Combined optical and X–ray interferometry for high–precision dimensional metrology

TLDR

The need to calibrate transducers with sub‑nanometre sensitivity drives the use of a combined optical and X‑ray interferometer, since optical fringes can be measured precisely but their subdivision introduces significant errors at that scale. The instrument uses an X‑ray interferometer to linearly subdivide optical fringes, with each X‑ray fringe equal to the silicon (220) lattice spacing (~0.19 nm); polarization encoding and phase modulation lock the optical interferometer to the fringe null, while traceability is achieved through calibrated silicon lattice parameters and laser frequency, and the system incorporates a silicon monolith interferometer, a parabolic X‑ray collimator, and servo control. Null‑point measurement yields maximum noise rejection, and the combined interferometer achieves 95 % confidence uncertainties of ±30 pm for displacements up to 1 m, ±35 pm up to 100 m, and ±170 pm up to 1 mm.

Abstract

The requirement for calibrating transducers having subnanometre displacement sensitivities stimulated the development of an instrument in which the displacement is measured by a combination of optical and X–ray interferometry. The need to combine both types of interferometry arises from the fact that optical interferometry enables displacements corresponding to whole numbers of optical fringes to be measured very precisely, but subdivision of an optical fringe may give rise to errors that are significant at the subnanometre level. The X–ray interferometer is used to subdivide the optical fringes. Traceability to the meter is achieved via traceable calibrations of the lattice parameter of silicon and of the laser frequency.Polarization encoding and phase modulation allow the optical interferometer to be precisely set on a specific position of the interference fringe—the null point setting. The null point settings in the interference fringe field correspond to dark or bright fringes. Null measurement ensures maximum possible noise rejection. However, polarization encoding makes the interferometer nonlinear, but all nonlinearity effects are effectively zero at the fringe set point. The X–ray interferometer provides the means for linear subdivision of optical fringes. Each X–ray fringe corresponds to a displacement that is equal to the lattice parameter of silicon, which is ca .0.19 nm for the (220) lattice planes. For displacements up to 1 m the measurement uncertainties at 95% confidence level are ± 30 pm, and for displacements up to 100 m and 1 mm the uncertainties are ± 35 and ± 170 pm, respectively.Important features of the instrument, which is located at the National Physical Laboratory, are the silicon monolith interferometer that both diffracts X–rays and forms part of the optical interferometer, a totally reflecting parabolic collimator for enhancing the usable X–ray flux and the servo–control for the interferometers.