Table of contents

In a ballistic gravimeter, when a test body rotates during free fall an optical path error results, unless the centre of mass (COM) and the optical centre of the corner cube are exactly co-located. The error associated with the rotation needs to be held to 1 µGal (1 µGal = 10⁻⁸ m s⁻²) or less, so as to not compromise the accuracy of today's absolute gravimeters. This error is systematic, difficult to monitor and can be decreased in only two ways: (1) by reducing the rotation rate of the falling object and/or (2) by minimizing the distance between the COM of the dropping object and the optical centre of the corner cube embedded in it. We report here on a new direct and extremely sensitive method for minimizing the distance between the COM and the optical centre.

In the context of experimental information shortage, uncertainty evaluation of a directly measured quantity involves obtaining its standard uncertainty as the standard deviation of an assigned probability density function (pdf) that is assumed to apply. In this article, we present a criterion to select the appropriate pdf associated with the estimate of a quantity by seeking that pdf which is the most probable among those which agree with the available information. As examples, we apply this criterion to assign the proper pdf to a measurand assuming that we know just its estimate, or both its estimate and its standard uncertainty. Our results agree with those obtained by applying the principle of maximum entropy to both situations.

In recent years the Comité International des Poids et Mesures has assigned the unit one to all dimensionless quantities and to some countable quantities. This article examines the reasons for that decision and questions their logical basis. It draws attention to some of its undesirable consequences.

Results of International Key Comparisons of National Measurement Standards provide the technical basis for the Mutual Recognition Arrangement (MRA) formulated by Le Comité International des Poids et Mesures (CIPM). With many key comparisons already completed and a number of new key comparison experiments currently under way, we now have a better understanding of the statistical issues that need to be addressed for successfully analysing data from key comparisons and making proper interpretations of the results. There is clearly a need for a systematic approach to statistical analyses of key comparison data that can be implemented routinely by all participating laboratories.

The determination of a key comparison reference value (KCRV) and its associated uncertainty and the degrees of equivalence are the central tasks in the evaluation of key comparison data. A satisfactory definition of a KCRV, however, is based on the assumption that all laboratories are estimating the same unknown quantity of the common circulating artefact, that is, the results from the different laboratories are mutually consistent. In this paper, we compare a number of statistical procedures for testing the consistency assumption.

A statistical analysis for key comparisons with linear trends is proposed. The approach has the advantage that it is consistent with the no-trend cases. The uncertainties for the key comparison reference value, which is time dependent in this case, and the degrees of equivalence are also provided. As an example, the approach is applied to key comparison CCEM-K2.

Measurement of the (220) Bragg-plane spacing of Si using combined x-ray and optical interferometry with an uncertainty lower than 10⁻⁸ requires the study of influence factors not considered in the past. In this paper the Bragg-plane spacing definition itself is re-examined and the influence of a constant strain gradient is studied by means of Takagi's equations. Their analytical and numerical solutions indicate that, contrary to our previous assumption, the period of the travelling fringes is affected by the Si atom spacing at the analyser entrance surface.

The uncertainty of a primary spectral irradiance scale based on filter radiometers (FRs) is studied by analysing the propagation of uncertainties and covariances through a spectral interpolation process, when a modified Planck's radiation law is fitted to the measurement data. The advantage of performing the uncertainty analysis in optimizing the selection of the FR wavelengths is demonstrated. We also estimate the effect that correlations in the FR signals have on the uncertainty of the fitted spectral irradiance values. In the case of correlated input data, the results of the uncertainty propagation are found to be within two practical limits: uncertainty values in the FR data and the values obtained by uncertainty propagation with uncorrelated FR signals.

A new primary standard for generation of vacuum pressures between 9 × 10⁻⁴ Pa and 10³ Pa has been completed at the Ulusal Metroloji Enstitüsü (UME). It is based on the static expansion method, whereby the range is extended to lower pressures by multiple expansions. The apparatus consists of six vessels that provide a pressure reduction by a factor of about 10⁻⁶ in the main calibration vessel after a three-step expansion. Seventeen platinum resistance thermometers are mounted on the vessels to determine the correction due to temperature effects. The whole apparatus is built using the UHV technique and can be baked up to 400 °C. The expanded (k = 2) relative uncertainties of pressures, generated by this new standard, range from 2.1 × 10⁻³ at 9 × 10⁻⁴ Pa to 9.5 × 10⁻⁴ at 10³ Pa.

In cooperation with the Time and Frequency Group of the National Institute of Standards and Technology, the Communications Research Laboratory has developed an optically pumped primary frequency standard (PFS) which is named CRL-O1. The accuracy of CRL-O1 has been evaluated and reports have been sent to the Bureau International des Poids et Mesures. The results of the evaluations have been published in Circular T. We estimate the biases of the frequency shifts and the so-called type A and type B uncertainties. The combination of type A and type B uncertainties is about 7 × 10⁻¹⁵. The evaluated frequency of CRL-O1 is in good agreement with that of other PFSs.

