High-Sensitivity Absorption Spectroscopy

The general method for measuring absorption spectra is based on the absorption coefficient $k(\omega)$ from the spectral intensity

$$I(\omega) = I_0 e^{-k(\omega)l},$$ (75)

where $I(\omega)$ is the light intensity transmitted through the path length $l$. For small absorption coefficients $k l \ll 1$ and we can approximate the exponent $exp(-kl)\simeq 1-kl$ and eq. (75) can be reduced to

$$I(\omega) = I_0 [1-k(\omega)l].$$ (76)

and therefore,

$$k(\omega) = \frac{I_0-I(\omega)}{I_0l}.$$ (77)

The absorption coefficient $k_{ik}(\omega)$ of the transition $\vert i> \rightarrow \vert k>$ is determined by

$$k_{ik}(\omega) = [N_i - \frac{g_i}{g_k}N_k]\sigma_{ik}(\omega) = \Delta N \sigma_{ik}(\omega),$$ (78)

where $\sigma_{ik}(\omega)$ is an absorption cross section, and $N_i$ and $N_k$ are densities of the molecules in the $\vert i>$ and $\vert k>$ states, respectively.

The method of absorption spectroscopy is widely used in the UK spectral range. It is seen from eq. (76) that in order to get a high sensitivity for absorbing molecules, $k(\omega)l$ should not be not small. However, in case if this factor is very small, the direct absorption method cannot be accurate enough because one has to determine a small difference $I_0-I$ of two large quantities $I_0$ and $I$, while small fluctuation of the value $I_0$ can severely influence the measurement.

Therefore, several other techniques have been developed in order to increase the sensitivity of the absorption experiment. We now consider some of these techniques in more details.

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