# Laser Absorption Sensing Systems: Challenges, Modeling, and Design Optimization
## 4 Strategies for Noise Reduction and Design Optimization
### Sources of Noise
#### 4.1.3 Optical Interference Fringe Noise  
In a multi-element optical system with coherent light source, many flat surfaces can lead to optical interference fringes, often referred to as optical etalons. These optical fringes often exhibit a free-spectral-range (FSR) comparable to the linewidth of the absorbing species, so that they are difficult to be distinguished from target absorption features. Various means have been attempted to minimize the influence of optical etalons, including careful optical design [74; 75; 76], mechanical dithering of optics [77; 78; 79], balanced-ratio detection schemes [80; 81], calibration-free WMS [82; 83; 84], and digital filtering techniques [85; 86; 87; 88; 89]. A summary of these approaches is given in Table 3 and briefly discussed in the following. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type of noise** & **Cause** & **Feature** & **Frequency Range** \\ \hline Laser excess noise & Intensity fluctuation & Frequency dependent & 1–10 kHz \\ \hline \multirow{2}{*}{Detector thermal noise} & Thermal agitation of the charge carriers & Frequency independent & 0.1–140 kHz \\ \hline \multirow{2}{*}{Detector shot noise} & Discrete nature of electric charge & Frequency independent & 0.1–140 kHz \\ \hline Detector excess noise & Intensity fluctuation & Frequency dependent & 1–10 kHz \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of laser and detector noises. Optical etalons essentially arise from the constructive and destructive interferences when light bounces back and forth between parallel surfaces, similar to the way optical cavity modes are formed. Optical designs to avoid etalons are therefore approaches to reduce reflections and to scramble these standing-wave modes. This includes using wedged or anti-reflective (AR) -coated windows, optical isolators, and placing the optical elements at \"etalon-immune distances\" to avoid etalon effects from optical feedback. Collimated laser beams can be intentionally diverged before passing through optical thins and re-collimated thereafter. In addition to these passive optical designs, an active control of the optical system can be applied to effectively reduce etalons. Mechanical modulations, such as dithering or rotation of the mirrors and use of a Brewster-plate spoiler, are active control approaches taken in high-performance optical systems. However, these do largely increase the system's cost and complexity and may limit the achievable detection bandwidth. Certain laser devices exhibit unsuppressed cavity mode noise or fiber-coupling noise due to imperfect optical isolation, which appear as etalons on the output scans. Balanced-ratio detection schemes, also known as common-mode rejection schemes, are commonly employed to reduce such optical fringes. The laser beam is split into a measurement and a reference beam, and signals from the two detectors are fed into a balanced-ratio detection circuit that automatically cancels out the noises commonly present in the two signals. Etalons originated from the optical path external to the laser cannot generally be canceled in this way, since it would be difficult to achieve exactly the same beam path other than the portion being absorbed. Etalon fringes often appear as low-frequency noises and can therefore be suppressed through the band-pass filtering process of WMS. On the other hand, fringe noises may add to the RAM and put additional constraint on selecting the optimal modulation parameters. This can lead to reduced SNR and larger uncertainties, especially since the optical alignment and etalon fringe profiles may change over time. Digital filtering techniques are extensively investigated in absorption signal processing, including wavelet transform, Kalman filter, and empirical mode decomposition (EMD). These methods are purely from a standpoint of digital signal processing and frequency-domain analysis, thus require no additional optical or mechanical components.