Abstract
Certain practical problems in astronomical optics require a detailed knowledge of aperture-to-aperture correlations in the instantaneous tilt of a wave-front distorted by atmospheric turbulence. The corresponding correlation coefficients are calculated by Fourier analysis. The results are expressed as one-dimensional integrals (over k space), which are equivalent to, but possess computational advantages over, the two-dimensional integrals (over aperture space) that appear in the literature. In addition, the angular dependence of the tilt correlation in these expressions is simple and explicit. Tables of these correlation coefficients, as well as analytic forms for the asymptotic values corresponding to large and small separations between the two apertures, are presented.
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