Highlights of 2018

The special least-squares adjustment of the values of the fundamental constants, carried out by the Committee on Data for Science and Technology (CODATA) in the summer of 2017, is described in detail. It is based on all relevant data available by 1 July 2017. The purpose of this adjustment is to determine the numerical values of the Planck constant h, elementary charge e, Boltzmann constant k, and Avogadro constant N_A for the revised SI expected to be established by the 26th General Conference on Weights and Measures when it convenes on 13–16 November 2018.

Sufficient progress towards redefining the International System of Units (SI) in terms of exact values of fundamental constants has been achieved. Exact values of the Planck constant h, elementary charge e, Boltzmann constant k, and Avogadro constant N_A from the CODATA 2017 Special Adjustment of the Fundamental Constants are presented here. These values are recommended to the 26th General Conference on Weights and Measures to form the foundation of the revised SI.

The definition of the kilogram in the International System of Units (SI) is expected to be revised in 2018. The present definition of the kilogram, the mass of the International Prototype of the Kilogram (IPK), adopted in 1889, would then be replaced by a definition based on a fixed numerical value of the Planck constant. The Consultative Committee for Mass and Related Quantities has requested that, as one of the essential steps before the redefinition, a comparison of kilogram realizations based on future realization methods, Kibble⁹ balances and x-ray crystal density (XRCD) experiments, be organized.

This comparison was carried out during 2016 in the form of a 'Pilot Study'. One aim of the study was to determine the uniformity of mass dissemination after the redefinition by comparing mass calibrations based on different future realization experiments. Another aim was to test the continuity of the mass unit across the redefinition by comparing mass calibrations based on Kibble balances and XRCD experiments with those based on the IPK. This paper describes the organization of the comparison and presents its results.

A list of standard reference frequency values (LoF) of quantum transitions from the microwave to the optical regime has been recommended by the International Committee for Weights and Measures (Comité international des poids et mesures, CIPM) for use in basic research, technology, and for the metrology of time, frequency and length. The CIPM LoF contains entries that are recommended as secondary representations of the second in the International System of Units, and entries that can be used to serve as realizations of the definition of the metre. The historical perspective that led to the CIPM LoF is outlined. Procedures have been developed for updating existing, and validating new, entries into the CIPM LoF. The CIPM LoF might serve as an entry for a future redefinition of the second by an optical transition.

The International Committee for Weights and Measures (CIPM), at its meeting in October 2017, followed the recommendation of the Consultative Committee for Units (CCU) on the redefinition of the kilogram, ampere, kelvin and mole. For the redefinition of the kelvin, the Boltzmann constant will be fixed with the numerical value 1.380 649  ×  10⁻²³ J K⁻¹. The relative standard uncertainty to be transferred to the thermodynamic temperature value of the triple point of water will be 3.7  ×  10⁻⁷, corresponding to an uncertainty in temperature of 0.10 mK, sufficiently low for all practical purposes. With the redefinition of the kelvin, the broad research activities of the temperature community on the determination of the Boltzmann constant have been very successfully completed. In the following, a review of the determinations of the Boltzmann constant k, important for the new definition of the kelvin and performed in the last decade, is given.

Metrological traceability is the property of a measurement result whereby it can be related to a stated reference through a documented unbroken chain of calibrations, each contributing to the measurement uncertainty. The stated reference can be the International System of Units, and more specifically a realisation of a primary standard with its value and uncertainty expressed in SI units, which offers many benefits such as long term stability and the ability to reproduce the standard within its stated uncertainty at any time. Alternatively, measurements can be made traceable to an empirical scale, an approach that has evolved for practical reasons to meet the needs of certain measurement communities. We explore the benefits and drawbacks of these two measurements systems as they have evolved for greenhouse gas measurements at background levels and outline the advantages of using elements from each to secure a more robust measurement infrastructure. In particular, this work examines the importance of compatibility, the accuracy of measurement results and the benefits of comparisons with independent primary standards.

Graphene-based quantised Hall resistance standards promise high precision for the unit ohm under less exclusive measurement conditions, enabling the use of compact measurement systems. To meet the requirements of metrological applications, national metrology institutes developed large-area monolayer graphene growth methods for uniform material properties and optimized device fabrication techniques. Precision measurements of the quantised Hall resistance showing the advantage of graphene over GaAs-based resistance standards demonstrate the remarkable achievements realized by the research community. This work provides an overview over the state-of-the-art technologies in this field.

The Kibble balance is expected to become an important instrument in the near future for realizing the unit of mass, the kilogram, in the revised international system of units (SI). The Kibble balance assumes an equality of two magnetic profiles measured in the weighing and velocity phases. A recent study conducted in the Kibble balance group at the Bureau International des Poids et Mesures (BIPM) showed that the coil current could significantly affect the magnetic profile, which should be carefully taken into account in the Kibble balance experiment. This paper gives a deeper understanding and investigation of the effect, and discusses the magnetic profile change due to the coil current, for both the classical two-mode and the one-mode Kibble balances. The coil current effect has been theoretically and experimentally investigated based on a typical magnet design with an air gap. One important conclusion found in the one-mode Kibble balance is that the magnetic profile change measured in the velocity phase is twice the change in the weighing phase. A compensation suggestion, to minimize the profile change due to the coil current in a BIPM-type magnet, is presented.

In both meteorological and metrological applications, it is well known that air temperature sensors are susceptible to radiative errors. However, it is not widely known that the radiative error measured by an air temperature sensor in flowing air depends upon the sensor diameter, with smaller sensors reporting values closer to true air temperature. This is not a transient effect related to sensor heat capacity, but a fluid-dynamical effect arising from heat and mass flow in cylindrical geometries. This result has been known historically and is in meteorology text books. However, its significance does not appear to be widely appreciated and, as a consequence, air temperature can be—and probably is being—widely mis-estimated.

In this paper, we first review prior descriptions of the 'sensor size' effect from the metrological and meteorological literature. We develop a heat transfer model to describe the process for cylindrical sensors, and evaluate the predicted temperature error for a range of sensor sizes and air speeds. We compare these predictions with published predictions and measurements. We report measurements demonstrating this effect in two laboratories at NPL in which the air flow and temperature are exceptionally closely controlled. The results are consistent with the heat-transfer model, and show that the air temperature error is proportional to the square root of the sensor diameter and that, even under good laboratory conditions, it can exceed 0.1 °C for a 6 mm diameter sensor.

We then consider the implications of this result. In metrological applications, errors of the order of 0.1 °C are significant, representing limiting uncertainties in dimensional and mass measurements. In meteorological applications, radiative errors can easily be much larger. But in both cases, an understanding of the diameter dependence allows assessment and correction of the radiative error using a multi-sensor technique.

Improvements of the systematic uncertainty, frequency instability, and long-term reliability of the two caesium fountain primary frequency standards CSF1 and CSF2 at PTB (Physikalisch-Technische Bundesanstalt) are described. We have further investigated many of the systematic effects and made a number of modifications of the fountains. With an optically stabilized microwave oscillator, the quantum projection noise limited frequency instabilities are improved to for CSF1 and for CSF2 at high atom density. The systematic uncertainties of CSF1 and CSF2 are reduced to and , respectively. Both fountain clocks regularly calibrate the scale unit of International Atomic Time (TAI) and the local realization of Coordinated Universal Time, UTC(PTB), and serve as references to measure the frequencies of local and remote optical frequency standards.

For decades, the quantum behavior of Josephson junctions has been employed as intrinsic standards for voltage metrology. Conventional dc Josephson voltage standards have been the primary standards for voltage, programmable Josephson voltage standards have been implemented in calibration services and precision measurements, such as the Planck constant, and Josephson arbitrary waveform synthesizers have been employed in ac voltage calibrations and precision measurements of the Boltzmann constant. With the anticipated redefinition of the Système International d'Unités, all types of Josephson voltage standards will become intrinsic standards and equivalent realizations of the unit volt. Here we review the state-of-the art performance, best practices, and current impact of these systems for various applications, with an emphasis on ac voltage metrology. We explain the limitations of each system, especially regarding the many potential systematic errors that affect their accuracy and performance for specific applications.

Cold atoms are excellent metrological tools; they currently realize SI time and, soon, SI pressure in the ultra-high (UHV) and extreme high vacuum (XHV) regimes. The development of primary, vacuum metrology based on cold atoms currently falls under the purview of national metrology institutes. Under the emerging paradigm of the 'quantum-SI', these technologies become deployable (relatively easy-to-use sensors that integrate with other vacuum chambers), providing a primary realization of the pascal in the UHV and XHV for the end-user. Here, we discuss the challenges that this goal presents. We investigate, for two different modes of operation, the expected corrections to the ideal cold-atom vacuum gauge and estimate the associated uncertainties. Finally, we discuss the appropriate choice of sensor atom, the light Li atom rather than the heavier Rb.

A primary-standard flowing-water optical power meter for measuring multi-kilowatt laser emission has been built and operated. The design and operational details of this primary standard are described, and a full uncertainty analysis is provided covering the measurement range from 1–10 kW with an expanded uncertainty of 1.2%. Validating measurements at 5 kW and 10 kW show agreement with other measurement techniques to within the measurement uncertainty.

Absolute measurements of water vapor densities have been carried out using a new concept of frequency-stabilized cavity ring-down spectroscopy. Our scheme is based on the use of a pair of phase-locked extended cavity diode lasers, emitting at 1.39 m, one of them being locked to a self-referenced optical frequency comb synthesizer. An intrinsically stable high-finesse optical cavity that tracks the laser frequency scans has been used. High quality, comb-calibrated, absorption spectra have been recorded in a certified H₂O/N₂ gas mixture at different gas pressures, in coincidence with the 2 transition of the H₂ ¹⁸O   +   band. Water vapor mole fractions have been determined with a statistical uncertainty of 0.6. Systematic deviations have been identified and carefully quantified, thus leading to an overall uncertainty of 0.8.

