Table of contents

We report the development of a self-validating high temperature thermocouple, whereby a high temperature fixed point of metal–carbon eutectic alloy forms an integral part of the thermocouple measuring junction, permitting in situ calibration.

There are currently nine caesium fountain primary frequency standards regularly reporting calibrations of International Atomic Time to the Bureau International des Poids et Measures (BIPM). An investigation has been carried out using data from the BIPM publication Circular T to evaluate the frequency differences among these standards and to determine whether these offsets are consistent with the stated uncertainties. The fractional frequency uncertainties of some Cs fountains are now in the range of 4 × 10⁻¹⁶ to 5 × 10⁻¹⁶. The results of this investigation show that the standards agree well with each other. An overall estimate of the caesium frequency is made using the weighted mean of all the fountains.

ARPANSA has calculated new Monte Carlo corrections for their low and medium energy x-ray free-air chambers. The new calculations include a diverging beam and details of the limiting aperture. The diverging beam simulations are compared with previous parallel beam simulations. The electron loss, scattering and fluorescence corrections do not change when beam divergence is included, even for the short source–detector distance of 30 cm used in post-2008 low energy calibrations. Transmission and scattering from the aperture are significant for both free-air chambers and dependent on the beam divergence. The constancy of the correction factors with changing air path length was investigated at low energies. In the extreme conditions of 100 kV and a distance of 30 cm the correction factors showed significant deviation.

At the new SPring-8 extreme ultraviolet free-electron laser in Japan, a radiometric comparison between a gas-monitor detector from Physikalisch-Technische Bundesanstalt/Deutsches Elektronen-Synchrotron/Ioffe Physico-Technical Institute (Ioffe) and a cryogenic radiometer from National Institute of Advanced Industrial Science and Technology was carried out. Radiant power in the range between 30 µW and 350 µW was measured at the wavelengths of 51.3 nm, 56.1 nm and 61.2 nm. The results obtained with the two different detectors agree within 2.6%, which is well below their combined relative standard uncertainty, which varies from 4.1% to 5.5%.

The weighted mean is widely used in combining data sets of experimental measurements with a weight proportional to the value of the data number divided by the sample variance in a conventional method. However, this standard procedure is not appropriate for obtaining the weighted mean frequency of a phase-stabilized signal with white phase noise, since the data are autocorrelated. The autocorrelation is obtained in the case of white phase noise and a new weighting method is proposed. Using this, the uncertainty associated with the weighted mean frequency of a phase-stabilized signal with white phase noise is given. The effect of counter dead-time is also discussed.

An algorithm of the Monte Carlo method applied to the computation of the spectral and total effective emissivity of a specular–diffuse, non-isothermal blackbody cavity formed by a cylindrical tube and a flat inclined bottom is described. The effect of cavity wall temperature non-uniformity on the cavity radiation characteristics is studied for various combinations of the affecting parameters.

The INRIM standard facility for low airspeed (0.20 m s⁻¹ to 5.00 m s⁻¹), called rotating arm (RA), is presented. This is a dragging facility, i.e. it is based on the reciprocity principle. This means that the relative movement between air and measurement instrument is obtained through the translation of the latter through nominally still air. The instrument is mounted on the tip of an arm approximately 3.5 m long, which rotates about an axis; measurement of the tip velocity is traceable to measurements of length and time primary standards because it is obtained through measuring the instrument positioning radius and the rotation frequency. The working principle, the design and the measurement chain of the RA are described in detail. Because of the movement of the arm, air movements arise in the measurement ambient; this can be seen as a systematic error connected to the functioning of the system; the methods for correcting this and other systematic errors are described in the paper, together with specific details and operating procedures aimed at reducing the uncertainty contributions. Finally, an evaluation of the uncertainty budget is discussed.

During the monitoring of the long term stability of two accelerometers intended for use in the CIPM Key Comparison CCAUV.V-K2, significant deviations of the magnitude results of the single-ended transducer were discovered. These deviations depend on whether the calibration was performed on an armature made of beryllium or of ceramic. Further investigations showed that this effect must be attributed to some not yet readily understood dynamic process between the contact surfaces of the accelerometer and the armature. The relative motion underlying the deviations has a significant systematic influence already at 5 kHz and beyond. Therefore, the effect needs to be considered in some way while comparing results within the key comparison, as some laboratories use beryllium armatures and some use ceramic armatures.

