Natural logarithm wavelength modulation spectroscopy

Natural logarithm wavelength modulation spectroscopy (ln-WMS) is demonstrated in this Letter. Unlike the conventional wavelength modulation spectroscopy (WMS)-2f technique, it is a linear method even for large absorbance, which is the core advantage of ln-WMS. The treating method used in ln-WMS is to take the natural logarithm of the transmitted intensity. In order to determine the proper demodulation phase, the η-seeking algorithm is introduced, which minimizes the absolute value of the first harmonic within the non-absorbing region. Subsequently, the second harmonic of the absorption signal is extracted by setting the demodulating phase as 2η. To illustrate the validity of ln-WMS, it was applied to water vapor experimentally. The result shows that even if the absorbance (base-e) is between 1.60 and 6.26, the linearity between ln-WMS-2f and volume fraction is still established. For comparison, measurement with conventional WMS-2f was also done, whose response no longer kept linearity. The η values retrieved in continuous measurements and the residuals were shown so as to evaluate the performance of the η-seeking algorithm. Time consumed by this algorithm was roughly 0.28 s per measurement. As an alternative WMS strategy, ln-WMS has a wide range of potential applications, especially where the absorbance is large or varies over a wide area.