Table of contents

There is potential for confusion between the term 'coverage interval', which is developing a common usage in metrology, and the term 'statistical coverage interval', as defined in the Guide to the Expression of Uncertainty in Measurement. The meaning of a 'statistical coverage interval' is explained further, and possible courses of action are suggested.

The usual method adopted for multipoint calibration of glass hydrometers is based on the measurement of the buoyancy by hydrostatic weighing when the hydrometer is plunged in a reference liquid up to the scale mark to be calibrated.

An image processing approach is proposed by the authors to align the relevant scale mark with the reference liquid surface level. The method uses image analysis with a data processing technique and takes into account the perspective error. For this purpose a CCD camera with a pixel matrix of 604H × 576V and a lens of 16 mm focal length were used.

High accuracy in the hydrometer reading was obtained as the resulting reading uncertainty was lower than 0.02 mm, about a fifth of the usual figure with the visual reading made by an operator.

The approach to evaluation of measurement uncertainty for influences impacting the evaluation of the fringe fraction using digital methods is presented. We also included uncertainty considerations regarding correction for platen flexing in long gauge block calibrations, where the phase of the platen reference surface is extrapolated to the side edge of the gauge block. Contributions to the uncertainty budget for a refractometer cell in the interferometer set-up for long gauge block calibration are outlined, including the effect of correlation between uncertainties in the wavefront phase used in refractivity and central length measurements.

This paper describes mathematical models for estimating measurement uncertainties of a new sampling primary standard for maintaining traceability of alternating current (ac) quantities to the time-invariant (or direct current (dc)) quantities of the International System of Units at the Physikalisch-Technische Bundesanstalt (PTB). A high-resolution analogue-to-digital conversion is used to determine effective values of ac quantities at low frequencies with uncertainty of some microvolts per volt and short measurement times. The system operates according to the synchronous generation and simultaneous analogue-to-digital conversion technique (Ramm G et al 1999 A new scheme for generating and measuring active, reactive and apparent power at power frequencies with uncertainties of 2.5 × 10⁻⁶IEEE Trans. Instrum. Meas.48 422–6 [1], Kürten Ihlenfeld W G 2001 Maintenance and traceability of ac voltages by synchronous digital synthesis and sampling PTB Report E-75, Braunschweig [2]), and extensive comparisons with the primary thermal converters of the PTB show that the sampling system and the ac–dc thermal transfer technique agree within about ±0.5 µV V⁻¹.

Several studies highlight the need for appropriate statistical and probabilistic tools to analyse the data provided by the participants in an interlaboratory comparison. In some temperature comparisons, where the measurand is a physical state, independent realizations of the same physical state are acquired in each participating institute, which should be considered as belonging to a single super-population. This paper introduces the use of a probabilistic tool, a mixture of probability distributions, to represent the overall population in such a temperature comparison. This super-population is defined by combining the local populations in given proportions. The mixture density function identifies the total data variability, and the key comparison reference value has a natural definition as the expectation value of this probability density.

The method of constrained least squares is applied to the determination of laboratory bias and degrees of equivalence in the analysis of measurement comparisons. The analysis assumes a measurement model with unknown values for all travelling artefacts and laboratory biases. Least-squares fitting applied to this model yields an infinite set of solutions, all with the same inter-laboratory and inter-artefact differences. The application of a constraint, which can be interpreted as the definition of the key comparison reference value, then yields a single solution. Different types of constraint may be applied for known-value comparisons, for key comparisons without known values, and when linking regional metrology organization or supplementary comparisons to key comparisons. Once the laboratory biases are determined, the degrees of equivalence can be determined using the generic equations provided. The constrained-least-squares approach provides a single mathematical framework for the analysis of a wide range of comparisons including those with multiple artefacts of varying attributes, circulated amongst multiple overlapping comparison loops, laboratories that provide an arbitrary number of measurements of one or more of the artefacts, and spectral dependence of laboratory bias.

This paper compares leading methods for combining information from interlaboratory evaluations of a common measurand through a random effects model of classical statistics. The leading methods are those of Cochran, Paule and Mandel, and DerSimonian and Laird. We show that all three methods are special cases of a unifying identity. The unifying identity suggests a new two-step method. This makes four methods for comparison. The comparison is based on six published data sets from three key comparisons. The method of Paule and Mandel is optimal in the sense of being conditionally restricted maximum likelihood under normality, the condition being that the estimated intralaboratory variances be treated as the true variances. The method of Paule and Mandel requires a simple iteration that can be easily done on a spreadsheet program. Therefore, it is the preferred method for combining results of interlaboratory evaluations through a random effects model. We compare the other three methods relative to the method of Paule and Mandel. The two-step method approximates the optimal method of Paule and Mandel better than the earlier methods of Cochran, and DerSimonian and Laird.

