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,T(u, v), 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 asR̄(u, v) = T(u, v) A(-u)B^{}(-v)whereA(u)andB(v)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,T₀(u, v), which is a generalization to two dimensions of the well-known principal solution,T₀(u), 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,T₀(u, v)=ε₀(u)ε₀^{}(v). For incoherent sources it is shown that the spatial frequency spectrum ofT₀(u, v)is a function of only the difference,x-y, of the spatial co-ordinates,t₀(x, y) = t₀(x- y).