Defocused travelling-fringes in scanning triple-Laue x-ray interferometry

The measurement of the silicon lattice parameter by a separate-crystal triple-Laue x-ray interferometer is a key step for the kilogram realisation by counting atoms. Since the measurement accuracy is approaching nine significant digits, a reliable model of the interferometer operation is demanded to quantify or exclude systematic errors. This paper investigates both analytically and experimentally the effect of defocus (a difference between the splitter-to-mirror distance on the one hand and the analyser-to-mirror one on the other) on the phase of the interference fringes and the measurement of the lattice parameter.