Calibration and validation of full-field techniques

. We review basic metrological terms related to the use of measurement equipment for verification of numerical model calculations. We address three challenges that are faced when performing measurements in experimental mechanics with optical techniques: the calibration of a measuring instrument that (i) measures strain values, (ii) provides full-field data, and (iii) is dynamic.


Vocabulary and Definitions
Working with engineering people from around the world we have noticed a lack of awareness regarding some basic concepts of measurement techniques.While much effort has been undertaken to promote the idea of measurement uncertainty in the last decade, confusion is still around when talking about traceability, calibration or validation, or the discussion is considered as being relevant to calibration laboratories only, but not the test bench of the practicing engineer.
We will briefly remind the reader of the commonly accepted definitions as given by the Vocabulaire International de métrologie (VIM -International Vocabulary of Metrology) [1].We will then apply the basic concepts and their implications on reference materials and their use.We focus on three challenges that are faced when performing measurements in experimental mechanics with optical methods: how to calibrate a measuring instrument that (i) measures strain values, (ii) provides full-field data, and (iii) is dynamic.

Traceability
VIM (2.41) defines traceability or more properly "metrological traceability" as "the property of a measurement result whereby the result can be related to a reference through a documented unbroken chain of calibrations, each contributing to the measurement uncertainty."For this definition, a 'reference' can be a definition of a measurement unit through its practical realization, or a measurement procedure including the measurement unit for a non-ordinal quantity, or a measurement standard.Metrological traceability requires an established calibration hierarchy which is called a metrological traceability chain.The ILAC (International Laboratory Accreditation Cooperation) considers the elements for confirming metrological traceability to be (i) an unbroken metrological traceability chain to a national or international measurement standard (ii) a documented a e-mail : erwin.hack@empa.chEPJ Web of Conferences measurement uncertainty (iii) a documented measurement procedure (iv) accredited technical competence (v) metrological traceability to the SI, and (vi) calibration intervals [2].

Calibration
VIM (2.39) defines calibration as the "operation that, under specified conditions, in a first step, establishes a relation between the quantity values with measurement uncertainties provided by measurement standards and corresponding indications with associated measurement uncertainties and, in a second step, uses this information to establish a relation for obtaining a measurement result from an indication."Often, the first step alone in this definition is perceived as being calibration.

Validation
VIM (2.44, 2.45) defines validation as "provision of objective evidence that a given item is adequate for an intended use".Hence, validation prevents the use of a measurement system which is inappropriate for the intended use although it might be calibrated.Adequateness of a strain measurement system for use in experimental mechanics involves e.g. the appropriateness for the strain level that is expected, for the necessary spatial resolution, the measurement rate, etc.

Challenge 1: Traceability to the SI
It is commonly accepted that the traceability chain should link to a primary standard, i.e. a realization of a unit within the SI (Système International d'Unités).While this is a straightforward process for deformation and displacement measurements which are naturally linked to the unit of length meter, it is less obvious how the measurement result of a derived quantity such as strain can be made traceable.In order to realize a measurement standard for strain, we recall VIM (5.1) which defines a measurement standard (or etalon) to be a "realization of the definition of a given quantity, with stated quantity value and associated measurement uncertainty, used as a reference."Such a "realization of the definition of a given quantity" can be provided by a measuring system, a material measure, or a reference material.VIM (5.1) defines reference material (RM) as a "material, sufficiently homogeneous and stable with reference to specified properties, which has been established to be fit for its intended use in measurement or in examination of nominal properties."Since these definitions do not detail the nature of the quantity to be realized, it applies to derived quantities as well.
It necessitates a model system to realize the derived quantity that must be controlled by input quantities for which the traceability chain is established and from which the derived quantity to be calibrated is calculated.If a simple analytic relation between input and (derived) reference value exists, the traceability is straightforward again.Considering strain, the use of the measurement of a base length L and an elongation " ' is viable, eq.( 1) -and indeed popularly used in tensile testingbecause both measurements can be traced back to the length scale and the unit meter.
However, other possibilities of realization of the unit strain can be envisaged [3].The combined measurement uncertainty for the strain value is calculated from the uncertainties of the input quantities (L and " ' in this simple case) and influence quantities (such as temperature, digital resolution, etc.) following the GUM [4].
14th International Conference on Experimental Mechanics

