CCL key comparison: calibration of gauge blocks by interferometry

Thalmann, R.

doi:10.1088/0026-1394/39/2/6

Cited by 23 publications

(27 citation statements)

References 1 publication

(4 reference statements)

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“…The wringing of gauge blocks has a long history. [41] During a recent Key Comparison [42], 11 laboratories wrung together pairs of gage blocks and measured the resulting lengths. The standard deviation of the repeatability of the lengths ranged from 3 to 12 nm, depending upon the laboratory.…”

Section: Dimensional Metrologymentioning

confidence: 99%

Optimizing acoustic measurements of the Boltzmann constant

Moldover

2009

Comptes Rendus. Physique

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We review the progress in acoustic metrology of gases that has occurred since the 1988 measurement of the universal gas constant R using a spherical acoustic resonator. The advances in understanding resonators and in calculating the thermophysical properties of helium ab initio suggest that today one could determine Boltzmann's constant k B from acoustic measurements using either helium or argon with a relative uncertainty less than 10 −6 . RésuméProgrès dans la détermination de la constante de Boltzmann par voie acoustique L'article récapitule les avancées effectuées en métrologie acoustique dans les gaz depuis la mesure de la constante universelle des gaz R effectuée en 1988 en utilisant un résonateur acoustique sphérique. Des progrès substantiels ont été réalisés, tant pour mieux comprendre le fonctionnement des résonateurs acoustiques que pour calculer ab initio, avec une fiabilité accrue, les caractéristiques thermo-physiques de l'hélium. Ils permettent d'envisager désormais une détermination de la constante de Boltzmann k B par voie acoustique avec une incertitude relative meilleure que 10 -6 , en utilisant soit l'argon, soit l'hélium.________________________________ 1. Introduction.

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Section: Dimensional Metrologymentioning

confidence: 99%

Optimizing acoustic measurements of the Boltzmann constant

Moldover

2009

Comptes Rendus. Physique

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“…We present calculations for data derived from the Consultative Committee for Length key comparison CCL-K1 [19], calibration of gauge blocks by interferometry. This data is used for illustrative purposes only as according to the technical protocol, key comparison data cannot be adjusted in the manner described in this paper.…”

Section: Example Calculationsmentioning

confidence: 99%

“…This data is used for illustrative purposes only as according to the technical protocol, key comparison data cannot be adjusted in the manner described in this paper. The measured values x j and associated standard uncertainties u 0,j are from 11 participating laboratories measuring 9 tungsten carbide gauge blocks of nominal lengths ranging from 0.5 mm to 100 mm ( [20], Tab. 5).…”

Section: Example Calculationsmentioning

confidence: 99%

Assessing interlaboratory comparison data adjustment procedures

Jagan

Forbes

2019

Int. J. Metrol. Qual. Eng.

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Interlaboratory comparisons (ILCs) are one of the key activities in metrology. Estimates x = (x1,…, xn) T of a measurand α along with their associated standard uncertainties u0 = (u0,1,…, u0,n) T, u0,j = u0 (xj) are provided by each of n laboratories. Employing a model of the form xj ∈ N(α, v0,j), j = 1,…,n, v0,j = u0,j2, we may wish to find a consensus value for α. A χ2 test can be used to assess the degree to which the spread of the estimates x are consistent with the stated uncertainties u0. If they are judged to be inconsistent, then an adjustment procedure can be applied to determine vj ≥ v0,j, so that x and v represent consistency. The underlying assumption behind this approach is that some or all of the laboratories have underestimated or neglected some uncertainty contributions, sometimes referred to as ‘dark uncertainty’, and the adjusted v provides an estimate of this dark uncertainty derived from the complete set of laboratory results. There are many such adjustment procedures, including the Birge and Mandel–Paule (M-P) procedures. In implementing an adjustment procedure, a desirable objective is to make as minimal an adjustment as necessary in order to bring about the required degree of consistency. In this paper, we discuss the use of relative entropy, also known as the Kullback–Leibler divergence, as a measure of the degree of adjustment. We consider parameterising v = v (b) as a function of parameters b with the input v0 = v (b0) for some b0. We look to perturb b from b0 to bring about consistency in a way that minimises how far b is from b0 in terms of the relative entropy or Kullback–Leibler divergence.

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“…Although we have not tested this concept yet, the flanged joints between sections of a steel cylinder can be robust, and, we expect, assembled reproducibly. Concerning reproducibility, we cite on an international comparison which required wringing together pairs of steel gauge blocks [28]. The standard deviation of the repeatability of the lengths of assembled pairs of blocks ranged from 3 nm to 12 nm, depending on the laboratory.…”

Section: Reducing the Effect Of The Endplatesmentioning

confidence: 99%

Cylindrical Acoustic Resonator for the Re-determination of the Boltzmann Constant

et al. 2010

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The progress towards re-determining the Boltzmann constant k B using two fixed-path, gas-filled, cylindrical, acoustic cavity resonators is described. The difference in the lengths of the cavities is measured using optical interferometry. Thus, a literature value for the density of mercury is not used, in contrast with the presently accepted determination of k B . The longitudinal acoustic resonance modes of a cylindrical cavity have lower quality factors Q than the radial modes of gas-filled, spherical cavities, of equal volume. The lower Qs result in lower signal-to-noise ratios and wider, asymmetric resonances. To improve signal-to-noise ratios, conventional capacitance microphones were replaced with 6.3 mm diameter piezoelectric transducers (PZTs) installed on the outer surfaces of each resonator and coupled to the cavity by diaphragms. This arrangement preserved the shape of the cylindrical cavity, prevented contamination of the gas inside the cavity, and enabled us to measure the longitudinal resonance frequencies with a relative standard uncertainty of 0.2 × 10 −6 . The lengths of the cavities and the modes studied will be chosen to reduce the acoustic perturbations due to non-zero boundary admittances at the endplates, e.g., from endplate bending and ducts and/or transducers installed in the endplates. Alternatively, the acoustic perturbations generated by the viscous and thermal boundary layers at the gas-solid boundary can be reduced. Using the techniques outlined here, k B can be re-determined with an estimated relative standard uncertainty of 1.5 × 10 −6 .

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CCL key comparison: calibration of gauge blocks by interferometry

Cited by 23 publications

References 1 publication

Optimizing acoustic measurements of the Boltzmann constant

Optimizing acoustic measurements of the Boltzmann constant

Assessing interlaboratory comparison data adjustment procedures

Cylindrical Acoustic Resonator for the Re-determination of the Boltzmann Constant

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