The contribution describes the details and outcome of the investigations performed on the topic so far and is intended to trigger the necessary discussion on consequences and solutions.

The uncertainty evaluation of CSF2, the second caesium fountain primary frequency standard at PTB, is presented. The fountain uses optical molasses to cool atoms down to 0.6 µK. The atoms are launched vertically in a moving optical molasses, and state selected in the |F = 3, m_F = 0⟩ hyperfine ground state. During their ballistic flight, the atoms interact twice with a microwave field, thus completing the Ramsey interaction. With a launch height of 36.5 cm above the cavity centre, the central Ramsey fringe has a width of 0.9 Hz. About 3 × 10⁴ atoms, 30% of the initial number in the |F = 3, m_F = 0⟩ state, are detected after their second interaction with the microwave field. Stabilizing the microwave frequency to the centre of the central Ramsey fringe, a typical relative frequency instability of 2.5 × 10⁻¹³(τ/s)^−1/2 is obtained. The CSF2 systematic uncertainty for realizing the SI second is estimated as 0.80 × 10⁻¹⁵. First comparisons with the fountain CSF1 at the Physikalisch-Technische Bundesanstalt and other fountain frequency standards worldwide demonstrate agreement within the stated uncertainties.

This paper continues a discussion generated by a recent paper of Hall (2008 Metrologia45 L5–8) regarding the performance of methods of uncertainty evaluation. The 'validity' of a method of generating intervals of measurement uncertainty is identified principally with the frequency with which these intervals contain the measurand. Two approaches to the evaluation of such intervals are described, and their performances are compared for the simple measurement function appearing in Hall's paper. The first is a Bayesian approach, which is consistent with the numerical method described in Supplement 1 to the Guide to the Expression of Uncertainty in Measurement. The second is an approach based on frequentist principles. Simulations with fixed values of the unknown parameters are conducted to find the rate at which the methods generate intervals containing the value of the measurand and to find the mean widths of the intervals produced. The results show that the standard Bayesian procedure and its modifications can perform poorly. In contrast, the frequentist procedure achieves the required rate of 0.95 while generating intervals of similar width.

An intercomparison of the melting temperatures of four Co–C eutectic fixed-point cells by using two Pt/Pd thermocouples was performed. The cells are usable for the calibration of thermocouples and were constructed in the participating laboratories of PTB, NPL, LNE and NMIJ/AIST. The measurements were performed in four different high-temperature furnaces but by applying the same measurement procedure. In spite of slightly different cell designs and different material sources the melting temperatures of the investigated Co–C cells agreed very well within their expanded uncertainties of k = 2. Furthermore, the mean maximum difference of the melting temperatures of the four Co–C cells measured in different laboratories by using different furnaces and Pt/Pd thermocouples was found to be of the order of 85 mK (2 µV).

A procedure is proposed for linking the results of a RMO key comparison to those of a related CIPM key comparison when different travelling standards are used. The approach is based on a relationship between unilateral and bilateral degrees of equivalence (DOEs) as defined in the MRA, and it assumes that the quantities being estimated by the unilateral DOEs for the linking laboratories are the same in the CIPM and the RMO key comparisons.

We show that in the particular situation of single stable travelling standards in the two key comparisons the assumptions and the results of the approach are in line with previously proposed linking procedures which employ an additive shift to the RMO data prior to their comparison with the CIPM key comparison reference value. However, the procedure put forward here yields (slightly) smaller linking uncertainties compared with these methods and, more important, it is generally applicable also in situations when several travelling standards are used or when the travelling standard shows a drift.

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Equations (21), (22) and (23) should be corrected by The text following equation (23) should be replaced by:

"The relation between ρ_λ and ρ₅₅₀ can be simplified in equation (23) because the reflectance factor is considered equal to one and stable over the spectral range from 380 nm to 780 nm."