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

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 hinges. 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 mu m the measurement uncertainties at 95% confidence level are +/-30 pm, and for displacements up to 100 mu 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

A nano-metrology system with a two-dimensional combined optical and X-ray interferometer and an atomic force microscope

“…The symmetrical separation of the two optical beams can be compensated through the difference between the displacements of the two beams. The value of the lattice parameter of the Si (220) crystal was that measured by Becker et al (Becker et al 1981) and Becker (Becker 2001) because the X-ray interferometer was made of the same crystal-sourced from Wacker GmbH in Germany-that Becker et al (Becker et al 1981) and Becker (Becker 2001) had used in their measurements (the corrected lattice parameter was 0.192 015 497 ± 1.2 9 10 -8 nm in air (Basile et al 2000)). The radiation source for the X-ray interferometer was a watercooled molybdenum X-ray tube.…”

“…The two combined interferometers cause the synergy effect in a new measuring tool with a nonlinearity-free scale in the nanometer region. The COXI was developed recently by several national metrological institutes (Basile et al 2000). It provides a system for measuring one-dimensional displacements with sub-nanometer sensitivities.…”

Development of a two-dimensional nano-displacement measuring system utilizing a combined optical and x-ray interferometer

“…In the x-ray interferometer, the variation of the silicon lattice parameter depends on the temperature, atmospheric pressure, and impurities in the silicon. [7] The lattice parameter error over the 633 nm range of movement of the analyzer lamella is 1.8 × 10 -5 nm. Noises on one x-ray fringe are determined by the position error of the analyzer lamella, less than 10 pm.…”

“…The COXI provides a displacement measurement of one dimension with sub-nanometer sensitivities. [7][8][9][10] X-ray interferometer bridged the gap in dimensional metrology as compensated the non-linearity in the optical interferometer.…”

LVDT calibration using a phase modulation optical interferometer calibrated by an x-ray interferometer

“…[3] As our experiment was carried out in air, we need to consider the change of lattice parameter because of the atmospheric pressure difference. The change is given by ∆L/L = ∆p/(C 11 + 2C 12 ) with C 11 = 1.657 × 10 11 Nm -2 and C 12 = 0.639 × 10 11 Nm -2 [5], giving a corrected lattice parameter of 0.192 015 494 ± 1.2 × 10 -8 nm.…”