Born's method is applied to the time-dependent wave equation. Exact solutions, valid for all wavelengths, are obtained for the first-order perturbation terms for monochromatic plane and spherical waves propagating in random media with stationary temporal fluctuations. It is shown that the temporal fluctuations of the medium can be neglected if the temporal frequencies of the fluctuations are much less than the frequency of the propagating wave and if the propagation time from the transmitter to receiver is much less than the coherence time of the medium. In the atmosphere for the case where (λ30/l40)L≪ 1, where l0 is the inner scale of turbulence, log-amplitude and phase covariance functions were calculated for the polarized and depolarized fluctuations of plane waves propagating in slightly different directions. Numerical evaluation revealed that the polarized log-amplitude fluctuations decorrelate for angular separations on the order of tan−1 [(λ0/L)1/2] while phase fluctuations decorrelate for angular separations on the order of tan−l(L0/L), where L0 is the outer scale of turbulence.