In this work, a new experimental method, based on non-invasive infrared thermograph techniques, has been developed to visualize and quantify the spatial temperature distribution of the convective air currents generated by a heated body.

Starting from that distribution of temperature and using some theoretical models, the corresponding velocity distribution of the air currents and drag forces were evaluated. Once the drag forces were obtained, their values were compared with the values of mass variations taken from the balance, proving the relationship between the inverse of the drag forces and the values of the variation of mass.

We present a method to analyse international measurement comparisons, including linking two or more comparisons. This method, which is based on linear generalized least-squares estimation, directly gives the degrees of equivalence required by the Mutual Recognition Arrangement, both relative to the key comparison reference value (KCRV) and between pairs of participating laboratories. The key features of the method are its ability to accommodate multiple travelling standards (including instabilities in the standards), multiple measurements by participating laboratories, multiple comparison loops, and known correlations between measurements (both intra- and interlaboratory). The method can be applied with or without a KCRV (but does not give a value for the KCRV). An analysis of the linked comparisons APMP.M.M-Kl and CCM.M-Kl is presented to illustrate the method. While best suited to comparisons with single-valued travelling standards, the method can be applied to most other comparison types.

A primary system based on the so-called static expansion of gases has been made available at IMGC-CNR for gauge calibration in the range 0.1 Pa to 1000 Pa.

As is known, in such systems the generated pressure is calculated by application of the ideal gas law and is a function of the inlet pressure, the temperatures of the various volumes and their ratios.

The uncertainty evaluation of the pressure measured with such system is the main subject of this paper.

At present, the system is operated with three volumes (≈0.01 litre, ≈0.5 litre and ≈50 litre) and two expansion ratios (R₄ ≅ 4761 and R₃ ≅ 95) determined by application of the multiple expansion method through pressure measurements performed with the best transfer gauges available at IMGC-CNR. The characteristics of such transfer gauges are discussed with respect to two different conditions of use: that is, for determination of the expansion ratio, R_j, and for measurements of the inlet pressure.

The combined expanded uncertainty of the generated pressure (p_xi) is then given by and

Considerations on participation in comparisons are also presented.

New quantum Hall array resistance standards (QHARS) with nominal values in the range from R_K/200 to 50R_K (i = 2 plateau) have been developed (R_K is the von Klitzing constant). The design of the QHARS based on the connection in parallel of Hall bars is made suitable for use in both magnetic field directions. Measurements performed with currents up to 4 mA at 1.3 K show that R_K/200 (∼129 Ω) and 16R_K/4130 (∼100 Ω) resistance standards have Hall resistances which agree with their nominal values within 5 parts in 10⁹ (1σ). While increasing the temperature, the Hall resistance varies linearly with the longitudinal resistance. Because the sign of this deviation depends on the magnetic field direction, the average of the Hall resistance values measured for both magnetic field directions remains constant within 5 parts in 10⁹ up to 4.2 K. Owing to their large working current, these QHARS have allowed an accurate calibration of a 100 Ω wire resistor using a commercial resistance bridge. An R_K/20 (∼1290 Ω) resistance standard made of ten Hall bars placed in parallel by quadruple connections has also been studied. It is found that the resistances measured by using three different voltage terminal pairs agree within 5 parts in 10⁹ in relative value.

We describe a quasi-spherical, noble-gas-filled cavity designed to determine the thermodynamic temperature of the gas from measurements of the frequencies and the half-widths of microwave and acoustic resonances in the cavity. The quasi-spherical shape retains the advantages of spherical acoustic resonators (non-degenerate, radially symmetric acoustic modes, negligible viscous damping at the boundary) while simplifying the determination of the cavity's thermal expansion using microwave resonances. As a specific example, we consider a cavity bounded by four quadrants of a perfect sphere of radius a connected to each other by narrow cylindrical sections of thickness 2₁a and 2₂a, where ₁ and ₂ are of the order of 10⁻³. The cylindrical sections split the degenerate microwave triplets (TM11, TE11, TM12, etc) into three easily resolved components with predictable orientations. Preliminary measurements show that two judiciously located microwave probes excite and detect all three components of each microwave triplet with approximately equal amplitudes. We discuss the placement of acoustic transducers and the dimensions of ducts that admit gas from a manifold into the cavity.

Corrections were made to this article on 14 June 2004. The corrected electronic version is identical to the print version. The corrections are in the first two paragraphs of section 5.2 and in table 6.

