Tunable diode laser absorption spectroscopy (TDLAS) is a non-intrusive diagnostic technology used extensively for measuring various gas properties, including temperature, pressure, concentration, and velocity. Owing to its non-intrusive nature, TDLAS has proven to be a valuable technique in various scientific fields and applications such as atmospheric and environmental monitoring [1, 2], combustion diagnostics [3, 4], and flow characterizing in aerospace engines [5, 6].

Determining gas properties using TDLAS is based on measuring the absorption line of the target gas species. The laser wavelength is scanned across one or several absorption lines of the target gas while the light intensity transmitted through the gas is measured. As the laser beam travels within a gas medium (e.g., a test section), the transmitted intensity I is related to the incident intensity I₀ by the Beer-Lambert law [7]:

where k_ν (cm⁻¹) denotes the spectral absorption coefficient, and L (cm) is the laser beam’s path length. Here, the product of k_νL is termed the spectral absorbance, A. Since the spectral absorbance is related to the beam path length, the absorption by the target gas in regions of the beam path external to the test section can cause errors in measurements. In order to eliminate the external absorption effect, the laser beam path is typically purged by nitrogen gas in most of the existing research [8–15]. Specifically, the work of Weisberger et al. [15] clearly highlights the critical importance of eliminating the external absorption effects by gas purging. The study demonstrates that, in the absence of effective purging, external gases can significantly distort absorption measurements, resulting in overestimated values. However, when gas purging was implemented, these external interferences were effectively removed, allowing the measurements to align precisely with the expected results. This underscores the essential role of gas purging in ensuring accurate measurements within conventional setups.

However, previous studies [8–15] have demonstrated that integrating a purging system into TDLAS setups considerably increases both the size and complexity of the system, resulting in a bulky design. This increase stems from the requirement to enclose the TDLAS system within a box and incorporate additional hardware components. From a practical standpoint, installing the TDLAS system with a purging mechanism presents significant challenges in confined spaces, such as flight vehicles, where these components consume valuable space and contribute to the overall weight and size of the system. Minimizing the size and weight of the TDLAS system thus becomes a crucial challenge, particularly for applications in flight vehicles.

Instead of using a purge system, a log-ratio detection technique that can cancel the absorption effect outside the test section is introduced. This technique is based on measuring the logarithmic value of the ratio of the sample signal that passes through the test section to the reference signal that does not pass through it [16, 17]. The two signals (sample and reference) are measured using two photodiodes that can detect the intensity of the laser beam. Because the external absorption effect over the common paths of the reference and sample laser beams can be canceled using the log-ratio detection technique, it can be applied to eliminate the need to purge the surrounding gas of the test section.

To eliminate the absorption effect other than in the test section, a theoretical approach was adopted in this study using the log-ratio detection in laser absorption spectroscopy. Experimental verification of the approach was conducted. To confirm the elimination of external absorption effects, pressure measurement was selected for verification because it is relatively easier to manage compared to other physical properties, such as temperature or concentration. The TDLAS system was configured with a distributed feedback (DFB) diode laser and a log-ratio amplifier circuit to detect the target gas. For pressure measurement, atmospheric oxygen was selected as the target gas species, given its stable concentration of 21% in the air. For the test conditions, a pressure range of 20 to 100 kPa at a room temperature of 293 K was generated in a gas cell. Raw absorption signals and gas pressure measurements were performed to verify the cancellation of the external absorption effect using log-ratio detection. The pressure measurement uncertainty was also investigated with an additional experiment.

2.1. Experimental Setup

Figure 1 shows a schematic diagram of the TDLAS system used for absorption line detection in a gas cell. Figure 1(a) shows a schematic of the sensor configuration, and Fig. 1(b) shows a schematic of the gas cell. A 40 mW DFB laser, centered at a wavelength of 760 nm, was used to detect the oxygen absorption lines. The laser was driven and temperature-stabilized using a laser driver and temperature controller (Cosmotec, Daejeon, Korea). A sawtooth waveform generated using a function generator (MFG-2230M; GW Instek Co., New Taipei City, Taiwan) was used to change the wavelength of the diode laser. Within the tunable wavenumber range of the DFB laser of 0.1 cm⁻¹, two absorption lines with a central wavenumber of 13,156.28 cm⁻¹ and 13,156.62 cm⁻¹ were chosen as target absorption lines.

Figure 1. Schematic diagram of the tunable diode laser absorption spectroscopy (TDLAS) system for absorption line detection: (a) Sensor configuration, (b) gas cell.

