imaged. Realize however that you can have too much resolution if your project depends on imaging extended emission. There is no point observing extended emission using such a small beamwidth that crucial features are close to, or below, the r.m.s. noise on the final images. You must therefore estimate the apparent brightness (flux density per synthesized beam area) that you expect important extended features to have at the resolution you will use for your final images. You can then determine the highest resolution (minimum ) that is appropriate for your project by estimating the total integration time needed to reach the required brightness sensitivity. As omitting this aspect of the project design can render the final images useless, it is worth restating the principles.
Recall from Lecture 4 that a point source with flux density S Jy images with an apparent brightness of S Jy per synthesized beam area regardless of the area of the synthesized beam. It follows that, for any synthesis array of identical antennas and receivers, all baselines are equally sensitive to a given point source (apart from the effects of confusion and phase stability). In contrast, the apparent brightness of an extended emission region in a synthesized image depends on the region's detailed structure, on how well the visibility function V(u,v) is sampled by the observations, and on the weighting and tapering functions and applied to the data when imaging (Lecture 7). When deciding on an observing strategy, it usually suffices to assume that:

• an extended region with uniform true brightness I Jy per square arcsec will be imaged with an apparent brightness Jy per synthesized beam area , and
• the final synthesized beam will be a Gaussian CLEAN beam, so that its area will be square arcsec, where and are the major and minor half-power widths of the Gaussian in arcsec.

If the r.m.s. noise on the image is Jy per synthesized beam, the signal-to-noise ratio of such extended emission on the image will be , which increases as the synthesized beam area . You must ensure that you do not observe at such small values of that interesting extended structure is undetectable, given the total integration time available and your choice of the IF bandwidth (see Field of View Restrictions and Total Integration Time).

There are circumstances however when enhanced resolution helps you to detect interesting features--for example, when searching for pointlike ``hot spots'' or linear ``jets'' in more diffuse emission such as large scale ``lobes''. While the flux density per synthesized beam of two-dimensional emission is roughly proportional to the beam area , that of linear emission is proportional to the beam width , and that of a point source is independent of beam size. These dependencies allow compact structure that is embedded in, or confused with, more extended emission to be recognized most easily on high-resolution images.

Note that it is also important to avoid unnecessarily high resolution (long baselines) in detection experiments. Although the theoretical sensitivity to a point source is independent of the size of the array (apart from the effects of confusion), the phase fluctuations produced by atmospheric irregularities will be greater on longer baselines (Lectures 5 and 6). It is therefore more difficult to reach the theoretical sensitivity by integrating coherently between calibrations when using long-baseline arrays. This is especially true at high frequencies, where the phase stability depends critically on conditions in the troposphere over the array. The severity of ionospheric or tropospheric phase fluctuations varies from site to site, and at any one site with the ``weather" from hour to hour, from day to day, and from season to season. It is generally true however that observations longer than about an hour with < 1" are often corrupted by atmospheric phase fluctuations and that observations with always are. The most powerful tool for dealing with these corruptions is self-calibration (Lecture 9). This technique is rarely applicable to detection experiments, however--unless they are unusually successful, so that all detected sources are strong!