X-RAY-SCATTERING FROM A RANDOMLY ROUGH-SURFACE

On the basis of the method of reduced Rayleigh equations we present a simple and reciprocal theory of the coherent and incoherent scattering of x-rays from one- and two-dimensional randomly rough surfaces, that appears to be free from the limitations of earlier theories of such s cattering based on the Born and distorted-wave Born approximations. In our approach, the reduced Rayleigh equation for the scattering amplit ude(s) is solved perturbatively, with the small parameter of the theor y eta(omega) = 1 - epsilon(omega), where epsilon(omega) is the dielect ric function of the scattering medium. The magnitude of eta(omega) for x-rays is in the range from 10(-6) to 10(-3) depending on the wavelen gth of the x-rays. The contributions to the mean differential reflecti on coefficient from the coherent and incoherent components of the scat tered x-rays are calculated through terms of second order in eta(omega ). The resulting expressions are valid to all orders in the surface pr ofile function. The results for the incoherent scattering display a Yo neda peak when the scattering angle equals the critical angle for tota l internal reflection from the vacuum-scattering medium interface for a fixed angle of incidence, and when the angle of incidence equals the critical angle for total internal reflection for a fixed scattering a ngle. The approach used here may also be useful in theoretical studies of the scattering of electromagnetic waves from randomly rough dielec tric-dielectric interfaces, when the difference between the dielectric constants on the two sides of the interface is small.