The DFB laser generates a beam that travels through a series of optical components and the gas cell before reaching the detection components. These optical components include a linear polarizer and a beam splitter. Initially, the laser beam passes through the linear polarizer and then through the beam splitter, where the beam is split into two laser beams: A reference and a sample laser beam. The linear polarizer is used to maintain the linear polarization at the constant polarization angle [18]. The reference laser beam is directed to the reference detector, while the sample laser beam passes through the gas cell and then proceeds to the sample detector. The laser beam paths of L₂ and L₅ vary with changes in ∆L₂ and ∆L₅, respectively. The gas cell is a cylindrical tube made of stainless steel, with a diameter of 30 mm and a length of 300 mm. Two quartz optical windows are installed on both sides of the cell to provide optical access to the laser beam. Pipelines are attached to the gas cell, connecting it to a vacuum pump and pressure gauge. A vent line and the vacuum pump are installed to create the test conditions.

The detection components for acquiring the raw signal consist of two detectors (reference and sample detectors), a log-ratio amplifier circuit, and a digital oscilloscope. Both detectors use a photodiode (Model FDS1010; ThorLabs, NJ, USA) capable of detecting wavelengths from 350 to 1100 nm to capture the laser beam. A log-ratio amplifier circuit built around an AD8305 (Analog Devices Co. MA, USA) integrated circuit was used to receive the detectors’ photocurrent output. In the log-ratio amplifier circuit, the reference and sample detectors are reverse-biased, and their corresponding photocurrents are supplied to the logarithmic amplifier. Further details regarding the circuit used in this study can be found in [18–20]. The log-ratio amplifier circuit’s output signal was acquired with a digital oscilloscope (GDS-1074B; GW Instek) at a 20 million samples/s rate.

2.2. Log-ratio Detection

The signal output from the logarithmic amplifier V [V] is given by V = G log₁₀ (I_samp/I_ref), where G is the built-in gain of the logarithmic amplifier and I_samp and I_ref are the intensity of the laser beam detected by the sample and reference photodiode, respectively.

The expressions for the laser beam intensities detected by the sample and reference detectors are I_samp = rτ_optic I₀ exp(−A_samp) = rτ_optic I₀ exp(−A_test) exp(−A_out) and I_ref = (1−r) I₀ exp(−A_ref), where I₀ represents the laser beam’s intensity from the laser, r is the transmittance of the beam splitter, τ_optic is the total transmittance of the optical components, A_samp and A_ref are the absorption line’s absorbance related to the reference and sample laser beam, respectively [17, 18]. A_samp can be separated with the absorbance inside the test section (gas cell) A_test and outside the test section A_out. Then, the raw spectral signal V_meas can be expressed as:

The use of log-ratio detection can remove the need to purge the surrounding gas of the test section because it can eliminate the absorption effect outside the test section. This can be achieved by canceling the term exp(−A_out)/exp(−A_ref ) on the right-hand side of Eq. (2), which leads to exp(−A_out)/exp(−A_ref) = 1. This can be rearranged to exp[−k_ν (L_out − L_ref)] = 1 using Eq. (1). As a result, the equation L_out − L_ref = 0 can be obtained, where L_out and L_ref denote the laser beam path lengths related to A_out and A_ref, respectively. Because L_out = L₁ + L₃ + L₅ and L_ref = L₁ + L₂, this can be expressed as: L₃ + L₅ = L₂.

Therefore, if the condition in L₃ + L₅ = L₂ is satisfied in the log-ratio detection system, the absorption effect other than in the test section can be eliminated without purging the surrounding gas of the test section. Because only the absorption effect in the test section remains, the output of the raw spectral signal can be expressed as V′_meas = G log₁₀[rτ_optic exp(−A_test)/(1−r)].

The baseline, raw spectral signal in the absence of the absorption line is typically obtained by applying polynomial fitting to the non-absorbing regions of the absorption signal, V′_meas. However, the baseline can equally be obtained by evacuating the gas cell in the experimental setup, as the absorbance within the test section A_test becomes zero. Under this condition, the raw spectral signal, without the presence of the absorption line, acts as the baseline. The spectral raw signal’s baseline V_bl,meas is represented as V_bl,meas = G log₁₀[rτ_optic /(1−r)].

Once the baseline has been determined, the absorbance inside the test section can be obtained by subtracting the baseline from the measured raw spectral signal. The baseline-subtracted output V′′_meas is expressed as V′′_meas = V′_meas − V_bl,meas = G log₁₀ exp(−A_test).

2.3. Measurement and Data Processing

To verify that the absorption effect outside the test section can be canceled when the condition L₃ + L₅ = L₂ is satisfied, pressure measurement was selected for verification because it is relatively easier to manage compared to other physical properties such as temperature or concentration. Pressure measurements were performed by varying the beam path lengths of L₂ and L₅ with identical increments of ∆L₂ = ∆L₅ = ∆L, so that L₃ + L₅ + ∆L = L₂ + ∆L.

The beam path length increment, ∆L, was set from 0 to 600 mm, and the test gas conditions of a pressure range of 20 to 100 kPa with a constant temperature of 293 K were generated in the gas cell. All measurements were conducted in a darkroom to prevent interference from ambient light.

