This paper relates the optical definition of the PSF to radio interferometer arrays. The statistical properties of the PSF including the effect of missing UV data are derived as a function of the number of antennas and array magnification, defined as the ratio of the primary beam width from an individual element to the synthesized beam width. The effect of earth rotation synthesis on the PSF is also calculated and the merits of various configuration strategies are discussed in terms of their PSFs. The concept of a pseudo-random array is introduced as an array whose large-scale average distribution matches an idealized continuous antenna distribution. The small-scale difference between the actual discrete distribution and the idealized continuous distribution produces far sidelobes in the PSF. It is shown that the statistical distribution of the sidelobes, s, of pseudo-random arrays of N antennas with sparse UV coverage is given by P(s)=N*exp(-N*s). The average sidelobe is ~1/N and the standard deviation is also ~1/N. Note that the single antenna measurements are included in the formulation of the PSF used in this work. The expected peak sidelobe for a pseudo-random array with a magnification mag is smax~2*ln(mag)/N and it is predicted that optimization can reduce the peak sidelobe to smax~2*[ln(mag)-ln(N)]/N. Pseudo-random arrays provide a benchmark against which proposed configurations can be compared.
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