Peter M. Harris

Recent advances in traceable nanoscale dimension and force metrology in the UK

It is now fully appreciated that metrology will play an integral role in the successful development and commercialization of micro- and nanotechnology. To this end, the UK Government, through the National Measurement System, funded several groundbreaking projects in its 2002–2005 Programme for Length. This paper will briefly describe the background of the research, concentrating on the technical details of the projects. The Programme for Length normally only funds work into dimensional metrology but this funding cycle also funded work into low force metrology as this area is crucial to most mechanical probing techniques. The projects described include a traceable areal contacting instrument designed to calibrate areal transfer artefacts and hence offer traceability for industrial areal instruments, the production of the areal transfer artefacts, the development of Internet-based softgauges for profile parameters, a primary low force balance with a force resolution of 50 pN and the development of methods for measuring complex micro-scale structures. Amongst others, the projects involved collaboration with PTB, TNO, Taylor Hobson, AWE, Rubert & Co. and the Universities of Warwick, Huddersfield and Eindhoven.

Implementation of a generalized least-squares method for determining calibration curves from data with general uncertainty structures

The determination of a best-fit calibration curve that describes the response of a measuring system to the value of a standard is one of the most widely used procedures in metrology. The mathematical basis for a generalized least-squares solution to this problem is reviewed. Examples of the application of a software implementation of the method are presented to illustrate the treatment of calibration problems with different uncertainty structures for the calibration data, including correlated data. The examples concern the calibration of analysers to measure the composition of natural gas and the calibration of a gas flow dilutor.

Measurement uncertainty and traceability

Obtaining confidence in a measured value requires a quantitative statement of its quality, which in turn necessitates the evaluation of the uncertainty associated with the value. The basis for the value and the associated uncertainty is traceability of measurement, involving the relationship of relevant quantities to national or international standards through an unbroken chain of measurement comparisons. Each comparison involves calibration of a standard at one level in the chain using a standard at a higher level. Global economy considerations mean that this basis also requires the national measurement institutes to carry out comparative assessment of the degree of equivalence of national standards through their participation in key comparisons. The evaluation of uncertainty of measurement is founded on the use of models of measurement for each stage of the chain and at the highest level to interrelate national standards. Basic aspects of uncertainty evaluation are covered in this paper, and forms for the above types of model considered, with attention given to least squares as a basis for calibration curves (and certain other types of calibration) and also for key comparison data evaluation.

Efficient implementation of a Monte Carlo method for uncertainty evaluation in dynamic measurements

Measurement of quantities having time-dependent values such as force, acceleration or pressure is a topic of growing importance in metrology. The application of the Guide to the Expression of Uncertainty in Measurement (GUM) and its Supplements to the evaluation of uncertainty for such quantities is challenging. We address the efficient implementation of the Monte Carlo method described in GUM Supplements 1 and 2 for this task. The starting point is a time-domain observation equation. The steps of deriving a corresponding measurement model, the assignment of probability distributions to the input quantities in the model, and the propagation of the distributions through the model are all considered. A direct implementation of a Monte Carlo method can be intractable on many computers since the storage requirement of the method can be large compared with the available computer memory. Two memory-efficient alternatives to the direct implementation are proposed. One approach is based on applying updating formulae for calculating means, variances and point-wise histograms. The second approach is based on evaluating the measurement model sequentially in time. A simulated example is used to compare the performance of the direct and alternative procedures.

Ambiguities in the definition of spacing parameters for surface-texture characterization

A range of instruments is available for surface-texture measurement. The instruments record the (x, z) coordinates of data points that represent a surface profile, and apply software to filter the data and compute various surface-texture parameters that aim to describe the properties of the surface. However, many current and proposed parameters are not unambiguously defined. The focus of this paper is on one such parameter, namely, the spacing parameter RSm. It is shown that the definition of the RSm parameter given in standards is ambiguous, leading to the possibility of different algorithms for calculating RSm whose implementations can give results that differ considerably. Results obtained from three algorithms for calculating RSm applied to a real measurement data set are presented.

An international key comparison of free-field hydrophone calibrations in the frequency range 1 to 500kHz

A description is given of the results of a Key Comparison of primary free-field standards for underwater acoustics at frequencies from 1 to 500kHz. This is the first such Key Comparison exercise in the field of underwater acoustic calibration and measurement. Laboratories from UK, Germany, USA, Russia, China, Canada, and South Africa participated by calibrating three reference hydrophones, with project coordination provided by the National Physical Laboratory, UK. The agreement between the results obtained from the comparison was generally encouraging, with the calibration values reported by the laboratories agreeing within quoted uncertainties over the majority of the frequency range, and the results generally lying within a ±0.5-dB band for frequencies up to 300kHz. A discussion is given of the general sources of uncertainties in the calibrations, in particular those which are thought to have contributed to the differences in the results between laboratories. The results of the participants have been us...

Uncertainty Modelling in Mass Comparisons

To evaluate uncertainty in mass measurements with accuracy and in accordance with recent international documents, a general model is developed, which takes account of the various contributing quantities in a multivariate context. On this basis, the variance-covariance matrix of the in-vacuo mass differences is constructed in its general form and tailored for application to some of the most commonly adopted weighing methods. The usual assumption of equal-variance, uncorrelated observations is shown to be inappropriate for mass comparisons.

A probabilistic approach to the analysis of measurement processes

We consider a probabilistic model of the measurement process, based on identifying two main sub-processes, named observation and restitution. Observation constitutes the transformations involved in producing the observable output. Restitution constitutes the determination of the measurand (the quantity measured) from the observable output, and includes data processing. After providing a probabilistic representation of the observation sub-process, we derive appropriate formulae for addressing restitution and describing the overall measurement process. The model allows the treatment in probabilistic terms of both the random and systematic effects that influence the measurement process, and may prove particularly useful in the formulation phase of uncertainty evaluation. We also discuss the different ways in which the measurand can be characterized by a probability distribution, and demonstrate the application of the approach to the analysis of risk in conformance testing.

Principal Component Compression Method for Covariance Matrices Used for Uncertainty Propagation

We investigate a principal component analysis approach for compressing the covariance matrices derived from real-time and sampling oscilloscope measurements. The objective of reducing the data storage requirements to scale proportional to the trace length n rather than n2 is achieved, making the approach practical for representing results and uncertainties in either the time or frequency domain. Simulation results indicate that the covariance matrices can be represented in a compact form with negligible error. Mathematical manipulation of the compressed matrix can be achieved without the need to reconstruct the full covariance matrix. We have demonstrated compression of data sets containing up to 10000 complex frequency components.

The evaluation of uncertainties in the analysis of calibration data

The National Physical Laboratory is involved, both internally and in collaboration with other National Measurement Institutes, in activities to promote sound methods of uncertainty evaluation. Some of the results of this work are described in this paper. A classification of measurement system models is presented that is more general than that considered in the ISO GUM. For each model type it is indicated how the uncertainty in the measurement result can be evaluated. The model types are illustrated using examples of real measurement systems. Sampling techniques are discussed and it is indicated how they can be used to estimate the statistical distributions of the model outputs, i.e., the results of measurement, without making some of the assumptions required by the mainstream GUM approach. The confidence intervals obtained by application of the GUM are compared with those obtained from sampling techniques for some of these examples.