Crystal bending in triple-Laue X-ray interferometry. Part I. Theory

The measured value of the (220) lattice-plane spacing of silicon 28 using scanning X-ray interferometry is essential to realize the kilogram by counting ²⁸Si atoms. An assumption made is that the measured lattice spacing is the bulk value of an unstrained crystal forming the analyser of the interferometer. However, analytical and numerical studies of the X-ray propagation in bent crystals suggest that the measured lattice spacing might refer to the analyser surface. To confirm the result of these studies and to support experimental investigations of the matter by phase-contrast topography, a comprehensive analytical model is given of the operation of a triple-Laue interferometer having the splitting or recombining crystal bent.

Crystal bending in triple-Laue X-ray interferometry. Part II. Phase-contrast topography

In a previous paper [Sasso et al. (2023). J. Appl. Cryst.56, 707-715], the operation of a triple-Laue X-ray interferometer having the splitting or recombining crystal cylindrically bent was studied. It was predicted that the phase-contrast topography of the interferometer detects the displacement field of the inner crystal surfaces. Therefore, opposite bendings result in the observation of opposite (compressive or tensile) strains. This paper reports on the experimental confirmation of this prediction, where opposite bendings were obtained by copper deposition on one or the other of the crystal sides.

Three-dimensional model of a split-crystal X-ray and neutron interferometer

The observation of neutron interference using a crystal interferometer having a separate analyser opens the way to the construction and operation of interferometers with vast arm separation and length. Setting the design specifications requires a three-dimensional dynamical theory model of their operation. This paper develops the required three-dimensional mathematical framework, which also comprises coherent and incoherent illuminations; it is applied to study the visibility of the interference fringes.

Neutron interference from a split-crystal interferometer

The first successful operation of a neutron interferometer with a separate beam-recombining crystal is reported. This result was achieved at the neutron interferometry setup S18 at the ILL in Grenoble by a collaboration between TU Wien, ILL, Grenoble, and INRIM, Torino. While previous interferometers have been machined out of a single-crystal block, in this work two crystals were successfully aligned on nanoradian and picometre scales, as required to obtain neutron interference. As a decisive proof-of-principle demonstration, this opens the door to a new generation of neutron interferometers and exciting applications.

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

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 travelling fringes in a separate-crystal triple-Laue X-ray interferometer.

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.

X-ray phase-contrast topography to measure the surface stress and bulk strain in a silicon crystal

The measurement of the Si lattice parameter by X-ray interferometry assumes the use of strain-free crystals, which might not be true because of intrinsic stresses due to surface relaxation, reconstruction and oxidation. X-ray phase-contrast topography was used to investigate the strain sensitivity to the finishing, annealing and coating of interferometer crystals. The topography capabilities were assessed by measuring the lattice strain due to films of copper deposited on the interferometer mirror crystal. A by-product has been the measurement of the surface stresses after complete relaxation of the coatings.

Diffraction effects in length measurements by laser interferometry

High-accuracy dimensional measurements by laser interferometers require corrections because of diffraction, which makes the effective fringe-period different from the wavelength of a plane (or spherical) wave λ₀. By using a combined X-ray and optical interferometer as a tool to investigate diffraction across a laser beam, we observed wavelength variations as large as 10^-8λ₀. We show that they originate from the wavefront evolution under paraxial propagation in the presence of wavefront- and intensity-profile perturbations.

Polarization delivery in heterodyne interferometry

Optically heterodyned laser interferometry, as applied to measuring linear displacements, requires different optical frequencies to be encoded onto unique polarization states. To eliminate non-linear contributions to the interferometer signal, the frequency difference must be introduced after beam splitting and the interfering beams must be recombined via spatially separated paths. The polarization jitter of the frequency-shifted beams still originates a noise in the beat-signal phase. A formula is given expressing the noise amplitude in terms of the illuminating beam's extinction ratio.

Determination of the Avogadro constant by counting the atoms in a 28Si crystal

The Avogadro constant links the atomic and the macroscopic properties of matter. Since the molar Planck constant is well known via the measurement of the Rydberg constant, it is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a definition of the kilogram in terms of a fundamental constant. We describe a new approach for its determination by counting the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope. It enabled isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, NA = 6.022,140,78(18) × 10(23) mol(-1), is the most accurate input datum for a new definition of the kilogram.

Accuracy of laser beam center and width calculations

The application of lasers in high-precision measurements and the demand for accuracy make the plane-wave model of laser beams unsatisfactory. Measurements of the variance of the transverse components of the photon impulse are essential for wavelength determination. Accuracy evaluation of the relevant calculations is thus an integral part of the assessment of the wavelength of stabilized-laser radiation. We present a propagation-of-error analysis on variance calculations when digitized intensity profiles are obtained by means of silicon video cameras. Image clipping criteria are obtained that maximize the accuracy of the computed result.