General lighting is undergoing a revolutionary change towards LED-based technologies. To provide firm scientific basis for the related colorimetric and photometric measurements, this paper presents the development of new white-LED-based illuminants for colorimetry, and their evaluation to recommend a new reference spectrum for calibration of photometers. Spectra of 1516 LED products were measured and used to calculate eight representative spectral power distributions for LED sources of different correlated colour temperature categories. The suitability of the calculated representative spectra for photometer calibration was studied by comparing average spectral mismatch errors with CIE Standard Illuminant A, which has been used for decades as the reference spectrum for incandescent standard lamps in calibration of photometers. It was found that in general, when compared with Standard Illuminant A, all the potential LED calibration spectra reduced spectral mismatch errors when measuring LED products. Out of the potential LED calibration spectra tested, the white LED spectrum with correlated colour temperature of 4103 K was found to be the most suitable candidate to complement Standard Illuminant A in luminous responsivity calibrations of photometers. When compared with Standard Illuminant A, employing the 4103 K reference spectrum reduced the spectral mismatch errors, on average, by approximately a factor of two in measurements of LED products and lighting. Furthermore, the new LED reference spectrum was found to reduce the spectral mismatch errors in measurements of daylight, and many types of fluorescent and discharge lamps, indicating that the proposed reference spectrum is a viable alternative to Standard Illuminant A for calibration of photometers.

We develop a relativistic treatment of interference between light reflected from a falling cube retroreflector in the vertical arm of an interferometer, and light in a reference beam in the horizontal arm. Coordinates that are nearly Minkowskian, attached to the falling cube, are used to describe the propagation of light within the cube. Relativistic effects such as the dependence of the coordinate speed of light on gravitational potential, propagation of light along null geodesics, relativity of simultaneity, and Lorentz contraction of the moving cube, are accounted for. The calculation is carried to first order in the gradient of the acceleration of gravity. Analysis of data from a falling cube gravimeter shows that the propagation time of light within the cube itself causes a significant reduction in the value of the acceleration of gravity obtained from measurements, compared to assuming reflection occurs at the face. An expression for the correction to g is derived and found to agree with experiment. Depending on the instrument, the correction can be several microgals, comparable to commonly applied corrections such as those due to polar motion and earth tides. The controversial 'speed of light' correction is discussed.

In the paper by Ashby (2018 Metrologia 55 1–10) the correction due to the time delay of light propagated through the prism retroreflector of absolute gravimeters is discussed. Accordingly, the correction of about  −6.8 µGal should be applied for a typical gravimeter such as the most precise FG5(X) gravimeter declaring standard uncertainty at the level of 2 µGal. In consequence, the present gravimetric results related to the Kibble balance or the global absolute gravity reference system should be significantly changed. However, such a change needs a deeper scientific consensus. In our comment, we would like to show that the proposed correction should not be applied since the author's consideration is incorrect.

The comment (Křen and Pálinkás 2017 Metrologia 55 314–5) claims that the paper Relativistic theory of the falling cube gravimeter (Ashby 2017 Metrologia 55 1–10) is incorrect. The authors of this comment assert that optical paths in the two interferometer arms of an absolute gravimeter shift only the absolute phase difference between interferometer arms and therefore cannot affect the measured value of g, and that the only needed relativistic correction is the commonly applied 'speed of light correction'. Neither claim stands up to scrutiny.

Although the equation of motion developed in the paper (Ashby 2018 Metrologia 55 1) depends on the parameters of the falling cube, such as the depth and refraction index, the parameters are only associated with powers of time no greater than one, and so do not affect the acceleration. The paper's correction due to light propagation within the cube is therefore not supported by the equation of motion, and was probably caused by omissions in the data analysis. The 'speed of light' component of the acceleration that follows from the equation agrees with the results obtained by other authors.

The comment (Nagornyi 2018 Metrologia) claims that, notwithstanding the conclusions stated in the paper Relativistic theory of the falling cube gravimeter (Ashby 2008 Metrologia 55 1–10), there is no need to consider the dimensions or refractive index of the cube in fitting data from falling cube absolute gravimeters; additional questions are raised about matching quartic polynomials while determining only three quantities. The comment also suggests errors were made in Ashby (2008 Metrologia 55 1–10) while implementing the fitting routines on which the conclusions were based. The main contention of the comment is shown to be invalid because retarded time was not properly used in constructing a fictitious cube position. Such a fictitious position, fixed relative to the falling cube, is derived and shown to be dependent on cube dimensions and refractive index. An example is given showing how in the present context, polynomials of fourth order can be effectively matched by determining only three quantities, and a new compact characterization of the interference signal arriving at the detector is given.

A recent paper (Ashby 2018 Metrologia 55 1) provides a rigorous relativistic treatment of the laser interferometer with a free-falling cube retroreflector. When considering the phase shift due to the light propagation within the glass cube, the associated effect was found to be 6.8 µGal. The constant phase shift was misinterpreted in the data analysis, producing a pseudo effect. We show that the time-dependent phase shift within the glass cube causes a negligible bias of the computed gravity acceleration and analyze the misconceptions that afforded a different conclusion.

In the subject paper Ashby (2018 Metrologia 55 1–10) of the comment Svitlov (2018 Metrologia 55 609–13), light propagation through an absolute gravimeter was analyzed, including the propagation delay through the falling retroreflector and through the vacuum. The resulting expression for the interference signal applies without any subsequent 'speed of light' correction. Other corrections appeared for the three fitting parameters and g, which are, respectively, the initial position and velocity, and the acceleration of gravity at the reference point. The comment assumes the value of Z₀ is known a priori; this case was not addressed in Ashby (2018 Metrologia 55 1–10). Also, the comment misunderstands statements made in Ashby (2018 Metrologia 55 1–10) regarding the derivation of the relativistic/non-relativistic parts of the corrections (equation (47) of Ashby (2018 Metrologia 55 1–10)), and mistakenly claims they apply to the undifferenced interference signal. In this reply we show why, because of inapplicable assumptions, approximations and misunderstandings, the comment does not apply to the results of Ashby (2018 Metrologia 55 1–10).

We report on characterizations of single-electron pumps at the highest accuracy level, enabled by improvements of the small-current measurement technique. With these improvements a new accuracy record in measurements on single-electron pumps is demonstrated: 0.16 µA · A⁻¹ of relative combined uncertainty was reached within less than 1 d of measurement time. Additionally, robustness tests of pump operation on a sub-ppm level revealed a good stability of tunable-barrier single-electron pumps against variations in the operating parameters.

We report the absolute frequency measurement of the unperturbed transition ${{}^{1}}{{\text{S}}_{0}}$ – ${{}^{3}}{{\text{P}}_{0}}$ at 578 nm in ¹⁷¹Yb realized in an optical lattice frequency standard relative to a cryogenic caesium fountain. The measurement result is 518 295 836 590 863.59(31) Hz with a relative standard uncertainty of $5.9\times {{10}^{-16}}$. This value is in agreement with the ytterbium frequency recommended as a secondary representation of the second in the International System of Units.

We give a pedagogical description of the method to extract the charge radii and Rydberg constant from laser spectroscopy in regular hydrogen (H) and deuterium (D) atoms, that is part of the CODATA least-squares adjustment (LSA) of the fundamental physical constants. We give a deuteron charge radius ${{r}_{\text{d}}}$ from D spectroscopy alone of 2.1415(45) fm. This value is independent of the measurements that lead to the proton charge radius, and five times more accurate than the value found in the CODATA Adjustment 10. The improvement is due to the use of a value for the $1S\to 2S$ transition in atomic deuterium which can be inferred from published data or found in a PhD thesis.

The fundamental limits of atomic fountains as operational clocks are considered. Four rubidium fountains in operation at the US Naval Observatory for over 5.5 years have demonstrated unprecedented long-term stability for continuously running clocks (Peil et al 2014 Metrologia 51 263–9, Peil et al 2016 J. Phys.: Conf. Ser. 723 012004). With only these rubidium fountains, a post-processed timescale can be created that demonstrates superior long-term performance to any individual clock by compensating for occasional frequency steps. By comparing to the world's primary standards we demonstrate instability of this rubidium fountain timescale reaching the mid 10⁻¹⁷'s and zero drift at the level of 1.3  ×  10⁻¹⁹ d⁻¹. We discuss fundamental limits due to common mode behaviour or individual fountain performance that cannot be corrected.

Gaiser et al published in 2013 (Metrologia 50 L7–11) a second, improved value of the Boltzmann constant k determined by dielectric-constant gas thermometry at the triple point of water (k  =  1.380 6509  ×  10⁻²³ J K⁻¹, relative standard uncertainty 4.3 parts per million (4.3 ppm)). Subsequently, the uncertainty was able to be reduced to 4.0 ppm by reanalysing the pressure measurement. Since 2013, further progress regarding this primary-thermometry method has been achieved in terms of the design and the assembly of the measuring capacitors, the determination of their effective compressibility, the sensitivity of the capacitance bridge, and the scattering and the evaluation of the data. Based on a huge amount of data, two new k values have been obtained by applying two different capacitors. The combination of these two values with the 2013 result, fully taking into account the correlations, has yielded a final result of k  =  1.380 6482  ×  10⁻²³ J K⁻¹ with a relative standard uncertainty of 1.9 ppm. This value is about 0.2 ppm smaller than the CODATA 2014 one, which has a relative standard uncertainty of 0.57 ppm.

