The coherent backscattering effect for moving scatterers

The constructive interference of backscattered waves that propagate along the same path in opposite directions doubles the intensity of these waves. When the scatterers move during wave propagation, the enhancement factor is reduced from 2 to a lower value. I derive the enhancement factor for coherent backscattering under the assumption that the scatterers move independently with a constant velocity. The resulting enhancement value depends exponentially on $\langle v^2 \rangle^{1/2} t /\lambda$, which is the ratio of the root-mean-square displacement of the scatterers during the wave propagation to the wavelength, and on the number of scatterers encountered.