Noise in optical synthesis images. I. Ideal Michelson interferometer

We study the distribution of noise in optical images produced by the aperture synthesis technique, in which the principal source of noise is the intrinsic shot noise of photoelectric detection. The results of our analysis are directly applicable to any space-based optical interferometer. We show that the signal-to-noise ratio of images synthesized by such an ideal interferometric array is essentially independent of the details of the beam-combination geometry, the degree of array redundancy, and whether zero-spatial-frequency components are included in image synthesis. However, the distribution of noise does depend on the beam-combination geometry. A highly desirable distribution, one of uniform noise across the entire image, is obtained only when the beams from the n primary apertures are subdivided and combined pairwise on n(n - 1)/2 detectors