This paper summarizes the final results of the electron counting capacitance standard experiment at the Physikalisch-Technische Bundesanstalt (PTB) achieved since the publication of a preliminary result in 2012. All systematic uncertainty contributions were experimentally quantified and are discussed. Frequency-dependent measurements on the 1 pF cryogenic capacitor were performed using a high-precision transformer-based capacitance bridge with a relative uncertainty of 0.03 µF F⁻¹. The results revealed a crucial problem related to the capacitor, which hampered realizing the quantum metrology triangle with an accuracy corresponding to a combined total uncertainty of better than a few parts per million and eventually caused the discontinuation of the experiment at PTB. This paper provides a conclusion on the implications for future quantum metrology triangle experiments from the latest CODATA adjustment of fundamental constants, and summarizes perspectives and outlooks on future quantum metrology triangle experiments based on topical developments in small-current metrology.

We report on the first comparison of distant caesium fountain primary frequency standards (PFSs) via an optical fiber link. The 1415 km long optical link connects two PFSs at LNE-SYRTE (Laboratoire National de métrologie et d'Essais—SYstème de Références Temps-Espace) in Paris (France) with two at PTB (Physikalisch-Technische Bundesanstalt) in Braunschweig (Germany). For a long time, these PFSs have been major contributors to accuracy of the International Atomic Time (TAI), with stated accuracies of around $3\times {{10}^{-16}}$. They have also been the references for a number of absolute measurements of clock transition frequencies in various optical frequency standards in view of a future redefinition of the second. The phase coherent optical frequency transfer via a stabilized telecom fiber link enables far better resolution than any other means of frequency transfer based on satellite links. The agreement for each pair of distant fountains compared is well within the combined uncertainty of a few 10⁻¹⁶ for all the comparisons, which fully supports the stated PFSs' uncertainties. The comparison also includes a rubidium fountain frequency standard participating in the steering of TAI and enables a new absolute determination of the ⁸⁷Rb ground state hyperfine transition frequency with an uncertainty of $3.1\times {{10}^{-16}}$.

This paper is dedicated to the memory of André Clairon, who passed away on 24 December 2015, for his pioneering and long-lasting efforts in atomic fountains. He also pioneered optical links from as early as 1997.

We present a summary of the Planck constant determinations using the NRC watt balance, now referred to as the NRC Kibble balance. The summary includes a reanalysis of the four determinations performed in late 2013, as well as three new determinations performed in 2016. We also present a number of improvements and modifications to the experiment resulting in lower noise and an improved uncertainty analysis. As well, we present a systematic error that had been previously unrecognized and we have quantified its correction. The seven determinations, using three different nominal masses and two different materials, are reanalysed in a manner consistent with that used by the CODATA Task Group on Fundamental Constants (TGFC) and includes a comprehensive assessment of correlations. The result is a Planck constant of 6.626 070 133(60)  ×10⁻³⁴ Js and an inferred value of the Avogadro constant of 6.022 140 772(55)  ×10²³ mol⁻¹. These fractional uncertainties of less than 10⁻⁸ are the smallest published to date.

We present precision measurements of the fractional quantized Hall effect, where the quantized resistance ${{R}^{\left[ 1/3 \right]}}$ in the fractional quantum Hall state at filling factor 1/3 was compared with a quantized resistance ${{R}^{[2]}}$, represented by an integer quantum Hall state at filling factor 2. A cryogenic current comparator bridge capable of currents down to the nanoampere range was used to directly compare two resistance values of two GaAs-based devices located in two cryostats. A value of 1–(5.3  ±  6.3) 10⁻⁸ (95% confidence level) was obtained for the ratio (${{R}^{\left[ 1/3 \right]}}/6{{R}^{[2]}}$). This constitutes the most precise comparison of integer resistance quantization (in terms of h/e²) in single-particle systems and of fractional quantization in fractionally charged quasi-particle systems. While not relevant for practical metrology, such a test of the validity of the underlying physics is of significance in the context of the upcoming revision of the SI.

Researchers at the National Institute of Standards and Technology (NIST) have measured the value of the Planck constant to be $\newcommand{\hres}{6.626\,069\,934(89)} h =\hres\times 10^{-34}\,$J s (relative standard uncertainty $\newcommand{\hrunc}{13} \hrunc\times 10^{-9}$). The result is based on over 10 000 weighings of masses with nominal values ranging from 0.5 kg to 2 kg with the Kibble balance NIST-4. The uncertainty has been reduced by more than twofold relative to a previous determination because of three factors: (1) a much larger data set than previously available, allowing a more realistic, and smaller, Type A evaluation; (2) a more comprehensive measurement of the back action of the weighing current on the magnet by weighing masses up to 2 kg, decreasing the uncertainty associated with magnet non-linearity; (3) a rigorous investigation of the dependence of the geometric factor on the coil velocity reducing the uncertainty assigned to time-dependent leakage of current in the coil.

A new single crystal from isotopically enriched silicon was used to determine the Avogadro constant N_A by the x-ray-crystal density method. The new crystal, named Si28-23Pr11, has a higher enrichment than the former 'AVO28' crystal allowing a smaller uncertainty of the molar mass determination. Again, two 1 kg spheres were manufactured from this crystal. The crystal and the spheres were measured with improved and new methods. One sphere, Si28kg01a, was measured at NMIJ and PTB with very consistent results. The other sphere, Si28kg01b, was measured only at PTB and yielded nearly the same Avogadro constant value. The mean result for both 1 kg spheres is N_A  =  6.022 140 526(70)  ×  10²³ mol⁻¹ with a relative standard uncertainty of 1.2  ×  10⁻⁸. This value deviates from the Avogadro value published in 2015 for the AVO28 crystal by about 3.9(2.1)  ×  10⁻⁸. Possible reasons for this difference are discussed and additional measurements are proposed.

To determine the Avogadro constant N_A by the x-ray crystal density method, the density of a ²⁸Si-enriched crystal was determined by absolute measurements of the mass and volume of a 1 kg sphere manufactured from the crystal. The mass and volume were determined by an optical interferometer and a vacuum mass comparator, respectively. The sphere surface was characterized by x-ray photoelectron spectroscopy and spectroscopic ellipsometry to derive the mass and volume of the Si core of the sphere excluding the surface layers. From the mass and volume, the density of the Si core was determined with a relative standard uncertainty of 2.3  ×  10⁻⁸. By combining the Si core density with the lattice constant and the molar mass of the sphere reported by the International Avogadro Coordination (IAC) project in 2015, a new value of 6.022 140 84(15)  ×  10²³ mol⁻¹ was obtained for N_A with a relative standard uncertainty of 2.4  ×  10⁻⁸. To make the N_A value determined in this work usable for a future adjustment of the fundamental constants by the CODATA Task Group on Fundamental Constants, the correlation of the new N_A value with the N_A values determined in our previous works was examined. The correlation coefficients with the values of N_A determined by IAC in 2011 and 2015 were estimated to be 0.07 and 0.28, respectively. The correlation of the new N_A value with the N_A value determined by IAC in 2017 using a different ²⁸Si-enriched crystal was also examined, and the correlation coefficient was estimated to be 0.21.

We report a new determination of the Boltzmann constant k_B using a cylindrical acoustic gas thermometer. We determined the length of the copper cavity from measurements of its microwave resonance frequencies. This contrasts with our previous work (Zhang et al 2011 Int. J. Thermophys. 32 1297, Lin et al 2013 Metrologia 50 417, Feng et al 2015 Metrologia 52 S343) that determined the length of a different cavity using two-color optical interferometry. In this new study, the half-widths of the acoustic resonances are closer to their theoretical values than in our previous work. Despite significant changes in resonator design and the way in which the cylinder length is determined, the value of k_B is substantially unchanged. We combined this result with our four previous results to calculate a global weighted mean of our k_B determinations. The calculation follows CODATA's method (Mohr and Taylor 2000 Rev. Mod. Phys. 72 351) for obtaining the weighted mean value of k_B that accounts for the correlations among the measured quantities in this work and in our four previous determinations of k_B. The weighted mean ${{\boldsymbol{\hat{k}}}_{\rm{B}}}$ is 1.380 6484(28)  ×  10⁻²³ J K⁻¹ with the relative standard uncertainty of 2.0  ×  10⁻⁶. The corresponding value of the universal gas constant is 8.314 459(17) J K⁻¹ mol⁻¹ with the relative standard uncertainty of 2.0  ×  10⁻⁶.

The new definition of the kilogram, which is expected to be adopted by the General Conference on Weights and Measures in 2018, will bring some major changes to mass metrology. The most fundamental change will be the replacement of the present artefact-based definition with a universal definition, enabling in principle any National Metrology Institute (NMI) to realize the kilogram. The principles for the realization and dissemination of the kilogram in the revised SI are described in the mise en pratique of the definition of the kilogram. This paper provides some additional information and explains how traceability can be obtained by NMIs that do not operate a primary experiment to realize the definition of the kilogram.

The SI unit of temperature will soon be redefined in terms of a fixed value of the Boltzmann constant k derived from an ensemble of measurements worldwide. We report on a new determination of k using acoustic thermometry of helium-4 gas in a 3 l volume quasi-spherical resonator. The method is based on the accurate determination of acoustic and microwave resonances to measure the speed of sound at different pressures. We find for the universal gas constant R  =  8.314 4614(50) J·mol⁻¹·K⁻¹. Using the current best available value of the Avogadro constant, we obtain k  =  1.380 648 78(83)  ×  10⁻²³ J·K⁻¹ with u(k)/k  =  0.60  ×  10⁻⁶, where the uncertainty u is one standard uncertainty corresponding to a 68% confidence level. This value is consistent with our previous determinations and with that of the 2014 CODATA adjustment of the fundamental constants (Mohr et al 2016 Rev. Mod. Phys. 88 035009), within the standard uncertainties. We combined the present values of k and u(k) with earlier values that were measured at LNE. Assuming the maximum possible correlations between the measurements, (k_present/〈k〉  −  1)  =  0.07  ×  10⁻⁶ and the combined u_r(k) is reduced to 0.56  ×  10⁻⁶. Assuming minimum correlations, (k_present/〈k〉  −  1)  =  0.10  ×  10⁻⁶ and the combined u_r(k) is reduced to 0.48  ×  10⁻⁶.

