Angular correlation function based on the second-order Kirchhoff approximation and comparison with experiments

The angular correlation function (ACF) of scattering amplitudes is presented using the second-order Kirchhoff approximation (KA) with angular and propagation shadowing functions. The theory is applicable to surfaces with large radii of curvature and high slopes of the order of unity. The correlation consists of contributions from single and second-order scattering. The single scattering provides the necessary condition for substantial correlation to occur. The second-order scattering yields high peaks in the correlation function. The ladder term gives a peak when two waves that have the same incident and scattering angles are traveling in the same direction. The cyclic term gives another peak in the time-reversed direction. These two peaks are related by the reciprocity condition. Although the second-order KA contains several approximations and the solution is simplified to yield a numerically tractable form, its agreement with experimental results is excellent. The theory correctly shows the peaks in the ACF observed in both co-polarization and cross-polarization responses. The width of the memory line is also very close to the value predicted by the theory.