New theoretical expression of X-ray reflectivity by using Green function

X-ray reflectivity is one of the most power analytical tools for observing the layered structures of thin films. So far, many calculations have been done by combining Parratt's recursive formalism with Nevot-Croce corrections on the Fresnel coefficients. The technique basically provides detailed information on the roughness of the surface and interfaces, in addition to the precise thickness values of each layer. However, the analysis of the roughness has not been always straightforward, because it is also necessary to consider multiple diffuse scattering. Recently, Dr. A. M. Polyakov (National University of Science and Technology 'MISiS', Russia) and his colleague published an interesting paper describing a novel approach to the calculation of X-ray reflectivity. Their method is based on the Green function formalism using Kirchhoff's integral equation for describing the X-ray wavefield propagation through a random rough surface separating vacuum and medium. Readers would find it interesting that the influence of multiple diffuse scattering effects upon grazing X-ray specular scattering is essential for the correlation lengths that are of the order of, and/or less than, the X-ray absorption length. Although the present calculation is only valid for the random surface heights described in the frame of Gaussian statistics, the present approach can be further extended in the future. For more information, see the papers, "X-ray specular scattering from statistically rough surfaces: a novel theoretical approach based on the Green function formalism", F. N. Chukhovskii et al., Acta Cryst., A66, 640 (2010).