$5\cdot 10^{-5}$ for $R = 0.9999$.

Therefore, we define the normalized CELIF signal as $$\label{eq:CELIF_norm}
S{^\text{CELIF}}= \frac{S{^\text{LIF}}}{I{^\text{CRD}}}.$$ Note that $S{^\text{CELIF}}$ is a relative quantity (unitless in our case) that can be calibrated to equal the absolute absorption coefficient, $\alpha$, derived from the measurement of ring-down times. The calibrated CELIF absorption coefficient is $$\label{eq:alpha_LIF}
\alpha = \sigma\rho = {\mathcal{K}}\cdot S{^\text{CELIF}},$$ where ${\mathcal{K}}$ is the proportionality factor that can be determined from a simultaneous LIF and CRD measurement, provided the absorption leads to a sufficient reduction in ring-down time (equations \[eq:alpha\_CRD\] and \[eq:alpha\_LIF\]): $$\label{eq:cal_LIF}
{\mathcal{K}}= \frac{I{^\text{CRD}}}{S{^\text{LIF}}} \frac{1}{c} \left(\frac{1}{\tau} - \frac{1}{\tau_0}\right).$$

This method provides an absolute calibration of the LIF signal. Therefore the limited dynamic range of the CRD method can be extended towards the generally lower detection limit of the LIF method. The combination of LIF and CRDS into CELIF enables the measurement of an absolute absorption coefficient over the combined dynamic range.

Equations \[eq:alpha\_LIF\] and \[eq:cal\_LIF\] hold true for an absorption measurement at a fixed wavelength. Generally, ${\mathcal{K}}$ is a function of the excitation wavelength (fluorescence quantum yield, mirror transmission) and the fluorescence spectrum (spectral response of the detection system). A single-pass LIF measurement needs to account for the wavelength dependencies 