The adsorption isotherms on SiO₂/Si(100) surfaces were measured using a vacuum mass comparator. Samples with a surface area difference of 816.6 cm² were used for the measurement, and a substitution weighing method was adopted to reduce the uncertainty due to the drift and non-linearity of the indication of the mass comparator. We measured adsorption isotherms of water vapour on the SiO₂/Si(100) surfaces outgassed at a temperature of 500 °C and found that dissociative adsorption caused an irreversible increase of 0.028 µg cm⁻² with an uncertainty of 0.004 µg cm⁻² (k = 1). We also found that the physical adsorption of water molecules on hydroxylated surfaces had a monolayer capacity of 0.004 µg cm⁻² with an uncertainty of 0.002 µg cm⁻² (k = 1). In addition, the adsorption isotherms for ethanol vapour and n-octane vapour, which were different from water vapour in adsorption properties, were measured and analysed.

It is known that the stability of time transfer with GPS common view in the low latitudes of Asia is worse than in Europe and the United States. The ionosphere fluctuates greatly within ±20° of the equator, which seems to have a large effect on time transfer stability. We compared the results of ionospheric corrections obtained using the Global Ionosphere Map (GIM) with those obtained from actual measurements from the ionosphere. The frequency stabilities of common-view results in the areas close to the equator were worse than those in higher latitudes when using the GIM correction, while the results compensated with the measured ionospheric delay were comparable with those in high latitude areas. We compared the GIM simulated variations with the actual variations in the ionosphere around the equator and found that the accuracies in the lower latitudes were not as good as those in the higher latitudes. This seems to degrade the time transfer stability throughout the lower latitudes of Asia.

The absolute optical frequency of a 633 nm, I₂-stabilized He–Ne laser system is measured with a femtosecond laser frequency comb. Results over a three-year period using chain- and comb-based measurements yield an operating frequency of f_f = (473 612 353 602 850 ± 570) Hz for the INMS 3 laser stabilized to the f or a₁₆ component of the 11-5 R(127) transition in ¹²⁷I₂ at the operating conditions specified for the realization of the recommended value of this radiation. The frequency of the NRC INMS 2 laser system has recently been measured with combs at NRC and BIPM and was shown to be reproducible to better than 600 Hz (1 × 10⁻¹²) after transport. These results indicate the high level of reproducibility attainable by such widely used optical frequency standards.

Several newly developed large area photoconductive (PC) mercury cadmium telluride (HgCdTe) radiometers have been tested for spatial and angular responsivity for the purpose of determining what mode of operation (or radiometric quantity) could provide the lowest measurement uncertainty. An infrared (IR) test facility has been developed for the characterization of long wavelength IR (LWIR) detectors and radiometers for spatial response uniformity in power measurement mode and angular responsivity in both power and irradiance measurement modes. We have measured 34% to 53% spatial response non-uniformities and 1.5% to 10.5% changes in angular power reponsivity at different beam positions within the f/4 field-of-view (FOV) of the PC HgCdTe radiometers. The lowest responsivity uncertainty is achieved when these non-uniform radiometers are operated in irradiance measurement mode, where the incident uniform field of radiation averages out the detector's non-uniformity related uncertainties. The angular response deviation from the cosine function within the 16° FOV of the radiometers dominates the uncertainty budget for irradiance responsivity measurements in the 3 µm to 20 µm sensitivity range of these working standard devices.

At NMi-VSL a humidity generator was built in the early 1990s. The generator is of the circulating single-temperature, single-pressure type. One pump recirculates air or nitrogen gas over two saturators, one of which can be selected, depending on the temperature range. Some components of the standard were found to operate not to the level that was anticipated during the design. The standard has been thoroughly refurbished. Experiments showed that the standard now operates from −60 °C to +70 °C, with much improved time constants and with lower uncertainties to within approximately 0.04 °C, depending on the temperature. Design considerations and requirements for this type of standard are given in the paper. The tests involved in evaluating the performance are discussed, and the results are presented with the resulting uncertainty budget.

