\[fig:transients\]d) did not cause a reduction in ring-down time with respect to the empty-cavity demonstrating the higher sensitivity of the CELIF setup.

To confirm the validity of eqs \[eq:ILIF\_accurate\] to \[eq:alpha\_LIF\], we measured the linearity of the LIF signal with respect to the laser intensity, as measured via the integrated CRD intensity, $I{^\text{CRD}}$, and the dependence of the CELIF signal, $S{^\text{CELIF}}$, on the sample density, $\rho$. Fig. \[fig:powerdep\](a) shows the fluorescence signal of acetone following laser excitation at 313 nm as a function of laser intensity. The cavity was filled with 0.1 and 0.3 mbar of acetone respectively. Each data point represents the average over 5000 laser shots. The standard errors in laser intensity and LIF signal are smaller than the size of the symbols. The linear least-squares fits demonstrate the validity of the shot-to-shot normalization using eq. \[eq:CELIF\_norm\] and show the absence of any saturation effects in the measurement range.

The linearity of the CELIF signal with respect to the sample density of a filled cavity was confirmed with N$_2$ Rayleigh scattering at 583.5 nm (fig. \[fig:powerdep\]b) in the pressure range 0.1–1000 mbar. The simultaneously measured ring-down times provide an absolute measurement for the absorption and therefore the photon 