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 iInterpolation 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
