= Radiative temperature uncertainty after background subtraction
{title2=$\sigma_T/T=\sigma_{P_{\rm total}-P_{\rm back}}/(4P)$}
If emitted <power> obeys $P=AT^4$ with known constant $A$, then small relative <temperature> uncertainty is one quarter of relative net-power uncertainty. For measured quantities $X,Y$ with <covariance> $C_{XY}$, $\operatorname{Var}(X-Y)=\sigma_X^2+\sigma_Y^2-2C_{XY}$. A weak net signal obtained by subtracting a large background can therefore have poor relative precision even when both original <powers> are measured accurately. Correlated <standard uncertainties> and worst-case error bounds require different propagation rules.
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