Theoretical analysis of wavelength modulation laser heterodyne spectroscopy

Abstract

In this paper, a comprehensive theory for wavelength modulation laser heterodyne spectroscopy is presented. Some necessary simplifications based on the Taylor series are introduced, the general formulas employed to demodulate the first harmonic signal (1f), the second harmonic signal (2f), and higher harmonic signal (nf) are derived in details, and hence the formulas are suitable for an arbitrary intensity modulation amplitude and modulation index. The purpose of this paper: an overview of how the laser heterodyne harmonic signal depends on the experimental parameters of intensity modulation amplitude and modulation index is reported. This overview is helpful to choose these parameters for the best laser heterodyne harmonic signal because it initiated a new pathway for systematically analyzing the relationships between the experimental parameters and the laser heterodyne harmonic signal.

Temperature measurement of SO2 based on mid‐infrared laser absorption spectroscopy

“…Similarly, the temperature expression of WMS and WMS-2f/1f can also be deduced with the following expressions. 5,10,11 ( )…”

“…Similarly, the temperature expression of WMS and WMS‐2f/1f can also be deduced with the following expressions 5,10,11 $$${T}_{\mathrm{WMS}}=\frac{\frac{{hc}}{k}\left({E}_{2}^{^{\prime\prime} }-{E}_{1}^{^{\prime\prime} }\right)}{\mathrm{ln}({R}_{\mathrm{WMS}})+\mathrm{ln}\left(\frac{{S}_{2}({T}_{0})}{{S}_{1}({T}_{0})}\right)+\left(\frac{{hc}}{k}\right)\left(\frac{{E}_{2}^{^{\prime\prime} }-{E}_{1}^{^{\prime\prime} }}{{T}_{0}}\right)+\mathrm{ln}\left(\frac{I(\bar{{\nu }_{2}}){M}_{2}}{I(\bar{{\nu }_{1}}){M}_{1}}\right)},$$$ $$${T}_{\mathrm{WMS}-2{\rm{f}}/1{\rm{f}}}=\frac{\frac{{hc}}{k}\left({E}_{2}^{^{\prime\prime} }-{E}_{1}^{^{\prime\prime} }\right)}{\mathrm{ln}({R}_{\mathrm{WMS}-2{\rm{f}}/1{\rm{f}}})+\mathrm{ln}\left(\frac{{S}_{2}({T}_{0})}{{S}_{1}({T}_{0})}\right)+\left(\frac{{hc}}{k}\right)\left(\frac{{E}_{2}^{^{\prime\prime} }-{E}_{1}^{^{\prime\prime} }}{{T}_{0}}\right)+\mathrm{ln}\left(\frac{{M}_{2}}{{M}_{1}}\right)},$$$…”

Influence of light source modulation on detection performance of trace-level SF6 fault gas using photoacoustic spectroscopy

“…In this study, a cylindrical single-pass PAS was used to investigate the effects of light source modulation methods on the performance of PAS gas detection system. We initially analyze The mechanisms of square wave signal-based intensity modulation and sawtooth wave signal superimposed with sinusoidal signal-based second harmonic wavelength modulation were analyzed [20][21][22], and the harmonic component order were established, following by using H 2 S as the target gas. The PAS experiments was conducted under these modulation methods, comparing the PA signal amplitudes under multiple conditions (modulation frequency and PC length), thereby analyzing the suitability of modulation methods for different experimental conditions and application scenarios.…”