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Measurement Good Practice Guide No. 39 • The standard deviation each of the measurements must be taken into account. Since each spot is measured 3 times we divide it by the square root of 3, giving the standard uncertainty of the mean (or standard deviation of the mean). Where N measurements are made, the standard deviation is divided by √N. So the combined standard uncertainty for each of the measurements, by summing in quadrature, is ±√ 0.079+ (SD/√3) 2 , where SD is the standard deviation of the measurements. This gives us a standard uncertainty of ±0.28 µm for the measurements and the expanded uncertainty is ±0.56 µm, for a 95% confidence level. By comparing results, it can be seen that the measurement uncertainty when using the system as a comparator is seven times smaller than when using it in a direct measurement mode. For highest accuracy measurements vision systems should therefore be used as comparators whenever possible. However, it is also worth noting that the accuracy of the results from the direct measurement mode example is well within the measurement uncertainty. It is, of course, up to the end user to decide what level of accuracy and uncertainty is acceptable for his particular measurements. Further information regarding the calculation of uncertainty may be found in the NPL Measurement Best Practice Guide No. 11, ‘A Beginner’s Guide to Uncertainty of Measurement.’ 8 WORDS OF WARNING Making accurate measurements is as much about being confident of the measuring system’s 1 performance history as it is about its day-to-day repeatability. Whilst modern vision systems generally exhibit excellent measurement repeatability and reproducibility, measurement errors can still be produced. This can be due for example to the use of incorrect or inappropriate measurement practices, technical problems with the equipment, calibration errors, changes in environmental conditions or operator errors. In order to minimize such problems and ensure that accurate measurements are made, users are recommended to take steps to regularly monitor the performance of their measuring systems by acquiring and analysing statistics on repeatability and reproducibility. This will enable departures from ‘the normal’ to be spotted at an early stage and allow action to be taken to identify and correct the source of the errors in order to return the measuring system to its desired operating state. 1 The measuring system here includes the vision system, any associated equipment or accessories required for the measurement and the operator. 57
Measurement Good Practice Guide No. 39 APPENDIX A LINKS TO OTHER USEFUL SOURCES OF INFORMATION A.1 NATIONAL ORGANISATIONS A.1.1 National Physical Laboratory The National Physical Laboratory (NPL) is a world-leading centre in the development and application of highly accurate measurement techniques. As the UK's national standards laboratory, NPL underpins the national measurement system (NMS), ensuring consistency and traceability of measurements throughout the UK. NPL offers a unique range of measurement services, contract research, consultancy and training services. Other areas of expertise include the design and characterisation of engineering materials, and mathematical software, especially its application to measurement and instrumentation. For information on the wide range of metrology services, facilities and research work carried out at NPL either visit the NPL web site at http://www.npl.co.uk Or contact the NPL Helpline at Tel: 020 8943 6880, Fax: 020 8943 6458, E-mail: enquiry@npl.co.uk For information on high-precision optical dimensional standards for vision systems (including line scales, image analyser standards, 2-D optical standards and photomask linewidth standards) visit the Dimensional and Optical Metrology web pages at http://www.npl.co.uk/npl/length/dmet/services/ms_rsg.html A.1.2 National Institute of Science and Technology (NIST) NIST is the equivalent of NPL in the United States of America. The NIST web site at http://www.nist.gov/ often contains relevant documents in pdf format. A.1.3 EUROMET EUROMET is a cooperative organisation between the national metrology institutes in the EU including the European Commission, EFTA and EU Accession States. The participating metrology institutes collaborate in EUROMET with the objective of promoting the co-ordination of metrological activities and services with the purpose of achieving higher efficiency. 58
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