This paper presents a new radiation pyrometry, multi-band pyrometry, obtained by increasing the narrow wavelength bandwidth of multi-wavelength pyrometry. The purpose of this paper is to evaluate the necessity for and the merit of multi-band pyrometry, compared with the traditional multi-wavelength pyrometry. Here, we propose theoretical optimization criteria, based on the temperature discrimination resolution, to analyse the characteristics of multi-band pyrometry. The simulation results indicate that the wavelength bandwidth of multi-band pyrometry does affect the temperature discrimination resolution, and the choice of the bandwidth range will have a significant influence on the performance of the radiation pyrometer. Finally, we conclude that the traditional multi-wavelength pyrometry with 'pure' wavelengths is sometimes not the optimum method for measurements of true surface temperatures. However, multi-band pyrometry with the appropriate bandwidth range may be the optimum method to achieve optimum measurements.

This paper demonstrates a calorimetric procedure for calibrating high-heat-flux sensors. The results are in agreement with calibrations obtained using black-body radiation. However, the proposed method has the potential of being more accurate than traditional approaches. This new procedure calibrates sensors to measure correctly under conditions of concentrated solar radiation. At present, the thermal balance calibration technique in the laboratory is limited to solar irradiances of approximately 100 kW m⁻². The next step is to demonstrate this methodology to higher irradiances under non-laboratory conditions in the CIEMAT solar furnace at Plataforma Solar de Almería.

A mass comparator for 1 kg weights has been designed and built at the BIPM based on our experience with a prototype flexure-strip balance named FB-1. The flexure-strip balance FB-2 is fully automated and mainly used for research. It consistently achieves a repeatability of weighings in air or in vacuum of 1 kg artefacts at least ten times better than that obtainable with the best knife-edge balances. The aim of this paper is to describe the design and capabilities of the FB-2, drawing on theoretical studies already published. Finally, results obtained with the FB-2 are given to illustrate its metrological possibilities.

This work is a follow-up to a previous study that was aimed at reducing the uncertainty of the air density correction used to correct mass comparisons for the effects of air buoyancy. To clarify the difference observed previously in moist air between two absolute methods (CIPM-81/91 formula and air buoyancy artefacts determination), additional measurements were carried out in moist air, dry nitrogen and vacuum. The results obtained by the two methods for nitrogen density were in good agreement while the discrepancy was confirmed for the moist air density. A comparison of a 1 kg stainless steel mass against a 1 kg Pt/Ir mass standard was carried out to compare the accuracy of these two methods. The results of this comparison made in moist air, dry nitrogen and vacuum by using buoyancy artefacts gave an agreement within 1 µg. Our particular results confirmed the good accuracy of the air buoyancy artefacts method and reinforced the hypotheses that the accuracy of the air density using the CIPM formula is limited by the estimation of its composition.

The purpose of this work is to study the effect of water vapour sorption on mass standards by means of two methods: (a) a global and direct gravimetric method determining the water vapour deposit on the total surface area of mass standards; (b) an optical and indirect ellipsometric method permitting the evaluation of the adsorbed water thickness on the localized surface of mass standards.

The coefficient of water vapour adsorption in moist air and the amount of water desorption from air to vacuum were determined on the surfaces of mass standards. Measurements were achieved by both methods using the same samples of Pt/Ir, stainless steel and silicon. Results obtained on stainless steel showed a good agreement between the two methods. For the Pt/Ir and the silicon samples, the sorption effect evaluated by the gravimetric method was about twice that inferred from ellipsometry.

An international Advisory Group on Uncertainties has published guidelines for the statistical analysis of a simple key comparison carried out by the Consultative Committees of the International Committee of Weights and Measures (CIPM) where a travelling standard of a stable value is circulated among the participants. We discuss several concerns regarding these guidelines. Then, we describe a statistical model based on the Guide to the Expression of Uncertainty in Measurement to establish the key comparison reference value, the degrees of equivalence, and their associated standard uncertainties on the basis of the data submitted by the participants. The proposed statistical model applies to all those CIPM key comparisons where the submitted results are mutually comparable and appropriate for determining the key comparison reference value and the submitted uncertainties are sufficiently reliable.

We have studied two kinds of reference detectors to be used for calibration of fibre optic power meters. The first type consists of an InGaAs photodiode mounted directly on an adapter using a standard FC connector. In the second type, a similar photodiode is fitted into a 5 cm diameter integrating sphere. The plain photodiodes are used for low power levels and the sphere detector for high power levels because of the low throughput (∼0.7%) of the sphere. The detectors, with their FC connectors removed, are calibrated using collimated laser beams, using as the reference a spectrally flat pyroelectric radiometer traceable to a cryogenic absolute radiometer. The spatial non-uniformities of the plain photodiodes are of the order of 0.3% throughout the active area of 5 mm diameter. The angular responsivity varies less than ±0.1% within the angle of ±8°, which covers 99% of the radiation emitted from the fibre end. The angular non-uniformity of the sphere detector is less than 0.1%. The results indicate that a plain photodiode can be used as a reference detector of fibre optic power. The calibration uncertainty at HUT is presently of the order of 1% (k = 2).