Coherent scattering from tilted objects

The extension of the Fresnel integral to tilted objects is studied using both analytical and numerical approaches. Exact solutions of the parabolic wave equation are used for this purpose. The wavefields produced by a beam propagating at an arbitrary angle θ≠π/2 relative to the object surface are investigated. The diffraction patterns are simulated for 1° ≤ θ ≤ 10°. It is shown that the inverse problem for tilted objects can be reduced to a Fredholm-type integral equation. Both 2D and 3D geometries are considered. The results may be useful as a theoretical framework for the development of coherent reflection imaging of tilted objects and x-ray imaging of submicron footprints of relativistic electron beams for measurement of their size and shape.

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