Water in its three ambient phases plays the central thermodynamic role in the terrestrial climate system. Clouds control Earth's radiation balance, atmospheric water vapour is the strongest 'greenhouse' gas, and non-equilibrium relative humidity at the air–sea interface drives evaporation and latent heat export from the ocean. On climatic time scales, melting ice caps and regional deviations of the hydrological cycle result in changes of seawater salinity, which in turn may modify the global circulation of the oceans and their ability to store heat and to buffer anthropogenically produced carbon dioxide. In this paper, together with three companion articles, we examine the climatologically relevant quantities ocean salinity, seawater pH and atmospheric relative humidity, noting fundamental deficiencies in the definitions of those key observables, and their lack of secure foundation on the International System of Units, the SI. The metrological histories of those three quantities are reviewed, problems with their current definitions and measurement practices are analysed, and options for future improvements are discussed in conjunction with the recent seawater standard TEOS-10. It is concluded that the International Bureau of Weights and Measures, BIPM, in cooperation with the International Association for the Properties of Water and Steam, IAPWS, along with other international organizations and institutions, can make significant contributions by developing and recommending state-of-the-art solutions for these long standing metrological problems in climatology.

Water in its three ambient phases plays the central thermodynamic role in the terrestrial climate system. Clouds control Earth's radiation balance, atmospheric water vapour is the strongest 'greenhouse' gas, and non-equilibrium relative humidity at the air–sea interface drives evaporation and latent heat export from the ocean. In this paper, we examine the climatologically relevant atmospheric relative humidity, noting fundamental deficiencies in the definition of this key observable. The metrological history of this quantity is reviewed, problems with its current definition and measurement practice are analysed, and options for future improvements are discussed in conjunction with the recent seawater standard TEOS-10. It is concluded that the International Bureau of Weights and Measures (BIPM), in cooperation with the International Association for the Properties of Water and Steam (IAPWS), along with other international organizations and institutions, can make significant contributions by developing and recommending state-of-the-art solutions, such as are suggested here, for what are long-standing metrological problems.

This paper describes a Josephson-based full digital impedance bridge capable of comparing any two impedances, regardless of type (R-C, R-L, or L-C), over a large frequency range (from 1 kHz to 20 kHz). At the heart of the bridge are two Josephson arbitrary waveform synthesizer systems that offer unprecedented flexibility in high-precision impedance calibration, that is, it can compare impedances with arbitrary ratios and phase angles. Thus this single bridge can fully cover the entire complex plane. In the near future, this type of instrument will considerably simplify the realization and maintenance of the various impedance scales in many National Metrology Institutes around the world.

The watt balance relates force or mass to the Planck constant h, the metre and the second. It enables the forthcoming redefinition of the unit of mass within the SI by measuring the Planck constant in terms of mass, length and time with an uncertainty of better than 2 parts in 10⁸. To achieve this, existing watt balances require complex and time-consuming alignment adjustments limiting their use to a few national metrology laboratories. This paper describes a simplified construction and operating principle for a watt balance which eliminates the need for the majority of these adjustments and is readily scalable using either electromagnetic or electrostatic actuators. It is hoped that this will encourage the more widespread use of the technique for a wide range of measurements of force or mass. For example: thrust measurements for space applications which would require only measurements of electrical quantities and velocity/displacement.

The PTB's (Physikalisch-Technische Bundesanstalt, Germany) nanonewton force facility, first presented in work by Nesterov (2007 Meas. Sci. Technol. 18 360–6), Nesterov (2009 Meas. Sci. Technol. 20 084012) and Nesterov et al (2009 Metrologia 46 277–82), has been significantly improved and used to measure the stiffness of a cantilever. The facility is based on a disc pendulum with electrostatic reduction of its deflection and stiffness. In this paper, we will demonstrate that the facility is able to measure horizontal forces in the range below 1 μN with a resolution below 5 pN and an uncertainty below 2.7% for a measured force of 1 nN at a measurement duration of about 20 s. We will demonstrate the possibility of using this facility as a calibration device that can accurately determine spring constants of soft cantilevers (K ≲ 0.1 N m⁻¹) with traceability to the SI units. The method and the results of measuring the spring constant of a soft cantilever (K  =  0.125 N m⁻¹) in air, in a medium vacuum, in a high vacuum and in nitrogen are presented. We will show that a relative standard uncertainty of the spring constant calibration of better than 0.3% (measurement in a medium vacuum) and a repeatability of better than 0.04% are achieved.

The redefinition of the kilogram, expected to be approved in the autumn of 2018, will replace the artefact definition of the kilogram by assigning a fixed numerical value to a fundamental constant of physics. While the concept of such a change is pleasing, the mass community as represented by the Consultative Committee for Mass and Related Quantities (CCM) was faced with a number of technical and procedural challenges that needed to be met in order to profit in any meaningful way from the proposed change. In the following, we outline these challenges and how the CCM has met and is meeting them. We focus especially on what the mass community requires of the new definition and the process by which the CCM has sought to ensure that these needs will be met.

Although mass is typically defined within the International System of Units (SI) at the kilogram level, the pending SI redefinition provides an opportunity to realize mass at any scale using electrical metrology. We propose the use of an electromechanical balance to realize mass at the milligram level using SI electrical units. An integrated concentric-cylinder vacuum gap capacitor allows us to leverage the highly precise references available for capacitance, voltage and length to generate an electrostatic reference force. Weighing experiments performed on 1 mg and 20 mg artifacts show the same or lower uncertainty than similar experiments performed by subdividing the kilogram. The measurement is currently limited by the stability of the materials that compose the mass artifacts and the changes in adsorbed layers on the artifact surfaces as they are transferred from vacuum to air.

The radian and steradian are unusual units within the SI, originally belonging to their own category of 'supplementary units', with this status being changed to dimensionless 'derived units' in 1995. Recent papers have suggested that angles could be handled in two different ways within the SI, both differing from the present system. The purpose of this paper is to provide a framework for putting such suggestions into context, outlining the range of options that is available, together with the advantages and disadvantages of these options.

Although less rigorously logical than some alternatives, the present SI approach is generally supported, but with some changes to the SI brochure to make the position clearer, in particular with regard to the designation of the radian and steradian as derived units.

The ratio $h/{{m}_{\text{u}}}$ between the Planck constant and the unified atomic mass constant should have a special status in the framework of the future international system of units. Currently (before the redefinition), this ratio allowed the comparison between determinations of h (watt balance) and determinations of ${{m}_{\text{u}}}$ (the XRCD method). In the future SI, as the Planck constant h will be fixed, the ratio $h/{{m}_{\text{u}}}$ will ensure the realization of the new kilogram (quantum kilogram) at the atomic scale. Furthermore as the Avogadro constant will be fixed, the carbon molar mass M(¹²C), which will no longer be equal to $12~\text{g}\centerdot \text{mo}{{\text{l}}^{-1}}$, will be determined from m_u. This ratio is also key data for the realization of the kilogram at the macroscopic scale using the XRCD method.

In this paper we present the state of the art on experiments that provide the most precise value of the ratio $h/{{m}_{\text{u}}}$. We focus on the one that is based on the measurement of the atomic recoil due to the photon momentum.

The purpose of this mise en pratique, prepared by the Consultative Committee for Photometry and Radiometry (CCPR) of the International Committee for Weights and Measures (CIPM) and formally adopted by the CIPM, is to provide guidance on how the candela and related units used in photometry and radiometry can be realized in practice. The scope of the mise en pratique recognizes the fact that the two fields of photometry and radiometry and their units are closely related through the current definition of the SI base unit for the photometric quantity, luminous intensity: the candela.

The previous version of the mise en pratique was applied only to the candela whereas this updated version covers the realization of the candela and other related units used for photometric and radiometric quantities. Recent advances in the generation and manipulation of individual photons show great promise of producing radiant fluxes with a well-established number of photons. Thus, this mise en pratique also includes information on the practical realization of units for photometric and radiometric quantities using photon-number-based techniques. In the following, for units used for photometric and radiometric quantities, the shorter term, photometric and radiometric units, is generally used.

Section 1 describes the definition of the candela which introduces a close relationship between photometric and radiometric units. Sections 2 and 3 describe the practical realization of radiometric and photon-number-based units, respectively. Section 4.1 explains how, in general, photometric units are derived from radiometric units. Sections 4.2–4.5 deal with the particular geometric conditions for the specific photometric units. Section 5 deals very briefly with the topic of determination of measurement uncertainties in photometry.

We report on the relative length fluctuation of two fixed-spacer Fabry–Pérot cavities with mirrors fabricated from silica/tantala dielectric coatings on fused silica substrates. By locking a laser to each cavity and reading out the beat note $\hat{\nu}={{\nu}_{1}}-{{\nu}_{2}}$ of the transmitted beams, we find that, for frequencies from 10 Hz to 1 kHz, the power spectral density of beat note fluctuation is ${{S}_{{\hat{\nu}}}}(f)={{\left(0.5\text{Hz}\right)}^{2}}/f$. By careful budgeting of noise sources contributing to the beat note, we find that our measurement is consistent with the fluctuation in this band being dominated by the Brownian noise of the mirror coatings. Fitting for the coating loss angle ϕ_c, we find it equal to 4 × 10⁻⁴. We then use a Bayesian analysis to combine our measurement with previous observations, and thereby extract estimates for the individual loss angles of the silica and tantala constituents of these coatings. With minor upgrades, the testbed described in this article can be used in the future to measure the length noise of cavities formed with novel mirror coating materials and geometries.

