Calibration-free wavelength-modulation spectroscopy based on a swiftly determined wavelength-modulation frequency response function of a DFB laser

Abstract

A methodology for calibration-free wavelength modulation spectroscopy (CF-WMS) that is based upon an extensive empirical description of the wavelength-modulation frequency response (WMFR) of DFB laser is presented. An assessment of the WMFR of a DFB laser by the use of an etalon confirms that it consists of two parts: a 1st harmonic component with an amplitude that is linear with the sweep and a nonlinear 2nd harmonic component with a constant amplitude. Simulations show that, among the various factors that affect the line shape of a background-subtracted peak-normalized 2f signal, such as concentration, phase shifts between intensity modulation and frequency modulation, and WMFR, only the last factor has a decisive impact. Based on this and to avoid the impractical use of an etalon, a novel method to pre-determine the parameters of the WMFR by fitting to a background-subtracted peak-normalized 2f signal has been developed. The accuracy of the new scheme to determine the WMFR is demonstrated and compared with that of conventional methods in CF-WMS by detection of trace acetylene. The results show that the new method provides a four times smaller fitting error than the conventional methods and retrieves concentration more accurately.

A new line-shape asymmetry model for wavelength modulation spectroscopy in gaseous flows

“…However, unlike previous investigators [3,4,6], we report here an alternative use of trigonometric series postulated by Gabor [8] for representation of an arbitrary elementary signal.…”

“…Here α k , β k , φ k and ψ k are amplitudes and phase shifts, respectively, of the corresponding term (Gabor function) and G w is a width-adjusted (reduced) Gaussian distribution function described below in more details, see (6).…”

“…For analytical purposes it is always desirable to evaluate line-shape profile [3,4,5,6], rather then simply estimate peak-to-peak parameters of WMS signal, which contains less-robust information on molecular absorption and spectral broadening. Therefore, line-shape fitting procedure needs to be addressed in WMS post-processing scheme as the level of uncertainties is a critical attribute of measurement outputs.…”

A novel methodology to directly pre-determine the relative wavelength response of DFB laser in wavelength modulation spectroscopy

“…Later Z. Qu has applied this idea successfully to CF-WMS [16,22,23]. Recently, in order to further consider the nonlinear response to the modulation, G. Zhao empirically suggested that the CMWR consists of two parts: a 1 st harmonic component with a linearly time-dependent amplitude and a nonlinear 2 nd harmonic component with a constant amplitude that can be expressed as [24] θ is the phase difference between the first and second harmonic of frequency modulation. This is here referred to "the Zhao's method".…”

“…This is here referred to "the Zhao's method". In [24], G. Zhao et al presented a comparison between these three models when fitted to an experimental spectrum. The results showed that the Zhao's method, due to its more completed description, obtained a smaller residual than others.…”