Interferometry and the spectral sensitivity island diagram

Basic principles of radio interferometry are expounded and a special diagram is established which helps with problems on interferometers, especially those with phase switching or other complications. The information on a record, or interferogram, made by scanning a compact source or target with an interferometer comprising an antenna with two well-spaced parts, is all in one complex number, the complex visibility of the interference fringes. Under appropriate conditions, the complex visibility observed is equal to the complex coherence of the field produced by the source between the points occupied by the two elements of the interferometer. (If the elements are not infinitesimal in extent, the complex visibility is equal, instead, to a weighted mean of the values of complex coherence between the pairs of points embraced by the elements.) Furthermore, this quantity gives the strength of one spatial Fourier component of the source distribution in amplitude and phase. To know all Fourier components would require the use of all spacings-two dimensions, this means all vector spacings. Measurements at a finite number of spacings yield the principal solution; if the source is finite in extent, only certain discrete spacings need be used. Spectral sensitivity of antennas depends on the complex autocorrelation function of the antenna aperture distribution. For interferometers, the spectral sensitivity is confined to islands in the spatial frequency plane whose shorelines may be delineated by a simple graphical procedure. The spectral sensitivity island diagram offers an alternative approach to interferometer problems. In an application of the diagram, it is explained how the resolving power of a Mills cross is not impaired by deleting half of one arm.