X-ray resonator cavities have been studied for many years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] to develop phase-contrast imaging, high-resolution x-ray optics, high-resolution x-ray scattering, spectroscopy and phase-contrast microscopy [2,4,7,8,11,12,16,17]. X-ray cavities have also been used to provide a coherent x-ray source for probing the dynamic structures of solid or liquid biological substances on the picosecond timescale [14] and for hard x-ray or γ-ray lasers [12,18].High-aspect-ratio x-ray resonator cavities have been fabricated with single-crystal silicon using deep etching [12,13]. However, under certain circumstances, single-crystal silicon mirrors demonstrate multiple-beam effects owing to 24-beam diffraction associated with the silicon diamond crystal structure [8,9,[12][13][14][15].