Background-subtracted radiative temperature uncertainty (${\sigma }_T/T=\sqrt{{\sigma }_A^2+{\sigma }_B^2-2\mathrm{Cov}(A,B)}/[4(A-B)]$)

If measured radiative flux is $S=A-B>0$ and $S=k{T}^4$ with known $k$, first-order uncertainty propagation gives the displayed result. Independent measurements have zero covariance; strict error bounds combine differently. Even a small fractional background contribution can matter if its relative uncertainty is large. Inferring the covariance or an unknown calibration factor from precision percentages alone is unjustified.