Depth-graded multilayer X-ray optics with broad angular response

A method of designing depth-graded multilayer structures with broad angular response for use as coatings in X-ray optics is presented. The design is based on the well-known Fresnel equations and recursive calculation, combined with a merit function plus random variation of the thickness of each layer. This allows the design of multilayer films for different requirements in X-ray optics. Results are presented on the layer thicknesses in depth-graded W/C multilayer films and their reflectivity as a function of the grazing incidence angle for Cu K alpha radiation. The required minimum number of bilayers in depth-graded multilayer films depends on the grazing incidence angle, i.e., the saturation effect observed in the design of periodic multilayer films also emerges in the design of depth-graded multilayers. The predicted performances of multilayers designed using this method are superior to those designed using existing methods. (C) 2000 Elsevier Science B.V. All rights reserved.