Giuseppe Basile

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

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.

Phase Modulation in High-resolution Optical Interferometry

The measurement of nanometre displacements with picometre resolution has been made possible by a phase-modulation recovery scheme applied to an optical Michelson interferometer using polarization encoding. In contrast to conventional schemes, phase modulation is carried out before the interferometer optics. In this way, the low-frequency components of the phase shift between the two interfering beams are locked at zero (within limits set only by shot noise) before beam splitting by a feedback loop driving the modulator. An interferometer prototype, illuminated by a beam thus modulated, was constructed and coupled to an X-ray interferometer to compare the optical and X-ray interferometric measurement values of sub-nanometre displacements. A resolution better than 1 pm over a 100 Hz bandwidth was obtained.

The (220) lattice spacing of silicon

Further details are given of an experiment based on combined X-ray and optical interferometry to measure the (220) lattice spacing of silicon. A resolution of 5/spl times/10/sup -9/ d/sub 220/ was achieved and the silicon d/sub 220/ was determined to 3/spl times/10/sup -8/ d/sub 220/ accuracy. The measured value is d/sub 220/=(192015.551/spl plusmn/0.005) fm. After correction for the impurity-induced lattice strain, d/sub 220/=(192015.569/spl plusmn/0.006) fm was obtained. >

A four reflection laser interferometer for vibration measurements

This paper describes the study of the characteristics of the four-reflection interferometer components, the interferometer realization and the experimental results concerning the vibration measurement by the Minimum-point method and the Sine approximation method. The theoretical study of the beam intensity losses in all the optical components was performed. The comparison between this interferometer and the two-reflection interferometer used in IMGC, by applying the Minimum-point method, has shown comparable results about the sensitivity of the same vibration transducer in the range up to 10 kHz, a higher short term stability and the extension of the frequency range up to 20 kHz with the four reflection interferometer. The basic configuration of the four reflection interferometer was modified in order to get two output quadrature signals, which allow the determination of the amplitude and phase of the displacement by the Sine approximation method. This solution (interferometer and Sine approximation method) makes possible a further extension of the frequency limit to 30 kHz, displacement measurements of the order of nanometers, with a standard uncertainty of 50 pm and the application of a complete and automatic calibration procedure.

A Bragg silicon lattice comparator

The basic principle and the results of the feasibility study of a Bragg lattice parameter comparator, developed within the framework of the Standards, Measurements, and Testing European Project silicon for mass unit and standard (SIMUS) are described. It combines a Bragg lattice comparator (Hart-Hausermann design) and an X-ray angle interferometer to determine the angular position of diffraction peaks. Comparisons between Si crystals with a relative uncertainty of 1/spl times/10/sup -8/ are expected.

Four-reflection interferometer configuration for vibration calibration

In this paper the characteristics of a test bed for checking the theoretical behavior of a multi reflection interferometer are described. This optical interferometer has to be coupled to a shaker for the absolute determination of the vibration amplitudes. Its capability of producing four reflections on the measuring beam on the vibrating table, before its recombination with the reference beam, allows to extend the frequency limit at which the optical signal is still satisfactory. The test bed reproduces the working conditions, including the limitations to tilting, optical path length, alignment... and has the objective of experimentally confirm the feasibility study.

A Bragg silicon lattice comparator [for Avogadro constant determination]

The basic principle and results of the feasibility study of a Bragg lattice comparator are described. It combines a Bragg lattice comparator, Hart-Hausermann (H-H) model, with an X-ray angle interferometer for the determination of the angular position of diffraction peaks. Comparisons between Si crystal lattices with an relative uncertainty of 1/spl times/10/sup -8/ are expected.

The silicon (220) lattice spacing: analysis of a new measurement

A new experiment has been run for the past year at the IMGC to measure the (220) lattice spacing in silicon by X-ray/optical/interferometry. The data so far collected show that the experiment is capable of 5/spl times/10/sup -9/ resolution. A new determination of silicon d/sub 220/ is reported.<<ETX>>

An experiment in X-ray interferometry: accuracy and resolution in Si d/sub 220/ determination

The authors analyze the resolution and the accuracy obtained in an experiment carried out to measure the silicon lattice spacing with scanning X-ray interferometry equipment. This study was prompted by the observation of a discrepancy in comparing results obtained by the authors with those obtained by other research groups. With the previous apparatus used by the authors, compensation and correction for systematic errors required considerable effort during interferometer coupling and experiment execution. With the use of a new X-ray/optical interferometer, cosine and Abbes errors are expected to remain below 10/sup -7/, even if, in the worst case, trajectory misalignment and offset occur. Contribution to the error budget of the crystal temperature and diffraction effects in the optical interferometer have also been considered and reduced to acceptable levels. Experimental tests and a theoretical analysis show that improvements are possible and that the desired accuracy can be obtained. A new set of lattice spacing measurements with the new apparatus is being carried out to reduce the overall uncertainty to a few parts in 10/sup -8/.<<ETX>>