Interstellar optics

We discuss the effects of finite source size on the diffraction pattern pro duced by scattering in a thin screen, particularly as applied to radio-wave scattering by density fluctuations in the interstellar plasma. Using the s tationary phase approximation, we express the Kirchhoff integral for the di ffracted electric field as a phasor sum and show that source structure intr oduces correlations between such sums, combined to form intensity or interf erometric visibility. We obtain expressions for the probability distributio n 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 Gaussi an distribution of intensity. We also present results for sources that radi ate Gaussian beams, possibly with imperfect spatial coherence. With these r esults, observations of the diffracted electric held yield information on t he structure of the scattered source with angular resolution corresponding to the diffraction limit of the scattering disk. These results are of inter est for studies of pulsars and other extremely compact radio sources.