In order to achieve nanometer accuracy, metrologists need to identify the sources oferror and develop solutions to eradicate or minimize their effects. A stabilized low powerdual-frequency laser heterodyne interferometer (ZMI-1000A) designed to measure linear andangular displacement with nominal measurement resolution 1.24 nm and 0.0025 arcsec,respectively, is used to achieve measurement of displacements over different travellingaxes by comparison with the electronically reference measurements of the stage over widerange 500 mm. The repeatability and reversal error of linear stage over the workingdistance have agreed opto-electronically and the positioning uncertainty been reduced. Amultivariable framework was implemented for the x-axis due to the crosscoupling between the forward and backward course of the linear stage. Thermal errorreduction 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 forfree form surface metrology: computerized tomography (CT), photogrammetry and coordinatemeasuring machines (CMM). The comparison has the aim of providing relevant information forthe selection of metrology equipment when measuring free form components. Resultsdemonstrate that there is the imperative need to assess the uncertainty andreproducibility of CT and photogrammetry measurements by applying some calibrationprocedures taking into account some recommendations for work piece alignment. This articlealso deals with costs issues, required standards, and necessary additional informationwhen selecting inspection equipment.

The optical frequency comb generator (OFCG) is an attractive optical reference source forvarious applications such as optical frequency metrology, precision spectroscopy andtelecommunications [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 assource for absolute frequency measurement, providing a precise ruler for length metrology.In the present work we describe the results of absolute frequency measurements of primarywavelength 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 SpanishCentre of Metrology, CEM. The values obtained with a femtosecond frequency comb (FC1500,Menlo Systems) at CEM are compared with the values recommended by the ConsultativeCommittee for Length (CCL) [T.J. Quinn, Metrologia 40, 103–133 (2003)]. Thisdetermination was made by beat frequency method between a femtosecond laser comb and aniodine-stabilized He-Ne laser. The difference between the mean frequency of the sixthcomponents of the standard laser and those of CCL recommended values for the samecomponents 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 fornon-destructive testing and has nowadays become a revolutionary tool for dimensionalmetrology, suitable for actual/nominal comparison and verification of geometrical anddimensional tolerances. This paper evaluates measurement results using different measuringstrategies applied in different inspection software packages for volume and surface dataanalysis. The strategy influence is determined by calculating the measurement uncertainty.This investigation includes measurements of two industrial items, an aluminium pipeconnector and a plastic toggle, a hearing aid component. These are measured using acommercial CT scanner. Traceability is transferred using tactile and optical coordinatemeasuring machines, which are used to produce reference measurements. Results show thatmeasurements of diameter for both parts resulted in smaller systematic errors compared todistance and height measurements. It was found that uncertainties of all measurandsevaluated on surface data were generally greater compared to measurements performed onvolume data.

Least squares regression is commonly used in metrology for calibration and estimation. Inregression relating a response y to a predictor x, thepredictor x is often measured with error that is ignored in analysis.Practitioners wondering how to proceed when x has non-negligible errorface 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}} $}β̂1, EIP for β1 and for anapproximation to covariance (\hbox{$\Hat{{\beta }}_{0, {\rm EIP}} $}β̂0, EIP, \hbox{$\Hat{{\beta }}_{1, {\rm EIP}} $}β̂1, EIP). It is assumed that there are measured datax = xtrue + ex,andy = ytrue + eywith errors ex in x andey in y and thevariances of the errors ex andey are allowed to depend onxtrue and ytrue, respectively.This paper also investigates the accuracy of the estimated cov(\hbox{$\Hat{{\beta }}_{0, {\rm EIP}} $}β̂0, EIP, \hbox{$\Hat{{\beta }}_{1, {\rm EIP}} $}β̂1, EIP) and provides a numerical Bayesian alternative usingMarkov Chain Monte Carlo, which is recommended particularly for small sample sizes wherethe approximate expression is shown to have lower accuracy than desired.