Sensitivity of optical interferometers with coherent image combination

Abstract

When multiple, adaptively-corrected telescopes are coherently combined at a common focal plane, interference appears as spatial structure in the point spread function (PSF). True images of deep fields can be reconstructed at resolution λ/b from multiple images recorded to cover the u-v plane with baselines up to b. Assuming no losses or detector noise, sensitivity improves with the number of elements, n, and of combined images, N. The formalism of PSF fitting is used here to determine signal/noise ratio for faint point sources seen against sky background noise. For two-element and dilute, non-redundant arrays the PSF fit is dominated not by any sharp peak, but by fringes or weak speckles, and the signal/noise ratio is proportional to square root N(2n-1). For close packed or highly redundant arrays the sensitivity increases as nsquare root N, and is the same as for a single dish with the same total collecting area and integration time. It follows that the signal/noise ratio for a two-element array is thus square root 3/2 = 86% of this maximum limit. We show that the requirement for PSF sampling with negligible detector read noise can be met with available optical and infrared array detectors, for baselines up to 10 times the element diameter. Low-loss combination could be realized in practice by an interferometer with two large moving elements, with baselines set up sequentially to sample the full u-v plane. In the 20/20 concept, two 21 m telescopes move continuously around a circular track during an integration, to keep the baseline oriented perpendicular to the source. Coheret combination is made at a station held midway between, to obtain aperture synthesis of images covering the full, one arc-minute field corrected by multiconjugate adaptive optics. With 16 images taken over 8 hours to fully cover baselines up to 100 m, the resolution in the K band is 4 mas, and the 10σ limiting magnitude for point sources will be 27.7.