Theory and numerical simulations of x-ray nanofocusing by bent crystal in back diffraction geometry

A point-to-point x-ray focusing of a spherical wave by means of cylindrically bent crystal in symmetric Bragg back diffraction geometry was investigated theoretically and simulated numerically. To separate the focal plane from an incident x-ray beam, a thin flat crystal was introduced into the setup. The effect of flat crystal diffraction on the focusing performance of the double crystal setup is discussed. It is shown that the aberration free focusing can be achieved with aspherical surface shape of the strongly bent crystal. A correction term for the surface displacement function free from spherical aberrations is derived. Thorough numerical simulations demonstrated agreement with the theoretical analysis and excellent focusing performance of 2.4 nm. Theoretically, the demonstrated result can be further improved almost by an order of magnitude.

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