Challenge 2: Full-field techniques
When calibrating an instrument, most often a single reference quantity is captured by a single transducer and compared to its reading.Figure 1 shows a typical calibration curve for an LVDT that is calibrated with a laser interferometer which serves as the traceable reference standard.The residual deviations from a linear function are reproducible within the random variations and hence could be corrected for.However, normally a single uncertainty value (or specification limit) is extracted from the graph, i.e. deviations are smaller than 0.01 mm across the entire range of values.But how can a full-field technique be calibrated?And how should the measurement uncertainty be expressed in this case?Obviously, a field of reference values must be provided to calibrate a fullfield technique.For camera calibration a well-known method is based on the use of a calibration plate.The calibration procedure provides the values of intrinsic and extrinsic parameters that are used to model the camera's imaging properties and to subsequently correct the images in order to obtain reliable coordinates of an object surface.In Digital Image Correlation such a camera calibration using specially designed chequerboard patterns is common use (Fig. 2) [5].

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In contrast to the calibration of the imaging properties (aberrations) for measuring coordinates in space, embodiments with representative line patterns (USAF target, Siemens star) for validation of imaging systems, have been around for decades (Fig. 2).They allow the assessment of the limitation of an imaging system and therefore are needed to define the applicability of the system, which is related to validation rather than calibration.
Similarly, for a full-field technique that measures a quantity different from surface coordinates, the need arises for an artefact that allows a full-field calibration of the quantity in question.As an example, specimens with artificial flaws are used to validate imaging or scanning NDE techniques.The requirements for such an artefact from the point of view of traceability of strain measurement, its realization for planar strain states and its use for calibrating an optical instrument is described elsewhere [6,7].Basically, the strain field can be expressed as where " ' is again a (single) measured displacement value which is traceable, and is an analytic function that describes the distribution of the strain values on the surface of the (planar) reference material.Calibration now involves not only the comparison of the values of the reference material and the measurement but also the identification of corresponding locations y x, which is a pre-requisite for a point-by-point comparison.The level of uncertainty with which this step can be performed adds to the calibration uncertainty.Figure 3 gives a full-field equivalent for the linear calibration of Fig. 1.The simulated system is measuring out-of-plane displacement.For an array detector the calibration field has to be provided simultaneously and not sequentially as in Fig. 1.In this example, a linear variation of displacement along the y-direction, but no variation along the xdirection is introduced which corresponds to a simple tilt of a reference plane.

Challenge 3: Dynamic measurements
A final challenge to be mentioned is to overcome the limitations of a static calibration in order to calibrate instruments for dynamic measurements of displacement or strain.This challenge adds still another degree of freedom to the calibration process: the time.Motivation of this extension is the use of optical measurement systems for dynamic events.Dynamic events, from vibrations to impact, are especially important in the transportation industry.In the 7 th Framework Programme of the European Union a collaborative project was started to tackle this challenge [8].ADVISE is a pre-normative 46003-p.4

Conclusion
We have discussed the needs for calibration and validation of imaging measurement systems in view of three challenges: derived quantity, full-field data, and dynamic data.It is the requirement of the application that defines the levels of accuracy for calibration and the validation of the system.Equally, the measurement uncertainty must be expressed in a way that is appropriate for the intended use.

Fig. 1 .
Fig. 1.Calibration curve of an LVDT and its residual deviations from a linear calibration function.

Fig. 2 .
Fig. 2. Pattern for calibration of a Digital Image Correlation system (left)., and Siemens star pattern for validating the resolution of an imaging system (modulation transfer function) (right).

Fig. 3 .
Fig. 3. Full-field equivalent to Fig.1 (simulated data).Calibration curve of a 2D-displacement measurement (left) and its residual deviations from the calibration values (right).