is also a function of $\lambda$ as the fluorescence spectrum may depend on the excited state. However, this dependence can only be considered if the dispersed fluorescence spectrum is recorded as a function of excitation wavelength. In order to obtain the absorption coefficient, $\alpha$, from a fluorescence excitation measurement, $S{^\text{LIF}}$ and $I{^\text{LIF}}$ need to be measured. The factor $g$ is an instrument function that is not readily available but can be determined via a meticulous external calibration. The fluorescence quantum yield, $\Gamma$, is generally unknown and needs to be measured or predicted from theory in a separate study.

Fundamentally, CELIF is a LIF measurement where the simultaneous CRD measurement is used for the normalization and the calibration of the LIF signal. In the following, we derive how the time-integrated CRD signal is correlated to $I{^\text{LIF}}$ and how it is subsequently used to provide the normalization of $S{^\text{LIF}}$ to eliminate shot-to-shot fluctuations in the laser intensity from eq. \[eq:SLIF\]. We then describe how the absolute absorption coefficient determined via the ring-down time measurement (eq. \[eq:alpha\_CRD\]) is used for the absolute calibration of the normalized LIF signal such that in a CELIF measurment prior knowledge of $g$ and $\Gamma$ is not required.

