X-ray angle interferometry: a practical set-up for calibration in the microrad range with nanorad resolution

X-ray interferometry is a crystallographic diffraction technique utilizing a moiré effect generated by the lattice. If almost perfect silicon single crystals are employed, scanning of the periodic moiré can be used for the calibration of translation or rotation on a nanometric scale since the lattice parameter is well known in terms of the SI unit of length. A monolithic x-ray angle interferometer consisting of two crystal blocks and a connecting flexure spring allowing relative rotation was manufactured. Each block supports two x-ray optical lamellae. Their optimum thickness for good visibility of the angular moiré fringes during rotation was calculated using the dynamical theory of x-ray diffraction. The main block serves as the base of the interferometer and also incorporates the piezoelectric drive. This arrangement of three bimorph actuator blades allows angular scanning through the zero degree position in order to use the full Bragg reflection width. Pre-tensioning of the flexure spring, balancing of the rotating part and angular scanning are possible simultaneously. Different operating modes, free-running and locked to the fringe slope, were tested. This very compact device can be used as a stand-alone instrument or as a fine scale in a large angle measuring calibrating facility.