Results are presented from a series of comparisons between two independent femtosecond frequency comb systems at NPL, which were carried out in order to assess their systematic uncertainty. Simultaneous measurements with the two systems demonstrate agreement at the level of 5 × 10⁻¹⁸ when measuring an optical frequency against a common microwave reference. When simultaneously measuring the ratio of two optical frequencies, agreement at the 3 × 10⁻²¹ level is observed. The results represent the highest reported level of agreement to date between Ti:Sapphire and Er-doped femtosecond combs. The limitations of the combs when operating in these two different manners are discussed, including traceability to the SI second, which can be achieved with an uncertainty below 1 × 10⁻¹⁶. The technical details presented underpin recent absolute frequency measurements of the ⁸⁸Sr⁺ and ¹⁷¹Yb⁺ optical clock transitions at NPL, as well as a frequency ratio measurement between the two optical clock transitions in ¹⁷¹Yb⁺.

The former University of Washington Penning Trap Mass Spectrometer (UW-PTMS), now located at the Max Planck Institute for Nuclear Physics in Heidelberg, Germany, was used in the decade before the move to determine new values for the deuteron atomic mass, M (²H⁺) = 2.013 553 212 745(40) u, and the deuterium atomic mass, M (²H) = 2.014 101 778 052(40) u, both of which are now more than an order-of-magnitude more accurate than the previous best 1994-MIT measurements of these quantities. The new value for the deuteron's mass can then be used with the accepted 2010-CODATA proton mass and the most recent 1999-measurement of the 2.2 MeV gamma-ray binding energy of the deuteron to refine the neutron's mass to m_n = 1.008 664 916 018(435) u which has about half the uncertainty relative to the value computed using that previous 1994-MIT deuterium measurement. As a result, further improvements of m_n must now come from a more accurate determination of the wavelength of this gamma ray.

In this same period of time, this spectrometer has also been used to determine new values for the helion atomic mass, M (³He²⁺) = 3.014 932 246 668(43) u, and the neutral helium-3 atomic mass, M (³He) = 3.016 029 321 675(43) u, which are both about 60 times more accurate than the 2006-SMILETRAP measurements, but disagree with the 4.4-times less-accurate 2015-Florida-State measurements by 0.76 nu. It is expected that these helium-3 results will be used in the future ³H/³He mass ratio (to be determined by the Heidelberg, Germany version of the old UW-PTMS) in order to generate a more accurate value for the tritium atomic mass.

For many years, the time community has been using the precise point positioning (PPP) technique which uses GPS phase and code observations to compute time and frequency links. However, progress in atomic clocks implies that the performance of PPP frequency comparisons is a limiting factor in comparing the best frequency standards. We show that a PPP technique where the integer nature of phase ambiguities is preserved consitutes significant improvement of the classical use of floating ambiguities. We demonstrate that this integer-PPP technique allows frequency comparisons with 1  ×  10⁻¹⁶ accuracy in a few days and can be readily operated with existing products.

This report presents the results of the first phase of the campaign of calibration carried out with respect to the international prototype of the kilogram (IPK) in anticipation of the redefinition of the kilogram (Extraordinary Calibrations). The definition of the kilogram was realized according to the procedure outlined in the 8th Edition of the SI Brochure. Thus the IPK and its six official copies have been cleaned and washed following the BIPM procedure.

The mass comparisons carried out during this campaign showed a very good repeatability. The pooled standard deviation of repeated weighings of the prototypes was 0.4 µg. The effect of cleaning and washing of the IPK was to remove a mass of 16.8 µg. The effect of cleaning and washing of the six official copies was found to be very similar, giving an average mass removed from the seven prototypes of 15 µg with a standard deviation of 2 µg.

The differences in mass between the IPK and the official copies have changed by an average of 1 µg since the 3rd Periodic Verification of National Prototypes of the Kilogram (1988–1992). These results do not confirm the trend for the masses of the six official copies to diverge from the mass of the IPK that was observed during the 2nd and 3rd Periodic Verifications.

All BIPM working standards and the prototypes reserved for special use have been calibrated with respect to the IPK as part of this campaign. All of them were found to have lower masses than when they were calibrated during the 3rd Periodic Verification. As a consequence, the BIPM 'as-maintained' mass unit in 2014 has been found to be offset by 35 µg with respect to the IPK. This result will be analyzed in a further publication.

New results are reported from an ongoing international research effort to accurately determine the Avogadro constant by counting the atoms in an isotopically enriched silicon crystal. The surfaces of two ²⁸Si-enriched spheres were decontaminated and reworked in order to produce an outer surface without metal contamination and improved sphericity. New measurements were then made on these two reconditioned spheres using improved methods and apparatuses. When combined with other recently refined parameter measurements, the Avogadro constant derived from these new results has a value of N_A = 6.022 140 76(12) × 10²³ mol⁻¹. The x-ray crystal density method has thus achieved the target relative standard uncertainty of 2.0  ×  10⁻⁸ necessary for the realization of the definition of the new kilogram.

AC Josephson voltage standards based on pulse-driven Josephson arrays (Josephson arbitrary waveform synthesizer—JAWS) have recently achieved an output voltage of at least 1 V root-mean-square. An ac quantum voltmeter (ac-QVM) based on a 2 V programmable Josephson array has been used to verify the quantization level of the new JAWS by performing a direct comparison in the frequency range from 30 Hz to 2 kHz. The comparison has demonstrated an excellent agreement between the two quantum standards of better than 1 part in 10⁸. Sources for systematic errors have been investigated. The overall uncertainty is found to be better than 1.2 parts in 10⁸ (k = 1) for measurements at a frequency of 250 Hz and 1 V amplitude.

Until a new definition of the kilogram has been adopted, the SI unit of mass remains defined in terms of an artefact, the international prototype of the kilogram $\mathfrak{K},$ which is not readily available for regular recalibration of BIPM prototypes used for the calibration of national prototypes. Since 1889 the working hypothesis has been that the platinum–iridium prototypes are stable mass standards, although mass comparisons indicate that this is not entirely true. In this paper we present a method for improving metrological traceability to the international prototype $\mathfrak{K}$ by modelling the change in mass of prototypes over time and evaluate the model parameters by a weighted least squares adjustment. The method has been applied to comparisons between 18 prototypes performed at the BIPM in the period 1889–2009. The mass values predicted by the model are compared to the mass values assigned by BIPM in the period 1992–2009 and to results of the Extraordinary Calibrations performed at BIPM in 2014 using the international prototype $\mathfrak{K}$ as reference standard.

Improved measurements on silicon crystal samples highly enriched in the ²⁸Si isotope (known as 'Si28' or AVO28 crystal material) have been carried out at PTB to investigate local isotopic variations in the original crystal. This material was used for the determination of the Avogadro constant N_A and therefore plays an important role in the upcoming redefinition of the SI units kilogram and mole, using fundamental constants. Subsamples of the original crystal have been extensively studied over the past few years at the National Research Council (NRC, Canada), the National Metrology Institute of Japan (NMIJ, Japan), the National Institute of Standards and Technology (NIST, USA), the National Institute of Metrology (NIM, People's Republic of China), and multiple times at PTB. In this study, four to five discrete, but adjacent samples were taken from three distinct axial positions of the crystal to obtain a more systematic and comprehensive understanding of the distribution of the isotopic composition and molar mass throughout the crystal. Moreover, improved state-of-the-art techniques in the experimental measurements as well as the evaluation approach and the determination of the calibration factors were utilized. The average molar mass of the measured samples is M  =  27.976 970 12(12) g mol⁻¹ with a relative combined uncertainty u_c,rel(M)  =  4.4 ×10⁻⁹. This value is in astounding agreement with the values of single samples measured and published by NIST, NMIJ, and PTB. With respect to the associated uncertainties, no significant variations in the molar mass and the isotopic composition as a function of the sample position in the boule were observed and thus could not be traced back to an inherent property of the crystal. This means that the crystal is not only 'homogeneous' with respect to molar mass but also has predominantly homogeneous distribution of the three stable Si isotopes.

Half-life measurements of radionuclides are undeservedly perceived as 'easy' and the experimental uncertainties are commonly underestimated. Data evaluators, scanning the literature, are faced with bad documentation, lack of traceability, incomplete uncertainty budgets and discrepant results. Poor control of uncertainties has its implications for the end-user community, varying from limitations to the accuracy and reliability of nuclear-based analytical techniques to the fundamental question whether half-lives are invariable or not. This paper addresses some issues from the viewpoints of the user community and of the decay data provider. It addresses the propagation of the uncertainty of the half-life in activity measurements and discusses different types of half-life measurements, typical parameters influencing their uncertainty, a tool to propagate the uncertainties and suggestions for a more complete reporting style. Problems and solutions are illustrated with striking examples from literature.

We review the principles, techniques and results from primary acoustic gas thermometry (AGT). Since the establishment of ITS-90, the International Temperature Scale of 1990, spherical and quasi-spherical cavity resonators have been used to realize primary AGT in the temperature range 7 K to 552 K. Throughout the sub-range 90 K < T < 384 K, at least two laboratories measured (T − T₉₀). (Here T is the thermodynamic temperature and T₉₀ is the temperature on ITS-90.) With a minor exception, the resulting values of (T − T₉₀) are mutually consistent within 3 × 10⁻⁶ T. These consistent measurements were obtained using helium and argon as thermometric gases inside cavities that had radii ranging from 40 mm to 90 mm and that had walls made of copper or aluminium or stainless steel. The AGT values of (T − T₉₀) fall on a smooth curve that is outside ±u(T₉₀), the estimated uncertainty of T₉₀. Thus, the AGT results imply that ITS-90 has errors that could be reduced in a future temperature scale. Recently developed techniques imply that low-uncertainty AGT can be realized at temperatures up to 1350 K or higher and also at temperatures in the liquid-helium range.

We have measured Planck's constant and have obtained a value of 6.626 070 34(12) × 10⁻³⁴ J s. To our knowledge this measurement of h has the lowest uncertainty reported to date. This result has been obtained from measurements of four masses of different material and nominal values varying from 1 kg to 250 g. The experimental procedures and the measurement uncertainties are described in detail.

