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

In such a case the program must be able to advise the

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In such a case, the program must be able to advise the operator of the mis- match, instead of just calculating and displaying a meaningless numeric. The mentioned test calculation provides a number with a value that is an effective measure for the correspondence of the measured spectrum s exp l with the the-
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Methodological Developments and Applications 573 oretically calculated s theor l ( l = channel number, runs across all N according to Feature 9 set channels). The mq-value is a measure of the mean square deviation of the measured versus theoretical spectrum, whereby the individ- ual channel contents are normalized according to their Poisson uncertainty u l (uncertainty of the difference due to the counting statistics, cf. [226], for example): mq 2 = (1 /N ) l ( s exp l s theor l ) 2 /u 2 l . (7.31) Thus, a value mq 1 is relatively good, while a value above 2 already indicates that there are certain small discrepancies present. The program accepts a maximum value of mq = 5 (default setting). This limit may be changed in the application. Evaluation The use of XRF instruments in process control or quality assurance requires a customized presentation of the measurement results. WinFTM offers nu- merous variants, even including an analysis of variance (ANOVA). Not all options can be presented here. Mention shall be made of only one option, which is set up factory side for each instrument: the stability test. It is used by the instrument to monitor itself with regard to intensity of the primary radiation, resolution, and amplification factor of the spectrometer (detector and electronics), and in doing so it utilizes some of the existing evalua- tion options. Figure 7.93 gives an example. Additional options for display- ing the evaluated measurement result are included in Sect. 7.4.6 (Application examples). Calibration—Measurement Uncertainty—Traceability With a consistent error calculation, WinFTM secures the traceability of the individual measurement result. Distinguishing it from other evaluation pro- grams, which are, for example, based on empiric characteristics (cf. Sect. 7.4.3 Characteristics), WinFTM already provides standard-free measurement re- sults, which, as a rule, are already relatively accurate. This measurement result is the solution of the non-linear equation system described in Sect. 7.4.3 Characteristics, with the boundary conditions given by the instrument and geometry parameters . To secure traceability, the theoretical (standard-free) measurement result is compared to the “correct” result. To this end, samples (standards) with known“correct” values are required. Based on this compari- son (Fig. 7.94), the program carries out a correction of the theoretical values. Due to this so-called calibration, the measurement results are then traceable to the used standards. As shown below WinFTM can indicate how “exact” or uncertain these corrected measurement results are.
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574 V. R¨oßiger and B. Nensel Peak position: the mean of each block (5 readings) is displayed Block Size n = 5 50 169.2 169.5 Pos.
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