Nonspecular x-ray scattering in a multilayer-coated imaging system

Abstract

We present a rigorous theoretical treatment of nonspecular x-ray scattering in a distributed imaging system consisting of multilayer-coated reflective optics. The scattering from each optical surface is obtained using a vector scattering theory that incorporates a thin film growth model to provide a realistic description of the interfacial roughness of the multilayer coatings. The theory is validated by comparing calculations based on measured roughness to experimental measurements of nonspecular scattering from a Mo–Si multilayer coating. The propagation of the scattered radiation through the optical system is described in the context of transfer function theory. We find that the effect of nonspecular scattering is to convolve the image with a point spread function that is independent of the coherence of the object illumination. For a typical soft x-ray imaging system, the scattering within the image field from the multilayer coatings is expected to be slightly greater than for single surfaces (as normalized to the reflectivity). This is because the roughness of the coatings includes both replication of the substrate roughness and the intrinsic roughness of the multilayer growth process. Our analysis indicates that the current multilayer coating technology is capable of producing soft x-ray imaging systems that have acceptably low levels of scattering, provided that the optical substrates are sufficiently smooth.