This paper explores a recent suggestion to use a bivariate form of the Gaussian 'error propagation law' to propagate uncertainty in the measurement of complex-valued quantities (Ridler N M and Salter M J 2002 Metrologia39 295–302). Several alterative formulations of the law are discussed in which the contributions from individual input terms are more explicit. The calculation of complex-valued sensitivity coefficients is discussed and a matrix generalization of the notion of a 'component of uncertainty' in a measurement result is introduced. A form of a 'chain rule' is given for the propagation of uncertainty when several intermediate equations are involved.

The gravimetric method is the most popular method for preparing reference gas mixtures with high accuracy. We have designed and manufactured novel mass measurement equipment for gravimetric preparation of reference gas mixtures. This equipment consists of an electronic mass-comparator with a maximum capacity of 15 kg and readability of 1 mg and an automatic cylinder exchanger. The structure of this equipment is simpler and the cost is much lower than a conventional mechanical knife-edge type large balance used for gravimetric preparation of primary gas mixtures in Japan. This cylinder exchanger can mount two cylinders alternatively on the weighing pan of the comparator. In this study, the performance of the equipment has been evaluated. At first, the linearity and repeatability of the mass measurement were evaluated using standard mass pieces. Then, binary gas mixtures of propane and nitrogen were prepared and compared with those prepared with the conventional knife-edge type balance. The comparison resulted in good consistency at the compatibility criterion described in ISO6143:2001.

The refractive index of helium at atmospheric pressure can be determined from ab initio calculations in combination with careful pressure and temperature measurements. Therefore, helium can serve as a theory-based standard of refractive index; it might be used as a medium of known refractive index for high-accuracy interferometric length measurements or it can be used to characterize and correct errors in a gas refractometer. We have used helium to correct for pressure-induced distortions of two refractometers built by us, where both refractometers basically consist of a laser locked to the transmission maximum of a simple Fabry–Perot cavity. As a proof-of-principle of the helium-correction technique, we have used our device to measure the molar refractivity of nitrogen and we find reasonable agreement with previous measurements. When our two refractometers simultaneously measure the refractive index of a common nitrogen sample, we find that the two systems agree with each other within a few parts in 10⁹.

Twelve platinum resistance thermometers (PRTs) were repeatedly calibrated between the triple point of water and the silver point. During each calibration their resistance was also determined at the Cu–Ag eutectic point. The temperatures indicated by the PRTs were within ±1 mK, except for one that differed by 4 mK from the average, 779.6360 °C, of the other eleven.

Four of these PRTs had a lower W (Ag) value than acceptable by the ITS-90, including the one that differed by 4 mK. Thus, within this set of PRTs all the 'acceptable' ones and three out of four 'unacceptable' ones indicated a unique temperature within 1 mK halfway between the aluminium and the silver points.

Previously verified models of windowless silicon photodiodes can be used to estimate their spectral response by purely relative measurements. The spectral reflectance is found from a single measurement at one wavelength to estimate the oxide thickness, from which the full spectral reflectance is calculated. The internal quantum deficiency of the silicon detector is found by fitting a physical model to a purely relative measurement to a spectrally invariant detector. The detector model ensures correct scaling of the responsivity. This method contributes to simplification of the traceability and promises a very cost efficient realization of an accurate independent spectral response scale. We have measured the responsivity of a silicon trap detector with this method. An uncertainty less than 0.20% was observed with 95% confidence in the spectral range from 455 nm to 760 nm. The uncertainty was calculated from the observed variance in the relative spectral response measurement. The uncertainty was limited by the signal to noise ratio (SNR) in the measurements of the relative spectral response of the silicon trap detectors.

A practical guide to experimental conditions such as statistical variation of signal intensity on quantitative solution state nuclear magnetic resonanace (NMR) analysis is discussed and presented. Statistical analysis showed that there is a relationship between a targeted precision and practical pulse intervals. The bandwidth of the audio filter needs to be set so that all the signals of interest fall into 80% of the centre part of the filter. When fulfilling these conditions, the relative standard deviation (RSD) of a signal area in repeated experiments can be estimated by determining the signal-to-noise ratio (SN) of a single spectrum. When the SN reached 1000, the RSD became constant with increasing SN. With such a condition, accuracy better than 1% should be obtained with quantitative NMR.

On page S12 of this article, 20 °C should be changed to 4 °C in three places, that is in the lines immediately above each of equations (30), (31) and (32).