Propagation of Uncertainty Due to Non-linearity in Radiation Thermometers

Abstract

The measurement of the non-linearity of radiation thermometers is important in the realization of ITS-90 above the silver point and in the calibration of primary or secondary radiation thermometers using multiple fixed points both above and below the silver point. A non-linearity function is usually derived, enabling correction of the measured signals. Uncertainties in this non-linearity function propagate to the uncertainty in the determination of an unknown temperature. Since the same non-linearity function is used both during calibration and in subsequent use of the thermometer, there is a high degree of correlation between the uncertainties in the corrected calibration signals and the corrected in-use signals. While these correlations obviously lead to zero uncertainty at the calibration points, it is difficult to determine the correlation coefficients for temperatures away from these points. This article sets out a mathematical framework, based on interpolation theory, for propagating the uncertainty due to non-linearity in which correlation is easily included. The method is illustrated for a thermometer realizing ITS-90 up to 3,000°C based on one fixed point (silver, gold, or copper), and also for alternative realization schemes based on two or more fixed points. The total non-linearity uncertainty for the multipoint schemes is considerably lower than for the ITS-90 method. The mathematical framework can also be applied to secondary calibrations below the silver point, where non-linearity is typically more problematic for the detectors used in this temperature range.