On the mapping by a cross-correlation antenna system of partially coherent radio sources

In this paper it is shown that by means of a crosscorrelation antenna system it is possible to measure the mutual power distribution, , of partially coherent radio sources. The two linear antennas of the system are scanned independently to give a two-dimensional output which can be written as where and are the patterns of the two antennas. A two-dimensional Fourier analysis of the output shows it to be a smoothed version of the true mutual power distribution. One can define a principal solution, , which is a generalization to two dimensions of the well-known principal solution, , which occurs when the sources are incoherent. The limiting cases of complete coherence and complete incoherence are considered. It is shown that for coherent sources the principal solution is factorable, . For incoherent sources it is shown that the spatial frequency spectrum of is a function of only the difference, , of the spatial co-ordinates, .