Detailed structure of harmonic signals in modulation spectroscopy and resulting precision improvement in non-intrusive laser based sensors

This paper presents a statistical analysis method to quantify the quality of fits between experimental and theoretical results, in a manner that illustrates the salient aspects of wavelength modulation spectroscopy (WMS), with higher harmonic detection. Variations in the signal characteristics, as a result of changes such as linewidths, lineshape profiles etc., in the underlying transition are analyzed. The analysis is based on calculations of variance of errors between experimental data points and theoretical models. A higher magnitude in such a variance is a consequence of larger scatter in errors across the wavelength regions of interest. It is seen that the greater structure of the higher harmonic signals generally gives a larger variance of these mismatches. This then leads to the tighter constraints, effectively resulting in a better fit and hence in a higher precision measurement.