An expansion scheme, which converges rapidly, is developed for computing the backscattered cross section of electromagnetic waves from turbulent media. The scheme is based on the average rather than actual field with the use of the distorted-wave Born approximation, in which the signal is modified to include attenuation due to scattering along its path length. If the receiver beamwidth is wide enough and the scattering is very directional, no net attenuation occurs. Net loss occurs when the receiver aperture is small and the scattering is diffusive. First-order modified Born is derived in detail, and relations are evaluated. It has the potential for providing saturation in the backscattered power as the level in refractive-index fluctuation is increased. Higher-order corrections are then calculated. Second-order modified Born provides a contribution to the transverse cross-polarization that is consistent with a modified version of the result in work by R. S. Ruffine and D. A. deWolf. Both of these in turn are consistent, within the limits of directional scatter, with J. W. Strohbehn and S. F. Clifford's cross-polarization, which results from fluctuations in refractive index gradients. It is also shown that the longitudinal cross-polarized component is related to diffusion effects and angle-of-arrival deviations. However, in several experiments the postulated attenuation implicit in first-order modified Born was found to be compensated for by other effects, probably by higher-order terms.