This paper presents analytic expressions for the wave structure function, frequency spread of the temporal frequency spectrum, and the temporal frequency spectrum of optical signals propagating through a random medium, specifically the Earth’s atmosphere. The results are believed to be valid for all optical turbulence conditions. These expressions are developed using the Rytov approximation method. Generally, the validity of statistical quantities obtained via this method is restricted to conditions of weak optical turbulence. However, in this work, by using a modification of the effective atmospheric spectral model presented by Andrews et al. for scintillation index, wave structure function expressions have been derived that are valid in all turbulence conditions as evidenced by comparison to experimental data. Analytic wave structure function results are developed for plane, spherical, and Gaussian-beam waves for one-way propagation. For the special case of a spherical wave, comparisons are made with experimental data. The double pass case is also considered. Analytic expressions for the wave structure function are given that incorporate reflection from a smooth target for an incident spherical wave. Additionally, analytic expressions for the frequency spread of the temporal frequency spectrum and the temporal frequency spectrum itself, after one-way propagation for horizontal and slant paths, are derived for plane and spherical waves. These results are also based on the Rytov perturbation method . Expressions that are believed to be valid in all turbulence conditions are also developed by use of the effective atmospheric spectral model used in the wave structure function development. Finally, double pass frequency spread expressions are also presented. As in the case of the wave structure function, reflection from a smooth target with an incident spherical wave is considered.