A series expression is developed for the fourth moment of a beamed field incident on a random phase screen or an extended medium. The series has a symmetry that allows its first few terms to generate useful approximations at both low and high spatial frequency. The parabolic wave equation, the Markov approximation, and Gaussian refractive index fluctuations are assumed. The result for the phase screen is obtained by Green's function techniques. The extended-medium result is derived in an analogous manner by using path integral methods. The same results are also derived by moment-equation methods. The behavior of the leading terms is compared to previous results for plane-wave and point-source geometries.