# Laser Absorption Sensing Systems: Challenges, Modeling, and Design Optimization
## 3 Fundamentals of Different LAS Measurement Schemes
### Summary of Measurement Schemes  
A summary of various scanned-wavelength LAS techniques discussed above is presented in Table 1. For the purpose of comparison, fitting parameter initialization, parameter predetermination, as well as features and limitations for each algorithm are listed.  
DAS is preferred for its calibration-free detection capability and simplicity, for applications where relatively isolated transitions are used. However, laser intensity fluctuations, excess noises, and baseline fitting errors put limitations to the use of this method especially for difficult environments. Thus, DAS is the method of choice for measurements with transitions of sufficient linestrength and narrow linewidth to allow laser access with wavelength scanning.  
By contrast, the WMS method is more promising for measurement systems with small absorbance, high pressure broadening, or blended absorption features precluding a straightforward determination of the non-absorbing baseline. With 1\(f\) normalization, the calibration-free WMS-2\(f\)/1\(f\) method can account for variations in laser intensity such as non-absorption losses due to light scattering or beam steering. This makes it advantageous for measurements in harsh environments involving high pressures, high opacity, high emission levels, and high temperatures.  
The accuracy of DAS lineshape recovery from harmonic signals is limited by the low-SNR high-order terms, making this method unsuitable for practical measurements. A time-division multiplexed spectroscopic scheme is applied by alternating laser modulation and allows the enhancement of precision and dynamic range. This is an attractive strategy for in-field trace gas measurements without any need for reference gases or measurement interruption.  
The LAS techniques discussed above typically provide a path-averaged parameter measurement over the zone of interest. Parameters including temperature, concentration, etc., are inferred by fitting measured and simulated spectral profiles. On the other hand, strategies have been developed to identify non-uniform characteristics in practical environments that commonly result from heat transfer, flow mixing, and combustion.  
Two types of approaches including single line-of-sight (LOS) absorption and tomography have been proposed and experimentally demonstrated for the measurement of non-uniform zones. The first approach is based on either the _a priori_ temperature (concentration) distribution profile or the probability density function along the LOS, namely, profile fitting and temperature binning, respectively [64]. It depends on simultaneous measurements of multiple absorption transitions with different temperature dependence. Tomography, on the other hand, relies on multiple LOS measurements and computational reconstruction algorithms. It reduces the requirements for spatially continuous optical access in traditional planar imaging and exhibits great potential for harsh and even optically dense environments [65]. However, this may complicate the optical system design and data processing of the experimental results.  
Improvement in laser source and tomographic algorithms will contribute to greater accuracy in the temperature and concentration distribution reconstruction, using either of the two approaches above. [PERSON] et al. have extended the single LOS technique from advanced and expensive diode lasers with much broader tuning range (up to 10-15 cm\({}^{-1}\)) to a dual-frequency comb spectrometer [66; 67]. The temperature distribution reconstruction accuracies increase as more absorption lines are incorporated. In addition, the development of hyperspectral laser sources enables measurements of a large number of absorption transitions and thereby significantly reduces the number of projections [68; 69]. A detailed summary of laser absorption tomography (LAT) algorithms has been given by [PERSON] et al. [65].