A modeling approach for x-ray dynamical diffraction from multilayer Laue lenses (MLLs) with rough interfaces is developed. Although still based on the principle of the distorted-wave Born approximation (DWBA), this model is formulated from the perspective of the physical scattering process, very different from the conventional DWBA formalism. Using this model, one can study x-ray scattering from rough interfaces in the regime of Fresnel diffraction and in the case of absorptive samples, for example, x-ray dynamical diffraction from MLLs with rough interfaces, which is hard to handle in the framework of the conventional DWBA. Theoretical simulations for various MLLs with rough interfaces are conducted. It is found that interfacial roughness results in a decrease in the local diffraction intensity, where the attenuation factor is a function of the root-mean-square (rms) roughness versus the local zone width ratio. This study shows that if all zones possess an identical rms roughness value that is less than half of the outmost MLL zone width, the focal broadening effect due to roughness is almost unnoticeable, provided that the mean position of the interface does not deviate from the required zone plate law. A further study shows that uncorrelated interfacial roughness can be treated the same as interfacial diffusion, in which case a roughness factor similar to the “Debye-Waller factor” can be used, and the pseudo-Fourier coefficients of the susceptibility function for an MLL [H. F. Yan et al., Phys. Rev. B 76, 115438 (2007)] have to be multiplied by this factor.

• Received 26 November 2008

DOI:https://doi.org/10.1103/PhysRevB.79.165410