Generalized coincident arrays for the direct measurement of the principal solution in radio astronomy

Linear receiving arrays of equispaced elements followed by square-law detection, when used to map the brightness distribution of radio sources, act as low-pass spatial frequency filters with bandwidths proportional to the size of the arrays. Moreover, within the passband, the arrays´ spatial frequency distribution (SFD) is non-uniform. This results in a brightness distribution map of the radio sources which has spatial frequency distortion within and no higher frequencies outside the finite passband of the conventional linear array. In this paper the original principal solution multiplicative array is first generalized to the case of an array of N+1 sub-arrays each of which has M+1 isotropic elements. Again, the element outputs are split and combined to form the outputs of two coincident arrays. Moreover, the uniform SFD necessary to directly measure the principal solution is achieved but with a fewer total number of elements. For large arrays approximately half as many elements are required. It is then demonstrated that for a given number of elements R=2/sup n/(n=1,2,...) the SF bandwidth is maximized when sub-arrays are successively divided until the smallest sub-array has two elements-a simple interferometer.