Uncertainty propagation through integrated quantities for radiation thermometry

Abstract

Uncertainty formulae are derived for propagating both correlated and uncorrelated components of uncertainty in spectral responsivity measurements directly through the Planck integrals for the radiation thermometry range of the international temperature scale of 1990 (ITS-90) and for absolute radiometry. These formulae are compared to those obtained using the Sakuma–Hattori equation as an approximation to the Planck integrals. It is shown that for typical spectral responsivity bandwidths, the differences are negligible, confirming that the Sakuma–Hattori approximation provides an excellent model for the basis of uncertainty propagation for radiation thermometry, resulting in simpler and more intuitive uncertainty equations.