# Error Analysis of Integrated Absorbance for TDLAS in a Nonuniform Flow Field
## 1 Introduction  
Tunable diode laser absorption spectroscopy (TDLAS) technology has a long history of use in the high-temporal-resolution, noninvasive, and quantitative measurements of the gas temperature, pressure, and composition in many practical, near-homogenous environments (e.g., environments of the atmosphere, shock tubes, scramjets, and internal-combustion engines) [1, 2]. However, because many flows of practical interest have strong nonuniformity, several researchers have advanced strategies for nonuniform flows to obtain the flow field parameters. Past efforts can be broadly divided into two categories [3, 4, 5]. Efforts in the first category improve the TDLAS to obtain the parameter distribution information along the optical path [6, 7, 8]. Efforts in the second category obtain the spatial resolution by combining TDLAS with tomography. This combination has resulted in the tunable diode laser absorption tomography (TDLAT) method. This method is mainly applied to combustion and reaction flow and is a two-dimensional measurement technique with great potential [9, 10, 11, 12, 13, 14, 15, 16]. Most TDLAS technology used in a nonuniform flow field, especially TDLAT technology, adopts direct absorption spectroscopy [14]. Figure 1 illustrates the application of direct absorption TDLAS in a nonuniform flow field. A spectral absorption signal is obtained after the laser light is absorbed. The absorption signal undergoes data processing (line-shape fitting) to obtain the integrated absorbance (IA; i.e., \(A\)). Depending on a few key parameters (including pressure, line parameters, etc. ), measurement results are obtained through the tomographic calculation of the IA. The IA is the key intermediate quantity in the measurement process. However, in a nonuniform flow field, the nonuniformity of the flow field is coupled with the absorption line features (including the spectroscopic parameters and absorption line overlap) and the measurement noise, resulting in distortion of the measured absorption signal. The distorted absorption signal interferes with the line-shape fitting, resulting in an IA error, which ultimately affects the measurement result. It is therefore necessary to study the IA error generated by signal distortion in a nonuniform flow field. Previous studies identified the nonuniformity of the flow field (especially the boundary layer effect) as an important factor affecting the accuracy of TDLAS measurement [17; 18; 19; 20]. [PERSON] et al. proposed an energy-temperature curve for estimating the effects of thermal and concentration boundary layers and assisting the selection of candidate absorption lines [17]. [PERSON] et al. quantified the uncertainty generated by various nonuniformities typically encountered in a velocity measurement [18]. [PERSON] et al. quantified the effects of the temperature gradient and thermal boundary layer thickness on the spectral collisional width and gas concentration measurement [19]. [PERSON] et al. quantified the uncertainty in the measurement of the TDLAS-determined temperature [20]. The above research provides a basis for the applicability of TDLAS in one-dimensional measurement of nonuniform flow field. However, when including multiple factors simultaneous (including IA, line parameters, pressure, etc.) in the study, there are challenges to apply TDLAS technology in nonuniform flow fields as a universal method. It is also difficult to perform general analysis of TDLAS measurement errors, especially to evaluate the uncertainty of two-dimensional measurement, which requires separate error analysis of IA. However, only a few researchers have studied the IA error. [PERSON] et al. proposed a hybrid line-shape fitting method, which combines direct integration and line-shape fitting to obtain the IA more accurately [6]. [PERSON] et al. applied this method in a nonuniform flow field measurement [7]. [PERSON] et al. used a series of low-temperature water absorption lines to further analyze the use of this method [21].