Table of contents

We present a new type of measurement and the first results of determination of the optical to electrical delay of a photon counting detector. This type of measurement has not been reported for photon counting. The absolute value of the time interval between the time of arrival of the signal photon onto the detector input aperture and the time when the electrical output signal exceeds the pre-defined level must be determined. The optical to electrical delay value is required for ground-to-space laser time transfer with picosecond accuracy. The laser time transfer link is under construction for the European Space Agency for its application in the experiment Atomic Clock Ensemble in Space. We have developed the measurement technique and have measured the detection delay of the solid state photon counter. The experiment is described along with the first results.

The conventional definition of amount of substance n is as a quantity proportional to number of entities N. This implies that n is discrete for small N while n is considered to be continuous at the macroscopic scale, leading to a sorites paradox. A practical criterion is proposed for distinguishing between amount of substance and number of entities, and the implications for the conventional definition of amount of substance are discussed.

Compact expressions for the GUM's 'law of propagation of uncertainty' and its extensions, including the possible effects of corrections for non-linearity and including the effects of correlation in the variables, are obtained in terms of simple manipulations on three basic tensors: the gradient, the Hessian and the third order third derivative tensor of the measurement function. These formulae are an alternative to those involving mixed matrix and differential algebra. They provide a systematic and reproducible way to arrange the terms provided by the derivatives of various orders of a measurement function. The proposed formulae, which appear mathematically complicated, are surprisingly easy to implement in spreadsheet programs and interpreted matrix oriented programming languages. This is illustrated by means of an example of the propagation of uncertainty for the ratio of two normal and correlated variables.

There is a common misconception among educators, and even some metrologists, that the Avogadro constant N_A is (or should be) a pure number, and not a constant of dimension N⁻¹ (where N is the dimension amount of substance). Amount of substance is (and always has been) measured as a ratio of other physical quantities, and not in terms of a specified pure number of elementary entities. Hence the Avogadro constant has always been defined in terms of the unit of amount of substance, and not vice versa. The proposed redefinition of the mole in terms of a fixed value of the Avogadro constant is examined, and it is shown that such a redefinition would not bring any significant metrological benefit. It is contended that such a redefinition would only add to the confusion in this field, and so should be rejected.

It is widely accepted that improvement of the current International System of Units (SI) is necessary, and that central to this problem is redefinition of the kilogram. This paper compares the relative advantages of two main proposals for a modern scientific definition of the kilogram: an 'electronic kilogram' based on a fixed value of Planck's constant, and an 'atomic kilogram' based on a fixed value for Avogadro's number. A concrete and straightforward atomic definition of the kilogram is proposed. This definition is argued to be more experimentally neutral than the electronic kilogram, more realizable by school and university laboratories than the electronic kilogram, and more readily comprehensible than the electronic kilogram.

The design, operating parameters and the accuracy evaluation of the NPL Rb atomic fountain are described. The atomic fountain employs a double magneto-optical arrangement that allows a large number of ⁸⁷Rb atoms to be trapped, a water-cooled temperature-stabilized interrogation region and a high quality factor interrogation cavity. From the uncertainties of measured and calculated systematic frequency shifts, the fractional frequency accuracy is estimated to be 3.7 × 10⁻¹⁶. The fractional frequency stability, limited predominantly by noise in the local oscillator, is measured to be 7 × 10⁻¹⁶ after one day of averaging. Based on the proposed quasi-continuous regime of operation of the fountain, the accuracy of the Rb standard of 5 × 10⁻¹⁷ reachable in two days of averaging is predicted.

The correction due to the finite speed of light is among the most inconsistent in absolute gravimetry. Formulae reported by different authors yield corrections scattered up to 8 µGal for no obvious reasons. The problem, though noted before, has never been studied, and nowadays the correction is rather postulated than rigorously proven. In this paper we make an attempt to revise the subject. Like other authors, we use physical models based on signal delays and the Doppler effect; however, in implementing the models we additionally introduce two scales of time associated with moving and stationary reflectors, derive a set of rules to switch between the scales and establish the equivalence of trajectory distortions as obtained from either time delay or distance progression. The obtained results enabled us to produce accurate correction formulae for different types of instruments, and to explain the differences in the results obtained by other authors. We found that the correction derived from the Doppler effect is accountable only for two-thirds of the total correction due to the finite speed of light, if no signal delays are considered. Another major source of inconsistency was found in the tacit use of simplified trajectory models.

