Signal Structure and Sensitive Detection of Molecular Species:Optimal experimental techniques in Modulation Broadened Wavelength Modulation Spectroscopy

摘要

Shannon's information theory is applied to Wavelength Modulation Spectroscopy (WMS) providing quantitative figures of merit such as the measurement precision and a prediction of the optimal detection harmonic order to be used.-The amount of information, in bits, that can be extracted in any WMS measurement is calculated. The theory is applied to experimental results we have obtained in WMS experiments in congested spectra with overlapping lines that have highly disparate absorption cross-sections. A key result is that the complexity of signal structure can play a much more important role than the conventional signal to noise ratio. We show that there are some parts (where it exhibits turning points and zero crossings) of the structurally-rich WMS signal that play a larger role in conveying information about the measurement than other parts of the signal. Practical applications follow immediately. We also show that, for a particular noise limitation of the apparatus, there is a finite amount of information that can be transmitted (to the detection equipment) by the probe laser as it samples the probed species. The apparatus is analogous to a Shannon's information channel. Application of the theory developed to our experimental absorption measurements in the Oxygen A-band shows why high detection harmonic orders (up to the 7th or 8th) yield the highest resolution. This is in contrast to statements in the literature, based on conventional signal to noise ratio considerations, that the best results are to be expected with second harmonic detection.