# Laser Absorption Sensing Systems: Challenges, Modeling, and Design Optimization
## 4 Strategies for Noise Reduction and Design Optimization
### Strategies Based On Laser Control Parameter Optimization  
The absorption signal can be enhanced by optimizing a number of laser control parameters including scanning amplitude, scan rate, modulation depth and frequency, and time delay constant of the lock-in amplifier. A number of researchers have discussed parameter selection criteria for the WMS system. [PERSON] et al. conducted a comprehensive analysis of the modulation degree so as to obtain maximum signal amplitude [8]; a Fourier series was utilized by [PERSON] et al. to analyze the relationship between modulated signals and optical penetration depth in frequency modulation [90]; [PERSON] et al. theoretically studied the effect of modulation frequency [91]; [PERSON] et al. studied the optimization of a number of modulation parameters in realizing a LAS oxygen sensing system [92]. Table 4 summaries the effect of different control parameters on the 2_f_-signal waveforms including maximum amplitude, SNR, peak width, and peak height ratio (PHR). Due to the complex intercorrelation between various laser characteristic parameters, no explicit mathematical expressions generally exist to describe the dependence of the WMS signal on the laser control parameters. Therefore, the selection and optimization of these control parameters usually rely on empirical attempts and maximization of the target signal. The laser scan range, for example, is simply set to cover the target absorption feature and just enough non-absorption portions for baseline fitting, without leaving excessive margin which will decrease the detection bandwidth. For WMS in general, the modulation depth is chosen so that the WMS-2\(f\) signal at absorption line center is maximized. It has been demonstrated that for an isolated absorption feature, the highest peak value can be achieved by selecting the modulation depth to be 1.1 times the full-width-at-half-maximum (FWHM) \(\Delta v\) of the absorption feature [55]. In conventional scanned-wavelength WMS, a high-frequency sinusoidal wave is superimposed on a linear ramp of the laser injection current. As the laser tuning function can now readily be controlled digitally, variation of this tuning waveform can bring increased flexibility to signal optimization. [PERSON] et al. employed a jump scanning function and dual fitting analysis to simultaneous optimize signals from two selected absorption profiles [93]. [PERSON] et al. modified the linear ramp function so that the laser scanned more slowly near the line center ([94], Figure 8). The scan portion with stronger absorption thus occupied a larger fraction of the scan, resulting in the improvement of the overall SNR. Consequently, a factor of 1.8 improvement was observed with 2\(f\) detection, and an even higher enhancement by a factor of 3.3 was obtained with direct absorption measurements. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Scanning Amplitude** & **Scanning Frequency** & **Modulation Depth** & **Modulation Frequency** & **Time Constant** \\ \hline Maximum 2\(f\) & -1 & \(\downarrow\)3 & \(\uparrow\downarrow\) & \(\uparrow\downarrow\) & \(\downarrow\) \\ SNR & - & \(\uparrow\) or \(\downarrow\) & \(\uparrow\downarrow\) & \(\downarrow\) & - \\ Peak width & \(\uparrow\)2 & \(\uparrow\) & - & \(\downarrow\) & - \\ PHR & \(\uparrow\) & \(\downarrow\) & - & \(\uparrow\) or \(-\)4 & - \\ \hline \hline \end{tabular}  
* no evident correlation, 2 increase, 3 decrease, 4 unchanged.  
\end{table} 
Table 4: Effects of different control parameters on 2\(f\) signals. PHR: peak height ratio. When multi-species detection is attempted by using closely spaced absorption lines accessible with a single laser scan, the different widths and line profiles of the target species may impose significantly different optimization targets according to the optimal modulation depth criteria stated above. [PERSON] et al.