The electromagnetic fields and eigen-frequencies of triaxially ellipsoidal resonators have been calculated. The method used is modal superposition, based on the decomposition of the fields inside the resonator into a series expansion, with unknown coefficients, of the eigen-states of a spherical resonator. The coefficients and eigen-frequencies have then been calculated by minimizing the rms electric field at the resonator surface using software designed within MatLab®. Accuracies of parts in 10¹⁰ have been obtained for the eigen-frequencies, and the dependence of the calculations on the ellipsoidal eccentricities and the resonator modes has been analysed. The results are compared with those of Mehl (2009 Metrologia46 554–9), who used a second-order approximation. The method of modal superposition has the potential for solving many similar problems in resonators of arbitrary shapes.

A piston prover determines the gas flow rate by measuring the time interval that a movable piston inside a cylinder needs to pass a known volume of gas at a defined pressure and temperature. This paper deals with the dynamic effects related to the operation of a high-speed, clearance-sealed realization of the piston prover concept. Its dynamic characteristics are analysed by means of pressure-response measurements and lumped-element mathematical modelling. The experimental results show that the pressure oscillations during the timing cycle increase significantly above a certain flow rate and have multiple frequency components. They could be related to the resonance effects of the piston oscillator, which is excited by the flow instabilities of the gas flowing in the cylinder below the piston. The simulations show that the sensitivity to the dynamic pressure effects depends on the properties of the thermodynamic gas processes being adiabatic, polytropic or isothermal. A new, modified flow equation of the piston prover, which considers the polytropic index as an input variable, is proposed.

The METAS watt balance project was initiated slightly more than a decade ago. Over this time, the apparatus has been through an uninterrupted series of upgrades that have improved its reliability to a point where continuous series of measurements can be taken fully automatically over periods of several months. A comprehensive analysis of possible systematic errors has now been completed and a large set of data has been analysed to calculate a value for the Planck constant h. This paper describes the watt balance in detail, explains the data acquisition and analysis thoroughly and presents the uncertainty budget. The value of the Planck constant determined with our apparatus is h = 6.626 069 1(20) × 10⁻³⁴ J s with a relative standard uncertainty of 0.29 × 10⁻⁶. This value differs from the 2006 CODATA adjustment by 0.024 µW W⁻¹.

The Boltzmann constant k was measured by comparing the Johnson noise of a resistor at the triple point of water with a quantum-based voltage reference signal generated with a superconducting Josephson-junction waveform synthesizer. The measured value of k = 1.380 651(17) × 10⁻²³ J K⁻¹ is consistent with the current CODATA value and the combined uncertainties. This is our first measurement of k with this electronic technique, and the first noise-thermometry measurement to achieve a relative combined uncertainty of 12 parts in 10⁶. We describe the most recent improvements to our Johnson-noise thermometer that enabled the statistical uncertainty contribution to be reduced to seven parts in 10⁶, as well as the further reduction of spurious systematic errors and electromagnetic interference effects. The uncertainty budget for this measurement is discussed in detail.

This paper discusses simultaneous gravity and vertical gravity gradient measurements obtained with a newly designed recoil-compensated dropping chamber adapted to an FG5 absolute gravimeter. The new dropping chamber incorporates counterweights to compensate recoil effects. It has the same physical length as the standard FG5 dropping chamber but the free-fall distance was increased from 20 cm to 25 cm. The new drive train pulls on the centre of the system to reduce unwanted horizontal velocity and rotation of the free-falling test mass. The test-mass material was chosen to reduce possible magnetic eddy-current damping caused by external magnetic field gradients. External lead masses were used to change the gravity and vertical gravity gradient. The measurements agree well with the theoretical gravity field changes derived from the position of the external weights. The experiment clearly demonstrates the efficacy of using an absolute gravity meter to measure both the gravity and the gravity gradient signals caused by variations in the external gravity field. This technique shows promise for passive gravity-monitoring applications.

