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Title:
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A Combinatorial Technique for Calibrating Mass Balances, Optical Detectors and Resistance Bridges
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Co-Authors:
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D. R. White, M. T. Clarkson, P.Saunders
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Abstract:
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For many quantities, the indicating instrument is calibrated only at a limited number of values, and the extension of the calibration to higher or lower values must rely upon the linearity of the instrument. A method for calibrating or determining the linearity of instruments that exploits the combinatorial properties of a set of different-valued, and mostly uncalibrated, artifacts is described. The paper presents the underlying principles of the method, its limitations, and examples of the application of the method to three very different quantities: mass balances, optical detectors and resistance bridges. The method is applicable to instruments where it is possible to combine stable artifacts with low uncertainties. For direct-reading instruments, at least one of the artifacts should be calibrated, and for ratio-indicating instruments, none of the artifacts need be calibrated. It is shown that for artifacts that can be combined linearly, a binary sequence generally comes close to maximizing the number of combinations available. Furthermore, the resulting uncertainty due to the linearity can be assigned from the residuals of the fitted functional form of the linearity to the measured signals.
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