For the past two years, measurements have been performed with a watt balance at the National Institute of Standards and Technology (NIST) to determine the Planck constant. A detailed analysis of these measurements and their uncertainties has led to the value h = 6.626 069 79(30) × 10⁻³⁴ J s. The relative standard uncertainty is 45 × 10⁻⁹. This result is 141 × 10⁻⁹ fractionally higher than h₉₀. Here h₉₀ is the conventional value of the Planck constant given by $h_{90}\equiv 4 /( K_{{\rm J\mbox{-}90}}^2R_{{\rm K\mbox{-}90}})$, where K_J-90 and R_K-90 denote the conventional values of the Josephson and von Klitzing constants, respectively.

It has been known for some time that the watt balance, which is based on the virtual work principle, is insensitive to some misalignments which would, at first sight, be expected to produce significant errors. In this paper we show that, in particular circumstances, this insensitivity applies to a whole range of misalignments. This effect can be exploited to design a watt balance, with a constrained coil motion, which offers advantages over conventional designs. We present three such new designs: one is based on a conventional balance and the other two are based on strip hinges, which are known to have excellent properties when measuring small force differences and with the production of precise linear movements having little motion in the other five degrees of freedom. A constrained design of this kind would have advantages for reproducing the forthcoming SI definition of mass in the range from milligrams to kilograms, whenever and wherever desired, and might well do so with improved accuracy.

In 2011, the General Conference on Weights and Measures (CGPM) confirmed its intention to adopt new definitions for four of the base units of the SI based on fixed numerical values of selected constants. These will be the kilogram, the ampere, the kelvin and the mole. The CGPM was not able to adopt the new definitions at that time because certain experimental and coordination work was not complete. This paper reviews criteria proposed by the Consultative Committees of the CIPM for such a 'new SI' to be adopted and reports on recent progress with work to address them. We also report on work being undertaken to demonstrate that the most important technical aspects of realizing such a new system are practicable. The progress reported here confirms the consensus developing amongst the Consultative Committees and the National Metrology Institutes that it will be possible for the CGPM to adopt these new definitions in 2018.

The concentration of nanometre-sized particles is frequently measured in terms of particle number concentration using well-established measuring instruments, e.g. condensation particle counters. Traceability for these measurements can be achieved by means of calibrations using an aerosol electrometer (AE) as a reference. A number of national metrology institutes (NMIs) and expert laboratories provide such calibrations, but the metrological basis is at present not well established because the equivalence between the unit realizations has not been investigated by means of an inter-laboratory comparison. This paper presents the results of the first comprehensive comparison of AEs involving NMIs and expert laboratories worldwide. The comparison covered the particle size and charge concentrations ranges 20 nm to 200 nm and 0.16 × 10⁻¹⁵ C cm⁻³ to 2.72 × 10⁻¹⁵ C cm⁻³ (equivalent to 1000 cm⁻³ to 17 000 cm⁻³ singly charged particles), respectively. The obtained results agreed to within about ±3%, which was within stated uncertainties, with only a few exceptions, such as at low concentrations. Additional measurements with sub-20 nm particles show that comparisons in this size range are more challenging and require special considerations, though agreement to within about ±5% was still found with 6 nm particles. This comparison is the first and vital step towards internationally recognized SI traceability in particle number concentration measurements.

The results of an absolute silicon molar mass determination of two independent sets of samples from the highly ²⁸Si-enriched crystal (AVO28) produced by the International Avogadro Coordination are presented and compared with results published by the Physikalisch-Technische Bundesanstalt (PTB, Germany), the National Research Council (NRC, Canada) and the National Metrology Institute of Japan (NMIJ, Japan). This study developed and describes significant changes to the published protocols for producing absolute silicon isotope ratios. The measurements were made at very high resolution on a multi-collector inductively coupled plasma mass spectrometer using tetramethylammonium hydroxide (TMAH) to dissolve and dilute all samples. The various changes in the measurement protocol and the use of TMAH resulted in significant improvements to the silicon isotope ratio precision over previously reported measurements and in particular, the robustness of the ²⁹Si/³⁰Si ratio of the AVO28 material. These new results suggest that a limited isotopic variability is present in the AVO28 material. The presence of this variability is at present singular and therefore its significance is not well understood. Fortunately, its magnitude is small enough so as to have an insignificant effect on the overall uncertainty of an Avogadro constant derived from the average molar mass of all four AVO28 silicon samples measured in this study. The NIST results confirm the AVO28 molar mass values reported by PTB and NMIJ and confirm that the virtual element–isotope dilution mass spectrometry approach to calibrated absolute isotope ratio measurements developed by PTB is capable of very high precision as well as accuracy. The Avogadro constant N_A and derived Planck constant h based on these measurements, together with their associated standard uncertainties, are 6.02214076(19) × 10²³ mol⁻¹ and 6.62607017(21) × 10⁻³⁴ Js, respectively.

The expression of uncertainty has hitherto been seen as an add-on—first an estimate is obtained and then uncertainty in that estimate is evaluated. We argue that quantification of uncertainty should be an intrinsic part of measurement and that the measurement result should be a probability distribution for the measurand.

Full quantification of uncertainties in measurement, recognizing and quantifying all sources of uncertainty, is rarely simple. Many potential sources of uncertainty can effectively only be quantified by the application of expert judgement. Scepticism about the validity or reliability of expert judgement has meant that these sources of uncertainty have often been overlooked, ignored or treated in a qualitative, narrative way. But the consequence of this is that reported expressions of uncertainty regularly understate the true degree of uncertainty in measurements.

This article first discusses the concept of quantifying uncertainty in measurement, and then considers some of the areas where expert judgement is needed in order to quantify fully the uncertainties in measurement. The remainder of the article is devoted to describing methodology for eliciting expert knowledge.

In the course of the twenty years since the publication of the Guide to the Expression of Uncertainty in Measurement (GUM), the recognition has been steadily growing of the value that statistical models and statistical computing bring to the evaluation of measurement uncertainty, and of how they enable its probabilistic interpretation. These models and computational methods can address all the problems originally discussed and illustrated in the GUM, and enable addressing other, more challenging problems, that measurement science is facing today and that it is expected to face in the years ahead.

These problems that lie beyond the reach of the techniques in the GUM include (i) characterizing the uncertainty associated with the assignment of value to measurands of greater complexity than, or altogether different in nature from, the scalar or vectorial measurands entertained in the GUM: for example, sequences of nucleotides in DNA, calibration functions and optical and other spectra, spatial distribution of radioactivity over a geographical region, shape of polymeric scaffolds for bioengineering applications, etc; (ii) incorporating relevant information about the measurand that predates or is otherwise external to the measurement experiment; (iii) combining results from measurements of the same measurand that are mutually independent, obtained by different methods or produced by different laboratories.

This review of several of these statistical models and computational methods illustrates some of the advances that they have enabled, and in the process invites a reflection on the interesting historical fact that these very same models and methods, by and large, were already available twenty years ago, when the GUM was first published—but then the dialogue between metrologists, statisticians and mathematicians was still in bud. It is in full bloom today, much to the benefit of all.

In December 2003, the Physikalisch-Technische Bundesanstalt (PTB) started the development of an optical-based primary flow rate standard for application in natural gas under high pressures (up to 5.5 MPa). The concept underlying this technology will be presented in this paper. The technical approach is based on the application of a conventional laser Doppler velocimeter (LDV) as well as on a new LDV-based boundary layer sensor. Both technologies are used to determine the characteristic values of the core flow and the boundary layer in a nozzle flow in a separated approach. Because of the high relevance to the demonstration of traceability and to the evaluation of the uncertainty, the related data processing (especially for the boundary layer) is explained in detail. Finally, after summarizing the uncertainty budget for the optical-based primary standard, we will demonstrate the approval of the new primary standard by means of a comparison with the established conventional traceability of PTB for high-pressure natural gas.

This work demonstrates accurate measurement of the amount of substance concentration of low concentration plasmid DNA by counting individual DNA molecules using a high-sensitivity flow cytometric setup. Plasmid DNA is a widely used form of DNA, and its quantity often needs to be accurately determined. This work establishes a reference analytical method for direct quantification of low concentration plasmid DNA prepared as reference standards for polymerase chain reaction-based DNA quantification. The model plasmid DNA pBR322 (4361 bp) was stained with a fluorescent dye and was detected in a flow stream in a micro-fluidic channel with laser-induced fluorescence detection, for which the DNA flow was electro-hydrodynamically focused at the centre of the channel. 200 to 8000 DNA molecules in a ∼1 µL sample volume were counted within 2 min in an 'exhaustive counting' manner, which facilitated quantitation without calibration. The sample volume was measured and validated from the close agreement of the results of two independent measurement methods, gravimetric determination of water filling the capillary and graphical estimation of actual cross sectional area of the capillary tubing with the image of calibrated scanning electron microscopy. Within the given concentration range, an excellent measurement linearity (R² = 0.999) was achieved with appropriate data processing for the correction of the events of double molecules (detection of double molecules opposed to single molecule detection assumed, which occurs due to their coincidental passing of the detection zone). The validity of the proposed method was confirmed from the close agreement with the results of quantitation of enzymatically released nucleotides using capillary electrophoresis.

The Birge ratio is applied in metrology to enlarge quoted uncertainties when combining inconsistent measurement results on the same measurand. We discuss the statistical model underlying such a procedure and argue that the resulting uncertainty associated with the adjusted value is underrated. We provide a simple modification of this uncertainty on the basis of an objective Bayesian inference. While the proposed uncertainty approaches that obtained by the conventional procedure for a large number n of combined measurement results, differences are significant for small n. For example, for n = 4 we get an increase of 73% in the standard uncertainty associated with the adjusted value, and for n = 10 the increase is still 13%. We derive the posterior distribution for the adjusted value in closed form, including a 95% credible interval. In addition, we show that our results do not only hold when the distribution of the measurement results is assumed to be Gaussian, but for a whole family of (elliptically contoured) location-scale distributions. We illustrate the modified Birge method by its application to data from the 2002 adjustment of the Newtonian constant of gravitation.

