In 2011, a discrepancy between the values of the Planck constant measured by counting Si atoms and by comparing mechanical and electrical powers prompted a review, among others, of the measurement of the spacing of 28 Si {220} lattice planes, either to confirm the measured value and its uncertainty or to identify errors. This exercise confirmed the result of the previous measurement and yields the additional value d 220 = 192 014 711.98(34) am having a reduced uncertainty.

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. We address this challenge by proposing a method that uses the Huygens integral to propagate the electromagnetic fields and ray tracing to achieve numerical computability. Toy models are used to test the method's accuracy. Finally, we recalculate the diffraction correction for an interferometer, which was recently investigated by paraxial methods.

This paper deals with a numerical simulation of the natural convection air flow and its influence on apparent mass in high precision mass measurements. Results are in reasonable agreement with the experimental values obtained on a 1 kg silicon sphere and a 1 kg mass standard. There is clear evidence that the three-dimensional finite element model studied, allowing inclusions of the boundary and initial conditions determined experimentally, captures the most important features of convection and estimates the relevant corrections.

Measurement of the (220) Bragg-plane spacing of Si using combined x-ray and optical interferometry with an uncertainty lower than 10 −8 requires the study of influence factors not considered in the past. In this paper the Bragg-plane spacing definition itself is re-examined and the influence of a constant strain gradient is studied by means of Takagi's equations. Their analytical and numerical solutions indicate that, contrary to our previous assumption, the period of the travelling fringes is affected by the Si atom spacing at the analyser entrance surface.

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. Crystal deformation in X-ray interferometry and two-crystal spectrometry are discussed and it is demonstrated that Si lattice-parameter measurements depend on the diffracting plane spacing on the crystal surface.