[B._Beckhoff,_et_al.]_Handbook_of_Practical_X-Ray_(b-ok.org).pdf

The evaluation software then makes the appropriate

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from the correct value. The evaluation software then makes the appropriate corrections (Fig. 7.94). Standards are the basis for the calibration. They are
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Methodological Developments and Applications 577 Fig. 7.95. Calibration standard set. Input of nominal values of the standard. Un- certainties (errors) must be entered as well. If default value Zero is not changed, the software will automatically use 1% from the nominal value for layer thicknesses and masses per unit area, 1% of mass as uncertainty for concentrations, referenced to k = 1 (68% confidence interval). Example applies to measurement application Au/AuCuCd/Ni/CuZnPb; Fig. 7.92 shows the DefMA for this application samples that correspond in structure to the measurement application and have values that are known within a specified uncertainty. The systematic error portion can be determined by measuring these standards. However, one has to take into account that this measurement has a random measurement uncertainty associated with it and the nominal value of the standard only has a finite accuracy. While the random errors described above can be characterized using sta- tistical means, for the systematic error portion this is only possible by com- paring the measurement result with standard samples. It would be possible to describe and even correct the systematic error if the nominal values of the used standard samples were exact and it were possible to measure them without a random failure portion. Neither one of these is possible. Both the uncertainty of the nominal value and the (random) measurement uncertainty of the calibration measurement determine the error of the calibration – and therefore the uncertainty of the correction that is based on the calibration (Fig. 7.96). Particularly, it must be taken into account that from experience, the uncertainty of the calibration increases for measurement results that are distant from the values of the standards. The uncertainty of the correction is of course dependent on the size of the correction itself. Due to the quality of the FP-supported evaluation program, the required corrections are rather small, such that this fact dominates the measurement error only in rare cases. It is important that this error can now be stated, therefore making the “risk” known. Details for determining the systematic measurement uncertainty are described in [247].
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578 V. R¨oßiger and B. Nensel Correction X Fig. 7.96. Principle of calibration. Three standards define a correction function. X is the theoretical uncorrected value. Its uncertainty is reflected by the width of the red rectangle. Its height equals the uncertainty of the standard value according to the inputs of Fig. 7.95, and the uncertainty of the calibration measurement A prerequisite for calculating the systematic measurement uncertainty is the knowledge of the uncertainties of the standards. This takes place in the definition the calibration standard set, where the corresponding information is provided to the program, cf. Fig. 7.95. If a calibration is not performed,
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