Since 1889 the international prototype of the kilogram has served as the definition of the unit of mass in the International System of Units (SI). It is the last material artefact to define a base unit of the SI, and it influences several other base units. This situation is no longer acceptable in a time of ever increasing measurement precision.

It is therefore planned to redefine the unit of mass by fixing the numerical value of the Planck constant. At the same time three other base units, the ampere, the kelvin and the mole, will be redefined. As a first step, the kilogram redefinition requires a highly accurate determination of the Planck constant in the present SI system, with a relative uncertainty of the order of 1 part in 10⁸.

The most promising experiment for this purpose, and for the future realization of the kilogram, is the watt balance. It compares mechanical and electrical power and makes use of two macroscopic quantum effects, thus creating a relationship between a macroscopic mass and the Planck constant.

In this paper the background for the choice of the Planck constant for the kilogram redefinition is discussed and the role of the Planck constant in physics is briefly reviewed. The operating principle of watt balance experiments is explained and the existing experiments are reviewed. An overview is given of all presently available experimental determinations of the Planck constant, and it is shown that further investigation is needed before the redefinition of the kilogram can take place.

The stability of reference masses has been a long-standing concern within the SI. More recently the requirements of potential non-artefact realizations of the kilogram have added gold and its alloys to the platinum alloys that have historically been the focus of attention.

Previously we proposed UV/ozone cleaning of standard-mass surfaces to improve stability with respect to carbonaceous contamination. Since then both NPL and BIPM have constructed prototypes of UV/ozone apparatus for cleaning kilogram standards. We have therefore tested a combined solvent wash and UV/ozone procedure, UVOPS or 'UV/ozone with pre-wash and stabilization', on both platinum and gold surfaces. X-ray photoelectron spectroscopy (XPS) shows this to be very successful in removing even gross contamination from these noble metal surfaces. Oxidation is negligible, limited to the outermost layer of noble metal atoms, and terminates at a level that is within the uncertainty of mass comparisons at the 1 kg level. This oxide has been seen in some earlier XPS studies but not others—we show that decomposition of the oxide by x-rays at XPS energies may be responsible for this disparity.

The removal of a high mercury contamination on a Pt reference mass by thermal desorption was studied directly by x-ray photoemission spectroscopy (XPS). Subsequently the contamination mechanism was investigated. Samples of PtIr and AuPt exposed to vapour of mercury in air were studied using XPS and gravimetric mass determination. We find an extremely rapid mercury contamination which takes place within minutes and reaches an initial equilibrium state after 2 h to 4 h. Roughly 1 to 2 monolayers of mercury adsorbs directly on the metal surface. A natural contamination of carbon and oxygen compounds is at the top. Due to the accumulation of mercury, we find a gain in mass which corresponds to 20 µg to 26 µg for a PtIr standard. XPS data from a historical Pt standard give strong evidence for further average mercury accumulation of (1.3 ± 0.1) µg/year during a period of more than a century. This can be explained by a two-step mechanism presented in this study. The speed of contamination depends on the initial surface conditions. Polishing activates the surface and results in an enhanced accumulation of mercury. Natural contamination by C and O can delay but not prevent contamination. We further demonstrate that the mercury contamination can be removed by both hydrogen plasma and thermal desorption. The removal of mercury by hydrogen plasma can directly be attributed to the synthesis of gaseous mercury dihydrides at low pressures.

This paper is an introduction to the principles developed for the application of metrology to the field of chemistry and particularly to analytical chemistry. It starts with a discussion of the mole, the base unit of the SI that is most relevant to analytical chemistry. The mole has become the subject of particular discussion recently, since the publication of proposals to re-define it along with three other base units of the SI. This discussion has also generated interest in the origin of the term 'amount of substance' used as the quantity for which the mole is the unit. This paper reviews the origin of this term and explains why it is not sufficient to replace it with an alternative such as a 'number of entities'. The paper concludes with some discussion of how the mole is realized through the use of primary methods of measurement.

This work explores the feasibility of acoustic gas thermometry (AGT) in the range 700 K to the copper point (1358 K) in order to more accurately measure the differences between ITS-90 and the thermodynamic temperature. To test material suitability and stability, we investigated microwave resonances in argon-filled cylindrical cavities machined from a Ni–Cr–Fe alloy. We measured the frequencies of five non-degenerate microwave modes of one cavity at temperatures up to 1349 K using home-made coaxial cables and antennas. The short-term repeatability of both the measured frequencies f_N and the scaled half-widths g_N/f_N was better than 10⁻⁶ f_N. Oxidation was not a problem while clean argon flowed through the cavity. The measurement techniques are compatible with highly accurate AGT and may be adaptable to refractive index gas thermometry.

The kilogram is the last unit of the international system of units (SI) still based on a material artefact, the international prototype of the kilogram (IPK). The comparisons made in the last hundred years have clearly revealed a long-term relative drift between the IPK and the official copies kept under similar conditions at the Bureau International des Poids et Mesures. A promising route towards a new definition of the kilogram based on a fundamental constant is represented by the watt balance experiment which links the mass unit to the Planck constant h. For more than ten years, the Federal Institute of Metrology METAS has been actively working in the conception and development of a watt balance experiment. This paper describes the new design of the Mark II METAS watt balance. The metrological characteristics of the different components of the experiment are described and discussed.

A stress exists in solid surfaces even if the underlying bulk material is stress-free. This paper investigates the effect of surface stress on the value of the Si lattice parameter measured by combined x-ray and optical interferometry. An elastic-film model has been used to provide a surface load in a finite element model on the x-ray interferometer crystal. Eventually, an interferometer design is proposed to determine a measurement where the effect of the surface stress is deemed to be detected.

The Comité international des poids et mesures (CIPM) has projected a major revision of the International System of Units (SI) in which all of the base units will be defined by fixing the values of fundamental constants of nature. In preparation for this we have carried out a new, low-uncertainty determination of the Boltzmann constant, k_B, in terms of which the SI unit of temperature, the kelvin, can be re-defined. We have evaluated k_B from exceptionally accurate measurements of the speed of sound in argon gas which can be related directly to the mean molecular kinetic energy, $\frac{3}{2}k_{{\rm B}} T$. Our new estimate is k_B = 1.380 651 56 (98) × 10⁻²³ J K⁻¹ with a relative standard uncertainty u_R = 0.71 × 10⁻⁶.

The design and construction of a predictable quantum efficient detector (PQED), suggested to be capable of measuring optical power with a relative uncertainty of 1 ppm (ppm = parts per million), is presented. The structure and working principle of induced junction silicon photodiodes are described combined with the design of the PQED. The detector uses two custom-made large area photodiodes assembled into a light-trapping configuration, reducing the reflectance down to a few tens of ppm. A liquid nitrogen cryostat is used to cool the induced junction photodiodes to 78 K to improve the mobility of charge carriers and to reduce the dark current. To determine the predicted spectral responsivity, reflectance losses of the PQED were measured at room temperature and at 78 K and also modelled throughout the visible wavelength range from 400 nm to 800 nm. The measured values of reflectance at room temperature were 29.8 ppm, 22.8 ppm and 6.6 ppm at the wavelengths of 476 nm, 488 nm and 532 nm, respectively, whereas the calculated reflectances were about 4 ppm higher. The reflectance at 78 K was measured at the wavelengths of 488 nm and 532 nm over a period of 60 h during which the reflectance changed by about 20 ppm. The main uncertainty components in the predicted internal quantum deficiency (IQD) of the induced junction photodiodes are due to the reliability of the charge-carrier recombination model and the extinction coefficient of silicon at wavelengths longer than 700 nm. The expanded uncertainty of the predicted IQD is 2 ppm at 78 K over a limited spectral range and below 140 ppm at room temperature over the visible wavelength range. All the above factors are combined as the external quantum deficiency (EQD), which is needed for the calculation of the predicted spectral responsivity of the PQED. The values of the predicted EQD are below 70 ppm between the wavelengths of 476 nm and 760 nm, and their expanded uncertainties mostly vary between 10 ppm and 140 ppm, where the lowest uncertainties are obtained at low temperatures.

The predictable quantum efficient detector (PQED) is intended to become a new primary standard for radiant power measurements in the wavelength range from 400 nm to 800 nm. Characterization results of custom-made single induced junction photodiodes as they are used in the PQED and of assembled PQEDs are presented. The single photodiodes were tested in terms of linearity and spatial uniformity of the spectral responsivity. The highly uniform photodiodes were proved to be linear over seven orders of magnitude, i.e. in the radiant power range from 100 pW to 400 µW. The assembled PQED has been compared with a cryogenic electrical substitution radiometer with a very low uncertainty of the order of 30 ppm. Experimental results show good agreement with the modelled response of the PQED to optical radiation and prove a near unity external quantum efficiency.

We report improvements to our previous (Zhang et al 2011 Int. J. Thermophys. 32 1297) determination of the Boltzmann constant k_B using a single 80 mm long cylindrical cavity. In this work, the shape of the gas-filled resonant cavity is closer to that of a perfect cylinder and the thermometry has been improved. We used two different grades of argon, each with measured relative isotopic abundances, and we used two different methods of supporting the resonator. The measurements with each gas and with each configuration were repeated several times for a total of 14 runs. We improved the analysis of the acoustic data by accounting for certain second-order perturbations to the frequencies from the thermo-viscous boundary layer. The weighted average of the data yielded k_B = 1.380 6476 × 10⁻²³ J K⁻¹ with a relative standard uncertainty u_r(k_B) = 3.7 × 10⁻⁶. This result differs, fractionally, by (−0.9 ± 3.7) × 10⁻⁶ from the value recommended by CODATA in 2010. In this work, the largest component of the relative uncertainty resulted from inconsistent values of k_B determined with the various acoustic modes; it is 2.9 × 10⁻⁶. In our previous work, this component was 7.6 × 10⁻⁶.

