Table of contents

A type-A uncertainty analysis of the magnitude of the local gravitational field can be used to validate type-B uncertainty estimates of calibrations of triaxial accelerometers by rotation in the gravitational field. We demonstrate the application of this method to validate a type-B uncertainty estimate at the sub 0.1% level of the errors introduced by a high-accuracy, two-axis, accelerometer-characterization system.

We show the implications of angles having their own dimension, which facilitates a consistent use of units as is done for lengths, masses, and other physical quantities. We do this by examining the properties of complete trigonometric and exponential functions that are generalizations of the corresponding functions that have dimensionless numbers for arguments. These generalizations provide functions of angles with the dimension of angle as arguments, but with no reference to units. This parallels most equations in physics which are valid for any units. This property also provides a consistent framework for including quantities involving angles in computer algebra programs without ambiguity that may otherwise occur. This is in contrast to the conventional practice in scientific applications involving trigonometric or exponential functions of angles where it is assumed that the argument is the numerical part of the angle when expressed in units of radians. That practice also assumes that the functions are the corresponding radian-based versions. These assumptions allow angles to be treated as if they had no dimension and no units, an approach that can lead to important difficulties such as incorrect factors of 2π, which can be avoided by assigning an independent dimension to angles.

Nowadays, the use of the (four-wire) automatic resistance bridge is widespread in thermometry, up to the point that it is believed to be the only method to measure the resistance of thermometers with the required accuracy. However, before the introduction of this type of bridge, other methods were used in thermometry that, specifically with the comparison of thermometers, may still have their advantages. One of these is the so-called two-wire potentiometric method, described here shortly, where—unlike the four-wire method—all thermometers of the same type are placed in a series configuration, and only voltages are measured with a carefully characterized potentiometer. Additionally, a variant of the method is given which may successfully be applied with future thermometer comparisons.

Atom interferometry provides an important method of high-precision absolute gravity measurement. As absolute gravimeters, various systematic errors of atom gravimeters have been identified and evaluated. Here a comprehensive evaluation of systematic errors for a transportable atom gravimeter Huazhong University of Science and Technology-Quantum Gravimeter (HUST-QG) is presented. HUST-QG exhibited a short-term sensitivity of 24 μGal Hz^−1/2 and a combined uncertainty of 3 μGal. The operation and evaluation of HUST-QG for transportable gravity measurements during the 10th International Comparison of Absolute Gravimeters are discussed. And the degree of equivalence for HUST-QG in this comparison is 1.3 μGal, which supports our evaluation.

As optical clocks are improved to reach the frequency uncertainty below the 10⁻¹⁷ level, the frequency shift due to the blackbody radiation (BBR) has been one of the major systematic effects hindering further improvement. To evaluate the BBR shift of an Yb optical lattice clock at KRISS, we installed an in-vacuum BBR shield and made radiation thermometry using a black-coated-sphere thermal probe. After we quantitatively measured the conduction loss of the thermal probe and the effects of all the external radiation sources, we determined the temperature at the atom trap site with an uncertainty of 13 mK, which corresponds to an uncertainty of 0.22 mHz in the clock frequency (a fractional frequency of 4.2 × 10⁻¹⁹). The total uncertainty of the BBR shift including the atomic response is 9.5 × 10⁻¹⁹.

The gravimetric method is widely used to prepare standard gas mixtures in gas cylinders. Several dilution steps are required to prepare a low-amount fraction gas mixture, such as at μmol mol⁻¹ level, using the gravimetric method. We have developed a new automatic weighing system (AWS) that is applicable to a mini cylinder (100 mL or less) to reduce the number of dilution steps. The developed mini-AWS is operated by an automatic cylinder exchange mechanism that is similar to the existing AWS. However, the minimum measurable mass was decreased to measure a small amount of target gas; therefore, the gas mixture can be prepared directly at the μmol mol⁻¹ scale. This study evaluated the fundamental performance of the developed mini-AWS, and we gravimetrically prepared several gas mixtures of nominal 100 μmol mol⁻¹ carbon monoxide (CO) in nitrogen (N₂). The uncertainties of prepared gas mixtures were consistent within 0.1% of the relative expanded uncertainty. They were then compared to the standard gas mixture, which was gravimetrically prepared using the existing AWS. The compared results agreed within their expanded uncertainties (k = 2).

This paper describes the calibration of a high precision AC current measurement device which is required in a system to measure AC voltages up to 800 kV in the frequency range of 10 Hz to 400 Hz. The AC current measurement unit of such a system requires the calibration of the input current in the milliampere range at a frequency of approximately 50 Hz, and all measurements have been made at a suitable frequency of 62.5 Hz. An AC quantum voltmeter (AC-QVM) is used to achieve a traceability chain from DC resistance calibration, when it works as DC quantum standard, and as AC quantum standard for the AC current measurement. All DC and AC measurements needed for one calibration point (one current level) can be done in a rapid sequence within 30 min using the same AC-QVM, such that the combined uncertainty is at a level of 1 μA A⁻¹ (k = 1).

