Operation model of a skew-symmetric split-crystal neutron interferometer.

The observation of neutron interference using a triple Laue interferometer formed by two separate crystals opens the way to the construction and operation of skew-symmetric interferometers with extended arm separation and length. The specifications necessary for their successful operation are investigated here: most importantly, how the manufacturing tolerance and crystal alignments impact the interference visibility. In contrast with previous studies, both incoherent sources and the three-dimensional operation of the interferometer are considered.

Fake tilts in differential wavefront sensing.

Two-beam interferometry is a tool of high-precision length-metrology, where displacements are measured to within sub-nanometer resolution and accuracy. Differential wavefront sensing - via phase detection by segmented photodiodes - adds the capability of simultaneously measuring the target translation and rotation. This paper gives an analytical model explaining the observation of fake tilts by a combined x-ray and optical interferometer.

Telescope jitters and phase noise in the LISA interferometer.

The Laser Interferometer Space Antenna aims to measure picometer changes of the 2.5 × 10 km sides of a triangular constellation of satellites. Each spacecraft hosts two telescopes that simultaneously transmit and receive laser beams measuring the constellation arms by heterodyning the received wavefronts with local references.

Impurities in a Si-Enriched Single Crystal Produced for the Realization of the Redefined Kilogram.

The practical realization of the unit of mass is possible by manufacturing a perfect one-kilogram sphere from a Si-enriched single crystal. The mass of the sphere can be determined in terms of a fixed value of the Planck constant by counting the number of silicon atoms in the core of the single crystal. To reach the target 2.

Measurement of the Si Mole Fraction in the New Avogadro Silicon Material by Neutron Activation and High-Resolution γ-Spectrometry.

The use of new silicon single crystals highly enriched in Si recently produced for the upcoming redetermination of the Avogadro constant requires knowledge of their molar masses. The isotopic composition data are collected independently in different laboratories but all using the virtual element technique with multicollector inductively coupled plasma mass spectrometers. In this framework, the comparison of the results with an independent measurement of the amount of at least one of the depleted isotopes is useful to limit hidden systematic errors.

Quantification of the Void Volume in Single-Crystal Silicon.

This paper investigates the use of a method based on Cu decoration and neutron activation to determine the total volume of voids in a silicon single crystal. A measurement protocol was developed and tested in an experiment carried out with a 5 cm volume and 10 g mass high-purity natural silicon sample. The few percent uncertainty reached in the determination of the Cu concentration, at a 10 cm level, makes this method a candidate to set an upper limit to the concentration of the vacancies contributing to the void volume in the enriched silicon material used to determine the Avogadro constant.

Purity of (28)Si-Enriched Silicon Material Used for the Determination of the Avogadro Constant.

At present, counting atoms in a one-kilogram sphere made of (28)Si-enriched silicon allows the determination of the Avogadro constant with the 2.0 × 10(-8) relative standard uncertainty required for the realization of the definition of the new kilogram. With the exception of carbon, oxygen, boron, nitrogen, and hydrogen, the claimed uncertainty is based on the postulation that the silicon material used to manufacture the sphere was above a particular level of purity.

Vectorial ray-based diffraction integral: erratum.

We report and correct errors in our recently published paper [J. Opt. Soc.

Vectorial ray-based diffraction integral.

Laser interferometry, as applied in cutting-edge length and displacement metrology, requires detailed analysis of systematic effects due to diffraction, which may affect the measurement uncertainty. When the measurements aim at subnanometer accuracy levels, it is possible that the description of interferometer operation by paraxial and scalar approximations is not sufficient. Therefore, in this paper, we place emphasis on models based on nonparaxial vector beams.

(30)Si mole fraction of a silicon material highly enriched in (28)Si determined by instrumental neutron activation analysis.

The latest determination of the Avogadro constant, carried out by counting the atoms in a pure silicon crystal highly enriched in (28)Si, reached the target 2 × 10(-8) relative uncertainty required for the redefinition of the kilogram based on the Planck constant. The knowledge of the isotopic composition of the enriched silicon material is central; it is measured by isotope dilution mass spectrometry. In this work, an independent estimate of the (30)Si mole fraction was obtained by applying a relative measurement protocol based on Instrumental Neutron Activation Analysis.

Observation of a bent crystal-lattice by x-ray interferometry.

he capability of operating a separate crystal x-ray interferometer over centimeter displacements has made it possible to observe minute strain fields of a bent crystal at the atomic scale resolution by means of phase-contrast x-ray topography. Measurement and predictive capabilities of lattice strain are key ingredients of a highly accurate measurement of the Si lattice parameter and of a determination of the number of atoms in a realization of the mass unit based on an atom mass. Here we show that the observed strain can be accurately predicted by a finite-element analysis of the crystal deformation.

Si lattice parameter measurement by centimeter X-ray interferometry.

A combined X-ray and optical interferometer capable of centimeter displacements has been made to measure the lattice parameter of Si crystals to within a 3 x 10(-9) relative uncertainty. This paper relates the results of test measurements carried out to assess the capabilities of the apparatus.

Aberration effects in two-beam laser interferometers.

In displacement measurements by two-beam interferometers, the wavefront curvature of a laser beam causes a systematic increase of the fringe period. This increase depends on beam collimation: It is null for a plane wave and proportional to the squared divergence of the beam. With interfering beams not perfectly recombined, an additional fringe-period error is caused, with the effect of counteracting and also of compensating for and prevailing over the usual error.

A Fourier optics approach to the dynamical theory of X-ray diffraction--continuously deformed crystals.

X-ray diffraction in continuously deformed crystals is considered by application of Fourier optics and from the viewpoint of the analogy between X-ray dynamics and the motion of two-level systems in quantum mechanics. Different forms of Takagi's equations are traced back to a common framework and it is shown that they are different ways to represent the same propagation equation. A novel way to solve Takagi's equations in the presence of a constant strain gradient is presented and approximation methods derived from quantum mechanics are considered.

A Fourier optics approach to the dynamical theory of X-ray diffraction--perfect crystals.

A new formalism is presented concerning the dynamics of X-rays in crystals. It is based on Takagi's equations and Fourier optics; it also offers an alternative to the usual Ewald-von Laue approach. The article does not give new results but shows a new way to formulate the dynamical theory of X-ray diffraction.