We report on our on-going effort to measure the Boltzmann constant, k_B, using the Doppler broadening technique. The main systematic effects affecting the measurement are discussed. A revised error budget is presented in which the global uncertainty on systematic effects is reduced to 2.3 ppm. This corresponds to a reduction of more than one order of magnitude compared with our previous Boltzmann constant measurement. Means to reach a determination of k_B at the part per million accuracy level are outlined.

The Electron Counting Capacitance Standard currently pursued at PTB aims to close the Quantum Metrological Triangle with a final precision of a few parts in 10⁷. This paper reports the considerable progress recently achieved with a new generation of single-electron tunnelling devices. A five-junction R-pump was operated with a relative charge transfer error of five electrons in 10⁷, and was used to successfully perform single-electron charging of a cryogenic capacitor. The preliminary result for the single-electron charge quantum has an uncertainty of less than two parts in 10⁶ and is consistent with the value of the elementary charge.

Measurements made with watt balances are paving the way to a new definition of the kilogram based upon a fixed value of the Planck constant. The Bureau International des Poids et Measures (BIPM) are developing a simultaneous moving and weighing variant of the watt balance technique, which requires a superconducting coil to reach its ultimate uncertainty. The BIPM technique has the advantage that it eliminates the requirement for extreme stability in the magnetic field employed by conventional watt balances, but requires cryogenic operation of parts of the balance to achieve a low uncertainty.

This paper proposes a simple method, by which the BIPM technique can be made to operate at room temperature with no loss of accuracy. The superconducting coil is replaced by a bifilar coil and the measurement procedure is modified to eliminate any inequality between the two conductors in the bifilar coil. The new technique is not subject to the many secondary sources of uncertainty arising from cryogenic operation.

After the elimination of significant mechanical problems, the NPL Mark II moving-coil watt balance made an initial series of measurements in the period from October 2006 to March 2007. Incremental improvements were made to the apparatus in the period from June 2007 to November 2008 and measurements of the Planck constant h were made up to June 2009, with the aim of providing further information to the ongoing efforts to redefine the SI kilogram in terms of a fixed value of the Planck constant. The apparatus was sold to NRC-INMS in early 2009 and was dismantled and shipped to Canada in the period between June and August 2009.

In June 2009, just prior to the shipment, a possible source of significant type-B uncertainty in the mass/force exchange was discovered. There was insufficient time to fully investigate and correct the effect so a component has been added to the uncertainty budget to account for its estimated magnitude. The standard uncertainty of the apparatus, without allowance for the mass/force exchange problem, is estimated to be 36 nW W⁻¹, which represents an improvement of almost a factor of two from the previously reported uncertainty of 66 nW W⁻¹, but, allowing for the problem, the uncertainty increases to 200 nW W⁻¹. Further work, once the apparatus is rebuilt in Canada, should eliminate the source of the added uncertainty. The value of h calculated from the measurements made from 2006 to 2009 is 6.626 071 23(133) × 10⁻³⁴ J s, which represents a change of 43 nW W⁻¹ from the value reported in 2007. The corresponding value of the Avogadro constant, N_A, is 6.022 139 78(120) × 10²³ mol⁻¹.

We calculated the eigenvalues of the radially symmetric acoustic modes of a gas-filled, spherical cavity to order (δ_t/a)², where δ_t is the thickness of the thermal boundary layer and a is the radius of the cavity. Our results explain an anomaly revealed by high-precision acoustic measurements made to redetermine the Boltzmann constant.

Volume is an input quantity in the measurement model for the mass of a body, say, a mass standard. The classical method to determine volume, hydrostatic weighing, is time-consuming, expensive and can introduce instability in the standard mass. Some years ago an alternative method was proposed, based on weighings in air at different densities. We generalize the method, showing that also the mass of the standard can be determined with it using a weighted-least-squares adjustment. To this purpose, we discuss a measurement model taking into account the covariances between the input estimates. The method, experimentally validated, yields uncertainties for the mass estimates that are smaller than those obtained with the traditional method, and gives the further advantage of directly providing the covariance between mass and volume.

The half-integer quantum Hall effect in epitaxial graphene is compared with high precision to the well-known integer effect in a GaAs/AlGaAs heterostructure. We find no difference between the quantized resistance values within the relative standard uncertainty of our measurement of 8.7 × 10⁻¹¹. The result places new tighter limits on any possible correction terms to the simple relation R_K = h/e², and also demonstrates that epitaxial graphene samples are suitable for application as electrical resistance standards of the highest metrological quality. We discuss the characterization of the graphene sample used in this experiment and present the details of the cryogenic current comparator bridge and associated uncertainty budget.

When the data do not conform to the hypothesis of a known sampling variance, the fitting of a constant to a set of measured values is a long debated problem. Given the data, fitting would require one to find what measurand value is the most trustworthy. Bayesian inference is reviewed here, to assign probabilities to the possible measurand values. Different hypotheses about the data variance are tested by Bayesian model comparison. Eventually, model selection is exemplified in deriving an estimate of the Planck constant.

The use of a magnetic levitation densimeter (MLD) currently represents the most sensitive way of measuring fluid density for a wide range of temperature and pressure conditions. However, due to magnetic force transmission errors, the accuracy of this approach is limited to approximately 100 ppm in density. Here, the authors propose an improved method to eliminate the uncertainty caused by magnetic forces acting on fluids based on the use of dual sinkers and control of the magnetic coupling's levitation height. The technique cuts out almost all force transmission errors and enables a level of density measurement precision better than 1 ppm. A new high-sensitivity MLD system was developed using a novel sinker exchange mechanism with a magnetic coupling. Single-crystal silicon and germanium were selected as the sinker materials because of their outstanding performance in terms of isotropy, stability and universality of thermophysical properties. A number of tests to check the measurement performance of the MLD were conducted by the National Metrology Institute of Japan. The experimental results for n-tridecane are also presented in this paper.

In order to study the practical means of a dissemination of the redefined kilogram, the mass laboratory of METAS has built a new and unique instrument, which combines high precision mass measurement and element-specific surface chemical analysis by x-ray photoelectron spectroscopy (XPS) under identical conditions. It is especially designed for the analysis of large samples such as real 1 kg standards and artefacts of up to 100 mm in diameter. In this paper, we first provide a detailed description of the apparatus. In a second step we demonstrate its performance by applying various processes, such as the transfer from ambient to vacuum, cleaning by low-pressure hydrogen plasma, transfer from vacuum to ambient and recontamination in air with time. Real 1 kg PtIr standards and surface artefacts have been monitored at individual steps gravimetrically, and in vacuum additionally by XPS. Values for the gain and loss of mass due to the application of different processes are provided. A model for the short-term recontamination after cleaning is presented, showing the initial growth of contaminants is self-limited.

This paper discusses the effects of non-linearity, some of the mechanisms responsible for non-linearity, and methods for measuring non-linearity in Johnson noise thermometry. Mechanisms considered include quantum tunnelling, bipolar junction transistor and junction field-effect transistor amplifiers, feedback, clipping, output-stage crossover, quantization and dither. It is found that even- and odd-order effects behave differently in correlator-based noise thermometers, with the dominant even-order effects contributing as intermodulation products whereas the dominant odd-order contributions are third-order and at the same frequencies as the parent signals. Possible test methods include the use of discrete tones, changes in spectral shape, and direct measurement using reference noise powers. For correlators operated at constant noise power, direct measurement of non-linearity using reference noise powers enables corrections to be made with negligible additional uncertainty and measurement time.

The 8th International Comparison of Absolute Gravimeters (ICAG2009) took place at the headquarters of the International Bureau of Weights and Measures (BIPM) from September to October 2009. It was the first ICAG organized as a key comparison in the framework of the CIPM Mutual Recognition Arrangement of the International Committee for Weights and Measures (CIPM MRA) (CIPM 1999). ICAG2009 was composed of a Key Comparison (KC) as defined by the CIPM MRA, organized by the Consultative Committee for Mass and Related Quantities (CCM) and designated as CCM.G-K1. Participating gravimeters and their operators came from national metrology institutes (NMIs) or their designated institutes (DIs) as defined by the CIPM MRA. A Pilot Study (PS) was run in parallel in order to include gravimeters and their operators from other institutes which, while not signatories of the CIPM MRA, nevertheless play important roles in international gravimetry measurements. The aim of the CIPM MRA is to have international acceptance of the measurement capabilities of the participating institutes in various fields of metrology. The results of CCM.G-K1 thus constitute an accurate and consistent gravity reference traceable to the SI (International System of Units), which can be used as the global basis for geodetic, geophysical and metrological observations of gravity. The measurements performed afterwards by the KC participants can be referred to the international metrological reference, i.e. they are SI-traceable.

The ICAG2009 was complemented by a number of associated measurements: the Relative Gravity Campaign (RGC2009), high-precision levelling and an accurate gravity survey in support of the BIPM watt balance project. The major measurements took place at the BIPM between July and October 2009. Altogether 24 institutes with 22 absolute gravimeters (one of the 22 AGs was ultimately withdrawn) and nine relative gravimeters participated in the ICAG/RGC campaign.

This paper is focused on the absolute gravity campaign. We review the history of the ICAGs and present the organization, data processing and the final results of the ICAG2009.

After almost thirty years of hosting eight successive ICAGs, the CIPM decided to transfer the responsibility for piloting the future ICAGs to NMIs, although maintaining a supervisory role through its Consultative Committee for Mass and Related Quantities.