Correlation function of gravitational deflection angles of light paths

The analytic formula for the correlation function of deflection angles of light paths due to the gravitational lens effect is derived for a simplified model universe. It is shown that the correlation function, which quantitatively expresses the strength of the gravitational lens effect due to inhomogeneities, is characterized by a single parameter. The correlation function is applied to the anisotropy of the cosmic background radiation, and the feature obtained by Sasaki (1988) and by Tomita and Watanabe (1989) is reproduced. The gravitational lens effect on the 'angular diameter distance' is discussed using the correlation function. The strength of the effect is again found to be given by the single parameter. The effect depends strongly on angular scale. 28 refs