The bandpass of spectrometers can cause appreciable errors when making radiometric measurements. This paper describes a practical method for correcting a set of equispaced measured values provided by a spectrometer with a finite bandwidth, an arbitrary bandpass function and at an arbitrary wavelength step. The paper reviews the limits of the approach for real spectra in the presence of measurement noise and suggests ways of reducing the effect of noise.

The overall uncertainty of a model prediction is a combination of the uncertainty of the input parameters and the uncertainty of the model assumptions. The former is referred to as parameter uncertainty; the latter model uncertainty. A method for quantifying model uncertainty is proposed for complicated numerical models that are not amenable to more traditional approaches. The method is based solely on comparisons of model predictions with experimental measurements, with the difference reported in terms of only two metrics, a bias factor and a relative standard deviation. The simplicity of the approach makes it ideal for models used for regulatory compliance because approving authorities often lack detailed training in modelling and uncertainty analysis.

A cleaning method using ultraviolet activated ozone has been developed at the National Physical Laboratory (NPL). A comparison to test the effectiveness of this cleaning method with nettoyage-lavage cleaning on platinum–iridium artefacts and kilogram mass standards was undertaken at the Bureau International des Poids et Mesures (BIPM). Three cleaning trials were performed to compare the effectiveness of the two methods at removing natural, medium and heavy levels of surface contamination.

Both the ultraviolet light/ozone method and the nettoyage-lavage method successfully removed both natural levels and medium levels of surface contamination. However, in the medium contamination trial nettoyage-lavage cleaning removed additional mass from the Pt/Ir mass standard under test that could not be accounted for in terms of surface contamination.

In the heavy contamination trial nettoyage-lavage cleaning successfully removed most of the contamination from the surface of the contaminated Pt/Ir mass standard. The ultraviolet light/ozone method removed about two thirds of the surface contamination and therefore for heavily contaminated mass standards it is advisable to pre-clean them with a solvent before ultraviolet/ozone cleaning.

In a free-fall absolute gravimeter usually a Michelson type interferometer is employed to track the trajectory of a freely falling retroreflector. The accelerated motion of the retroreflector produces a Doppler-shift in the laser wavelength. From the interference signal (beat signal) of the Doppler-shifted and the reference electromagnetic waves the relative motion of the freely falling retroreflector with respect to an inertial reference retroreflector is reconstructed. Considerations of second-order Doppler-shift terms lead to a correction in the acceleration due to gravity of several microgals (1 µGal = 10 nm s⁻²). This correction is commonly called speed of light correction. To date different correction formulae have been proposed, which differ by several microgals.

In this paper we review several previous publications and show the reasons for the different results.

Formal pair-wise temperature differences, a comparison reference value (CRV) and degree of equivalence, between the UK (NPL), Chinese (NIM) and Spanish (CEM) national measurement institutes (NMIs), are calculated from the results of a prototype key comparison of the ITS-90 above the silver point using high temperature fixed points (HTFPs) of Co–C (1324 °C), Pt–C (1738 °C) and Re–C (2474 °C). The local realizations of ITS-90 temperatures were assigned by NPL, NIM and CEM to their individual sets of HTFPs. NIM and CEM then transported their cells to NPL and the temperature was realized by all the cells determined in quasi-identical measurement conditions using a linear pyrometer. From these results the pair-wise temperature differences between the three institutes were established. In addition a non-weighted and a weighted CRV were calculated for the comparison and degree of equivalence estimated. The results show very close agreement of the ITS-90 as realized by the three institutes. It is argued that the ease of the comparison and the low uncertainties attained strongly suggest that HTFPs should be the scale comparison artefacts of choice when comparing primary realizations either of the ITS-90 or thermodynamic temperature.

