## 2 Atmospheric Spectroscopy
### Wavelength Modulation Spectroscopy (WMS) Technique  
By shifting detection to higher frequencies using modulation techniques [10] the \(1/f\)-noise can be reduced. WMS is the most common of these techniques. It is advantageous for applications with small absorbance at atmospheric pressures. The frequency of the laser is modulated at high \(f\) values (in the kHz range) leading to a modulation of the transmitted intensity near the transition. The detected signal is then demodulated at a multiple integer \(nf\) of the modulation frequency using a lock-in amplifier. This technique increases the sensitivity [11; 12; 13; 14] compared to direct absorption spectroscopy described above. Figure 1 shows the basic principle of this WMS technique.  
The principle of our developed spectrometer is based on the WMS technique which allows us to attain high-sensitivity detection. Besides that, working at atmospheric pressures is necessary in such light-weight instruments. Furthermore, second harmonic detection produces a zero baseline signal, thus eliminating the necessity of measuring small differences between two large intensities, \(I_{0}\) and \(I(v)\) (Figure 1), as in the case of direct absorption spectroscopy [15]. Therefore, the WMS technique allows us to overcome baseline artifacts and background measurements.  
All of the \(nf\) components of the WMS signal are proportional to laser intensity. At the absorption line center, the WMS-\(1\!f\) term is dominated by the laser intensity contribution [16]. Generally, the second harmonic (\(2\!f\)) is used because it is strongly dependent on spectral parameters and gas properties and can therefore be compared with spectral simulations to infer gas properties. Simultaneous wavelength and intensity modulation for the emitted laser light enables WMS-\(1\!f\) normalization of the WMS-\(2\!f\) signal to avoid the need to scan on and off the transition for the zero absorption baseline used in direct absorption spectroscopy technique which leads to non-absorption losses in laser power due to scattering, window fouling or laser power drift [11; 12]. This normalization allows quantitative measurements without determining a zero-absorption baseline which makes WMS an attractive  
Figure 1: WMS basic principle. The incident laser light (\(i_{0}\)) that passes through the gas sample having an absorption coefficient (\(\alpha(v)\)) on a defined path-length (\(L\)) is modulated at a specified frequency (\(f\)). The transmitted light is then attenuated by the absorption (\(I(v)\)) and measured by the detector (\(S(v)\)). This latter is demodulated at an integral multiple (\(n\)) of the modulation frequency in order to obtain a demodulated signal (\(S_{n}(v)\)). The function generator is used to sweep the laser frequency in order to obtain an absorption spectrum of the gas.  
technique for absorption measurements in harsh environments (high pressure, high temperature, high-opacity,... ) [11]. [PERSON] and [PERSON] [17] have demonstrated that the magnitude of the WMS-2\(f\) signal is related to the ratio of the modulation depth of the laser to the half-width at half-maximum (HWHM) of the selected spectral line. When this ratio is equal to 2.2 at a fixed pressure and temperature, the WMS-2\(f\) signal reaches its maximum.