This paper presents the evolution of LNE's impedance bridge (Wheatstone bridge) used to calibrate AC resistors defined in the two terminal-pair configuration. A new automated Wheatstone bridge, based on four resistances, was developed to operate in the full complex plane for resistances ranging from 400 Ω to 2 MΩ and for frequencies up to 20 kHz. A commercial dual precision arbitrary waveform generator supplies the bridge and PXI modules achieve the balance. Phase and frequency synchronization solutions between the arbitrary waveform generator source and the PXI modules were used. The choice of these instruments allows the bridge to be easily automated and to benefit from recent progress in the development of digital-analog converters, in particular those with high frequency sampling rates and resolution. The bridge is mainly dedicated to realize the periodic calibration of LNE's standard resistors, used for routine customer calibrations. The traceability of LNE's standard resistors is ensured, firstly, by the calibration of a 1 kΩ resistor by comparison to a calculable resistor up to 20 kHz. Then, this resistor is used as a reference element to ensure the traceability of all LNE's standard resistors using the new bridge. The validation was done by comparing the results obtained, for some resistors with very low drift, with those obtained during calibrations performed in 1983, 1995 and 2009. For resistors of 1 kΩ in a 1:1 ratio, the expanded uncertainty of series resistance variation and argument are, respectively, less than 1.3 µΩ Ω⁻¹ (k = 1) and 1.2 µrad (k = 1), up to 20 kHz.

The refractive index (RI) of a solid depends on the illumination wavelength, temperature and material properties, such as the chemical composition, crystal structure, and isotropy. RI measurements, however, also depend on environmental conditions, such as the temperature, pressure, CO₂ concentration and humidity of the surrounding air. As these environmental conditions are not always reported, reported values of the RI are often irreproducible. Here we describe a new optical set-up based on the angle of minimum deviation to traceably measure the RI at controlled temperature, pressure, humidity, and CO₂ concentration of the surrounding air. Advantages of the reported method are that (I) we perform RI measurements without the need for an independent measurement of the prism angles, and (II) correlations in the uncertainty propagation reduce the sensitivity coefficients greatly. The absolute RI of fused silica at 20.00 °C is 1.470 091 at 404.66 nm, 1.467 169 at 435.83 nm, 1.460 459 at 546.07 nm, and 1.459 237 at 579.07 nm. The expanded uncertainty (k = 2) of the set-up and procedure is 1.4 × 10⁻⁶ for 404.66 nm, 435.83 nm, and 546.07 nm and 1.7 × 10⁻⁶ for 579.07 nm. The main factors affecting the expanded uncertainty are the calibration uncertainty of the rotary stage, and the repeatability of the measurement.

A local time scale can be generated by steering flywheel clocks with state-of-the-art optical lattice clocks. This paper presents our simulations about the influence of the optical lattice clock's operational strategies and the flywheel clock's noise characteristics on the performance of the generated time scale. By post-processing the measured frequency difference between the optical lattice clock Sr1 and the hydrogen maser HM50 at the National Institute of Metrology (NIM), during the modified Julian date (MJD) 59029–59059, a local time scale with 0.68 ns time variation referencing to the TT(BIPM20) is demonstrated.

The pressure behind the reflected shock wave (RSW) in real shock tubes deviates from the ideal behavior. This results in lower measurement accuracy and thus affects experiments and interpretations. The deviations depend on several factors, such as the pressure magnitude, shock tube geometry, and working gas. This study investigated it quantitatively and attempted to accurately describe its characteristics via the introduction of two parameters: pressure gain and pressure rise. To improve the accuracy of the pressure gain measurement, a model of the incident shock wave (ISW) attenuation was proposed and the influence of the shock tube geometry was explored. The experimental results showed that the measurement accuracy was significantly improved: in the cases of 0.07, 0.14, 0.25, and 0.30 mm thick aluminum diaphragms, it was improved by approximately 4, 7, 12, and 22 times, respectively. In addition, a model of the pressure rise dependence on the Mach number of the ISW was constructed through a linear fit of the pressure rise data. Further, the effects of the working gas on the RSW were examined: the results demonstrate that by working with the air the pressure behind the RSW exhibited good stability and amplitude.

Temperature calibration labs all around the world typically maintain a set of several triple-point-of-water (TPW) cells for regular measurements using the International Temperature Scale of 1990 (ITS-90). This set often includes more-than-10-year-old TPW cells made from a borosilicate glass. In this paper we summarize the problems with old borosilicate TPW cells, using the available literature data, the results of CCT.K7-2021 key comparison and NRC TPW measurements, and highlight the solution to these issues—vitreous-silica TPW cells. The latter have an exceptional long-term stability, as we demonstrate by using: (a) comparative measurements of the same-age, same-manufacturer vitreous-silica and borosilicate TPW cells at NRC in a period from 2007 to 2021, and (b) inductively coupled plasma-mass spectrometry (ICP-MS) analysis of impurities present in the 18 year-old vitreous-silica outlier, cell Q325. Remarkably, not only all NRC vitreous-silica TPW cells remained stable over a 15 years time period, unlike their borosilicate counterparts, but the amount of impurities in the 'coldest' cell Q325 (−31 μK from the intercomparison reference value) is comparable to that in the newly purchased vitreous-silica cells. We argue that the most accurate TPW measurements, such as for defining the national TPW references and for the international key comparisons, should rely exclusively on vitreous-silica TPW cells.