The curvature of a single crystal of Si with a thin epitaxial film of a SiGe alloy has been determined by measuring the spatial variation of lattice-plane orientation across the surface. The technique uses the National Institute of Standards and Technology (NIST) lattice comparator (LC) with the capability to determine the orientation of lattice planes perpendicular to a curved crystal surface with a precision of approximately 2 × 10⁻⁹ rad. The test vehicle for technique development was a NIST Standard Reference Material, SRM 2000, with a 49 nm thick film of Si–15% Ge on the surface. This alloy has a lattice parameter ≈0.6% larger than that of Si, and as the film was epitaxial with the Si substrate, the resultant stress in the Si–Ge film caused the die to be deformed into a curved shape. Measurement of the lattice-plane orientation as a function of position across the die surface allowed the die curvature to be determined, yielding a radius of curvature of 275.6 m ± 3.6 m (two standard deviations). Precise measurements were enabled in part by careful characterization of systematic variations in the LC such as the beam profile and sample-stage repeatability. From the LC plane-orientation data, the surface topography along the data line was calculated and found to be well described by a parabola, with the residual having a standard deviation less than 1 nm. More detailed examination of the LC data showed that the curvature of the die varied across the width of the die, decreasing towards the edges. Comparisons between the LC-determined topography profile and data obtained using an interferometric technique have resulted in valuable insights into issues such as establishing consistency across multiple measurement techniques, the role of within-die and within-wafer variations in curvature, and the implications of those issues for the development of standard reference materials and for the performance of devices fabricated using strain-engineering techniques.

Absolute gravity measurements are based on the reconstruction of the free-falling motion of a test body in vacuum. In this paper, two large disturbing effects are studied, namely the non-gravitational accelerations originated by rotation and translation of the flying body. Their contribution to the uncertainty of the free-fall acceleration is evaluated using the Monte Carlo method as proposed in Supplement 1 to the GUM. The analysis is specifically applied to the IMGC-02 absolute gravimeter, but can be easily extended to other instruments, including cold-atom gravimeters currently under development.

The spectral radiant intensity of synchrotron radiation from electron storage rings can be calculated from basic electrodynamic relations (Schwinger equation). A storage ring can, thus, be used as a radiometric primary source standard. The Metrology Light Source (MLS), the dedicated electron storage ring of the Physikalisch-Technische Bundesanstalt, can be operated as a primary radiation source standard from the near infrared up to the soft x-ray region and its operational parameters can be adjusted and accurately measured in a wide range. The MLS electron beam current can be varied from 1 pA (one stored electron) up to 200 mA and, thus, the radiant intensity, being directly proportional to the stored current, can be varied by more than 11 decades. The electron energy, which has a large effect on the spectral shape of the spectrum, can be varied from 105 MeV up to 630 MeV. For the radiometric comparison, the total power irradiated into a well-defined solid angle was directly measured by a cryogenic radiometer as a primary detector standard and compared with the power calculated from the storage ring parameters. These measurements were performed for various electron energies in the range from 200 MeV to 630 MeV, thus varying the shape of the spectrum. For each electron energy setting, the power level was varied within the dynamic range of the cryogenic radiometer by a variation of the electron beam current. Good agreement was found for all parameter settings, thus validating the performance of the cryogenic radiometer and the storage ring parameter measurements within the related uncertainty budget.

Equations (45) and (47) in our paper [1] in this issue have incorrect sign and should read The error traces back to our formula (3), inherited from the paper [2]. According to the technical documentation [3, 4], the formula (3) is implemented by several commercially available instruments. An incorrect sign would cause a bias of about 20 µGal not known for these instruments, which probably indicates that the documentation incorrectly reflects the implemented measurement equation.

Our attention to the error was drawn by the paper [5], also in this issue, where the sign is mentioned correctly.

References

[1] Nagornyi V D, Zanimonskiy Y M and Zanimonskiy Y Y 2011 Correction due to the finite speed of light in absolute gravimeters Metrologia48 101–13

[2] Niebauer T M, Sasagawa G S, Faller J E, Hilt R and Klopping F 1995 A new generation of absolute gravimeters Metrologia32 159–80

[3] Micro-g LaCoste, Inc. 2006 FG5 Absolute Gravimeter Users Manual

[4] Micro-g LaCoste, Inc. 2007 g7 Users Manual

[5] Niebauer T M, Billson R, Ellis B, Mason B, van Westrum D and Klopping F 2011 Simultaneous gravity and gradient measurements from a recoil-compensated absolute gravimeter Metrologia48 154–63