Natural logarithm wavelength modulation spectroscopy: A linear method for any large absorbance.

In this paper, we proposed the technique of Natural Logarithm Wavelength Modulation Spectroscopy (ln-WMS). Unlike conventional WMS, the amplitudes of the harmonics are linear to the absorbance regardless how large it is. The treating method used in ln-WMS is taking the natural logarithm of the transmitted intensity. The key to ln-WMS is to find out the demodulation phase. We introduced the η-seeking algorithm, which works to find the demodulation phase η so that the 1st harmonic of the unabsorbed intensity comes to zero. Then the nth harmonic of the absorbed intensity is demodulated at phase nη. With simulations, we validated the effectiveness of ln-WMS as well as illustrated the shapes of 1st, 2nd and 3rd harmonics. Then we utilized ln-WMS for measuring water vapor experimentally. It turns out that the linearity is established between the amplitudes of the 1st, 2nd and 3rd harmonics and concentration, although the absorbance is as large as 0.76. We evaluated the stability of the system with coefficient of variation and Allan deviation analysis, proved the effectiveness of the η-seeking algorithm and investigated how the modulation amplitude influenced the amplitudes of the harmonics.