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X-ray diffraction imaging using perfect crystals.

The imaging properties of perfect crystals, used for controlling and directing x-ray beams in imaging systems, are analyzed using optical transfer functions. The optical transfer functions are related to the point-spread functions for the crystal imaging system and are derived from a one-dimensional Fourier transform of the Takagi-Taupin equations. Images obtained using diffracting crystals as optical elements are simulated for the Laue and Bragg geometries using a Fourier transform method and the imaging characteristics of each of these crystal configurations are analyzed. It is demonstrated that the perfect crystals act as spatial filters of the object wave.