Defocused travelling fringes in a scanning triple-Laue X-ray interferometry setup

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