In order to achieve nanometer accuracy, metrologists need to identify the sources of error and develop solutions to eradicate or minimize their effects. A stabilized low power dual-frequency laser heterodyne interferometer (ZMI-1000A) designed to measure linear and angular displacement with nominal measurement resolution 1.24 nm and 0.0025 arcsec, respectively, is used to achieve measurement of displacements over different travelling axes by comparison with the electronically reference measurements of the stage over wide range 500 mm. The repeatability and reversal error of linear stage over the working distance have agreed opto-electronically and the positioning uncertainty been reduced. A multivariable framework was implemented for the x-axis due to the cross coupling between the forward and backward course of the linear stage. Thermal error reduction is achieved using environmental temperature control (20 ± 0.2 °C) to help reduce thermal errors.

Typically, a measurement is regarded as being incomplete without a statement of uncertainty being provided with the result. Usually, the corresponding interval of measurement uncertainty will be an evaluated confidence interval, assuming that the classical, frequentist, approach to statistics is adopted. However, there are other types of interval that are potentially relevant, and which might wrongly be called a confidence interval. This paper describes different types of statistical interval and relates these intervals to the task of obtaining a figure of measurement uncertainty. Definitions and examples are given of probability intervals, confidence intervals, prediction intervals and tolerance intervals, all of which feature in classical statistical inference. A description is also given of credible intervals, which arise in Bayesian statistics, and of fiducial intervals. There is also a discussion of the term “coverage interval” that appears in the International Vocabulary of Metrology and in the supplements to the Guide to the Expression of Uncertainty in Measurement.

This research work describes a novel approach for comparing different technologies for free form surface metrology: computerized tomography (CT), photogrammetry and coordinate measuring machines (CMM). The comparison has the aim of providing relevant information for the selection of metrology equipment when measuring free form components. Results demonstrate that there is the imperative need to assess the uncertainty and reproducibility of CT and photogrammetry measurements by applying some calibration procedures taking into account some recommendations for work piece alignment. This article also deals with costs issues, required standards, and necessary additional information when selecting inspection equipment.

The optical frequency comb generator (OFCG) is an attractive optical reference source for various applications such as optical frequency metrology, precision spectroscopy and telecommunications [D.J. Jones, S.A. Diddams, J.K. Ranka, A. Stentz, R.S. Windeler, S.T. Cundiff, Science 288, 635–639 (2000); T. Udem, R. Holzwarth, T.W. Hänsch, Nature 416, 233–237 (2002); T.W. Hänsch, J. Alnis, P. Fendel, M. Fischer, C. Gohle, M. Herrmann, R. Holzwarth, N. Kolachevsky, Th. Udem, M. Zimmermann, Philos. Trans. R. Soc. A 363, 2155–2163 (2005)]. In particular, the OFCG can be used as source for absolute frequency measurement, providing a precise ruler for length metrology. In the present work we describe the results of absolute frequency measurements of primary wavelength standards at 633 nm on the sixth components, d, e, f, g, h and i of the R(127) 11-5 hyperfine transition of the 127I2 molecule, at the Spanish Centre of Metrology, CEM. The values obtained with a femtosecond frequency comb (FC1500, Menlo Systems) at CEM are compared with the values recommended by the Consultative Committee for Length (CCL) [T.J. Quinn, Metrologia 40, 103–133 (2003)]. This determination was made by beat frequency method between a femtosecond laser comb and an iodine-stabilized He-Ne laser. The difference between the mean frequency of the sixth components of the standard laser and those of CCL recommended values for the same components was found to be 6.557 kHz.

We consider the comparative calibration problem in the case when linear relationship is assumed between two considered measuring devices with possibly different units and precisions. The first method for obtaining the approximate confidence region for unknown parameters of the calibration line applies the maximum likelihood estimators of the unknown parameters. The second method is based on estimation of the calibration line via replicated errors-in-variables model. Essential point in this approach is approximation of the small sample distribution of the Wald-type test statistic. This enables to construct the interval estimators for the multiple-use calibration case.

Computed tomography has entered the industrial world in 1980’s as a technique for non-destructive testing and has nowadays become a revolutionary tool for dimensional metrology, suitable for actual/nominal comparison and verification of geometrical and dimensional tolerances. This paper evaluates measurement results using different measuring strategies applied in different inspection software packages for volume and surface data analysis. The strategy influence is determined by calculating the measurement uncertainty. This investigation includes measurements of two industrial items, an aluminium pipe connector and a plastic toggle, a hearing aid component. These are measured using a commercial CT scanner. Traceability is transferred using tactile and optical coordinate measuring machines, which are used to produce reference measurements. Results show that measurements of diameter for both parts resulted in smaller systematic errors compared to distance and height measurements. It was found that uncertainties of all measurands evaluated on surface data were generally greater compared to measurements performed on volume data.

Least squares regression is commonly used in metrology for calibration and estimation. In regression relating a response y to a predictor x, the predictor x is often measured with error that is ignored in analysis. Practitioners wondering how to proceed when x has non-negligible error face a daunting literature, with a wide range of notation, assumptions, and approaches. For the model ytrue = β0 + β1   xtrue, we provide simple expressions for errors in predictors (EIP) estimators \hbox{$\Hat{{\beta }}_{0, {\rm EIP}} $}β̂0, EIP for β0 and \hbox{$\Hat{{\beta }}_{1, {\rm EIP}} $}β̂1, EIP for β1 and for an approximation to covariance (\hbox{$\Hat{{\beta }}_{0, {\rm EIP}} $}β̂0, EIP, \hbox{$\Hat{{\beta }}_{1, {\rm EIP}} $}β̂1, EIP). It is assumed that there are measured data x = xtrue + ex, and y = ytrue + ey with errors ex in x and ey in y and the variances of the errors ex and ey are allowed to depend on xtrue and ytrue, respectively. This paper also investigates the accuracy of the estimated cov(\hbox{$\Hat{{\beta }}_{0, {\rm EIP}} $}β̂0, EIP, \hbox{$\Hat{{\beta }}_{1, {\rm EIP}} $}β̂1, EIP) and provides a numerical Bayesian alternative using Markov Chain Monte Carlo, which is recommended particularly for small sample sizes where the approximate expression is shown to have lower accuracy than desired.