= Solution
Use $x=t$ in picoseconds and $y=\ln(R/R_*)$. Since the time uncertainty is negligible, only the vertical errors enter. First-order <propagation of uncertainty> gives
$$
\sigma_y\simeq\left|\frac{dy}{dR}\right|\sigma_R
=\frac{\sigma_R}R=0.15.
$$
The transformed measurements are
$$
\boxed{\begin{array}{r|r|c}
x\ (\mathrm{ps})&y&\sigma_y\\ \hline
0.25&7.19968&0.15\\
0.75&5.88610&0.15\\
1.25&4.70048&0.15\\
1.75&3.43399&0.15\\
2.25&2.63906&0.15\\
2.75&1.09861&0.15
\end{array}}
$$
Thus the <logarithmic transformation> converts constant fractional rate uncertainties into approximately equal absolute log-rate uncertainties. The equality is the linear error approximation; finite error bars would become slightly asymmetric under an exact logarithm.
Back to article page
