Abstract

New devices combining the Bragg reflection from periodic multilayer structures with Fraunhofer or Fresnel diffraction arising from lateral patterning of the multilayer are now available for x-ray optics. Using the Green’s-function method, we establish an integral equation for the scattered amplitude that is valid in the framework of both Fraunhofer and Fresnel diffraction. The scattered amplitude is given in the first and the second Born approximations for multilayer mirrors, laminar and sawtooth-profile multilayer gratings, and linear multilayer zone plates. The main diffractive properties of these devices are deduced. The efficiencies are computed in the first and/or in the second Born approximation and are compared with efficiencies obtained from a rigorous electromagnetic theory when they are available.

© 1993 Optical Society of America

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