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The 18SIB04 QuantumPascal EMPIR project aims for development of photon-based standards that can replace primary standards of the SI unit of pressure, the Pascal. In this project, four partners simulated the pressure-induced deformation of a given Fabry-Pérot cavity, using various versions of two types of software, COMSOL Multiphysics (R) and ANSYS Workbench. It was demonstrated that, for a given geometry and set of material parameters, simulations of the deformation could be performed by the various partners with such small discrepancies that methodological mistakes of the simulation procedures will solely contribute to a sub-ppm uncertainty in the assessments of refractivity of N₂.

A homodyne Michelson interferometer was developed to realize a dynamic vacuum standard. The interferometer measures variation in optical path due to refractive index changes related to the pressure of the gas. The measurement arm of the interferometer is formed by two quasi-parallel mirrors which act as a multiplication set-up to allow an increment of the optical path and consequently of the sensitivity. The interference signal is detected by a high speed camera: starting from the recorded interference pattern, two quadrature regions are identified and analyzed by custom software to obtain the quadrature phase signals. The dynamic vacuum system is mainly composed of a large low-pressure chamber VA (about 800 L) connected by a valve and a replaceable orifice to a high pressure chamber VB of about 2 L, hosting the interferometer. The fast pressure drop from 100 kPa to 100 Pa is obtained by a gas expansion from VB to VA. The velocity of the expansion process can be easily varied by substituting the orifice connecting the two chambers. The response of the system was first tested with a slow process of about 40 s at different gains of the measurement arm of the interferometer. Subsequently, a fast process (< 3 s) was considered and the result of the optical device was compared to the measurements performed by two capacitance diaphragm gauges (133 kPa and 1.33 kPa full scale). The gauges are equipped with special electronics to give each nominal reading every 0.7 ms. The two measurements performed by the dynamic vacuum standard and capacitance diaphragm gauges showed an agreement better than 12%.

The volume of 28 Si spheres of about 94 mm diameter is an input datum for the determination of the Avogadro constant. We report about a finite element analysis of the self-weight effect on the volume determination via optical interferometric measurements of the sphere diameters. The self-weight expansion or shrinkage of the equatorial diameters, which ranges from 31 pm to +180 pm, depends on the southern latitude of the supports.

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