Extending the applicability of the Arndt formula in wavelength modulation spectroscopy for absorbance in the lower percent range

- Extension of the Arndt expression for high absorbance.
- Accuracy increases greater than 75.
- Over 20 times faster than a numerical approach.
- Applicable on a microcontroller.

The Arndt formula for Lorentzian signals broadened by modulation is enhanced for the usage on 2f WMS (wavelength modulation spectroscopy) signals produced by spectroscopic lines with high absorption (percent range). Next to the first order approach of the Beer-Lambert law, which is covered by the Arndt formula, a second order term is included for a better approximation of the damped Lorentzian line shape. This second order approximation of the 2f signal can be described by a combination of several components created by the Arndt formula. The error of a pure Arndt evaluation and the improvement of the Arndt extended technique are illustrated in the example of a humidity measurement performed at 100 °C and up to 100 vol%. The energy transition at ν=10,526.274910 cm−1 is used in this setup. With the presented technique, the error is reduced by a factor of 90.