Interstellar Optics

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Abstract
We discuss the effects of finite source size on the diffraction pattern produced by scattering in a thin screen, particularly as applied to radio-wave scattering by density fluctuations in the interstellar plasma. Using the stationary phase approximation, we express the Kirchhoff integral for the diffracted electric field as a phasor sum and show that source structure introduces correlations between such sums, combined to form intensity or interferometric visibility. We obtain expressions for the probability distribution functions of intensity of a source of finite size and of interferometric visibility on a baseline shorter than the scale of the diffraction pattern. We also present expressions for the first and second moments of intensity and visibility, for arbitrary source structure, and for sources with Gaussian distribution of intensity. We also present results for sources that radiate Gaussian beams, possibly with imperfect spatial coherence. With these results, observations of the diffracted electric field yield information on the structure of the scattered source with angular resolution corresponding to the diffraction limit of the scattering disk. These results are of interest for studies of pulsars and other extremely compact radio sources.