Cairns, B., and J.T. Foley, 1993: Contribution of the second-order Born approximation to the scattered intensity. Opt. Comm., 101, 144-150.
Weak scattering is usually analyzed by using the first-order terms for the field to calculate the scattered intensity. We investigate the contribution to the scattered intensity made by the product of the zeroth-order and second-order terms of the Born approximation for the field, for two different geometries, for the case in which the scattering potential is a zero-mean random process and the scattering medium is quasi-homogeneous. It is shown that in some situations the product of first-order terms is sufficient for calculating the scattered intensity, but that in other situations the contribution from the product of the zeroth-order and second-order terms must be included. This result is directly applicable to the question of whether spectral shifts will be observed in scattering from elastic media.