Two-dimensional Aerial Smoothing in Radio Astronomy

Abstract

The visibility of a Fourier component of a two-dimensional temperature distribution which is scanned by certain kinds of rigid aerial is given by the normalized complex autocorrelation function of the field distribution over the aerial aperture (assuming that turning the aerial in its own plane is not allowed). Hence, for finite aerials, the visibility of the Fourier components falls to zero at finite values of spatial frequency. Consequently observations need only be made at certain peculiar intervals whose size is worked out. Interpolation between observations so spaced can be carried out by a method which then, by a simple extension, permits filtering of data which are to be freed from high spatial frequencies. Both interpolation and filtering are basic processes in the handling of two-dimensional data and contour maps in radio astronomy. The restoration of smoothed data is discussed from the viewpoint that only the simplest operations on extensive two-dimensional data are feasible, and details of a suitable technique of restoration are summarized. Application of further smoothing to existing data is shown to be important, and a method for doing it is given, again under the restriction to simple operations. The flux density of a source is shown to be given exactly by summing one in four of the isolated values observed at the peculiar intervals.