Figure 2 shows the post-processing procedure for the raw signal used in pressure measurement. The post-processing steps are as follows: (i) The measured baseline-subtracted raw signal data, V′′_meas is imported. (ii) Wavenumber calibration is conducted to convert the temporal raw signal into the spectral raw signal, using the time values corresponding to the two absorption lines with central wavenumbers of 13,156.28 cm⁻¹ and 13,156.62 cm⁻¹ to compute the temporal variation in wavenumber. (iii) Voltage-to-absorbance conversion is conducted to convert the spectral raw signal into the measured absorbance using the following relation [18–20]:

Figure 2. Flowchart of the post-processing of raw signal for pressure measurement.

where A_meas is the measured absorbance, V′′_meas is the measured baseline-subtracted voltage, and G is the built-in gain of the logarithmic amplifier. (iv) When the measured absorbance is obtained, gas pressure is determined by comparing the measured spectra with the theoretical spectra. The theoretical spectra are generated using the HITRAN molecular spectroscopic databases [21]. An iterative nonlinear least-squares fitting method is employed to determine the measured pressure that produces the smallest difference between the theoretical and experimental spectra.

3.1. Absorption Line Measurement

Figure 3 shows the measured baseline-subtracted raw signal V′′_meas along the beam path length increment ∆L from 0 to 600 mm for test conditions from 20 to 100 kPa. To increase the signal-to-noise ratio, the measured baseline-subtracted raw signal V′′_meas was obtained by averaging 256 data. It was observed that the absorbance of the target absorption lines increased as the set gas pressure increased from 20 to 100 kPa. This is because the magnitude of absorbance is proportional to the magnitude of pressure. As shown in Fig. 3, the measured baseline-subtracted raw signal V′′_meas is approximately equal, regardless of the beam path length increment ∆L from 0 to 600 mm for all test conditions. These results imply that the absorption effect external to the test section was removed by satisfying L₃ + L₅ = L₂. If a log-ratio detection system is not used, the measured absorbance of the absorption lines should increase as the beam path length increment increases from 0 to 600 mm. However, because the measured baseline-subtracted raw signal is approximately equal, regardless of the beam path length increment ∆L from 0 to 600 mm, it can be experimentally verified that the absorption effect outside the test section can be eliminated if the condition of L₃ + L₅ = L₂ is satisfied in the log-ratio detection system.

Figure 3. Measured baseline-subtracted raw signal V′′_meas along the beam path length increment ΔL for test conditions: (a) P_set = 20 kPa, (b) P_set = 40 kPa, (c) P_set = 60 kPa, (d) P_set = 80 kPa, and (e) P_set = 100 kPa.

3.2. Pressure Measurement Results

Figure 4 shows the measured gas pressure P_meas along ∆L/L₄ under the test conditions. The dimensionless term ∆L/L₄ is introduced to express the relative increase in the length increment ∆L over the length of the test section L₄. As ∆L ranged from 0 to 600 mm and L₄ was 300 mm, ∆L/L₄ increased from 0 to 2. The error bars of the measurement values indicate a 95% confidence level based on the standard deviation of 10 measurements. As illustrated in Fig. 4, the measured gas pressure for all test conditions matches well with the set gas pressure for all conditions of ∆L/L₄, which means that the measured gas pressure is equal regardless of the beam path length increment. This implies that, similar to the results shown in Fig. 3, the absorption effect outside the test section can be removed by satisfying L₃ + L₅ = L₂. Therefore, from the pressure measurement results, it was verified that the absorption effect outside the test section could be removed when the log-ratio detection system was used while satisfying the condition of L₃ + L₅ = L₂.

Figure 4. Measured gas pressure P_meas along ΔL/L₄.

These findings suggest that the performance of the log-ratio detection method is comparable to that of the conventional gas purging method. As highlighted by Weisberger et al. [15], eliminating external absorption effects is essential for achieving accurate measurements, a goal traditionally accomplished by gas purging. Similarly, the proposed method in this study demonstrated equivalent effectiveness, achieving the same results without the need for purging. This highlights the potential of the log-ratio detection technique to maintain measurement precision while offering the added advantages of reducing system size and complexity by eliminating the need for a gas purging system.

3.3. Effect of Reference Beam Path Length on Measurement Accuracy

When using the proposed technique in an actual application, there may be cases where the condition of L₃ + L₅ = L₂ cannot be accurately satisfied. For example, the reference beam path length (L₂) can be shorter or longer than L₃ + L₅, which can lead to measurement error. As beam path length could be a major source of error, it is important to assess the extent of measurement error introduced when the condition L₃ + L₅ = L₂ is not precisely met, as well as how discrepancies in physical property between inside and outside of the test section influence this error. To investigate the effect of reference beam path length on measurement accuracy, an additional pressure measurement experiment at various reference beam path length changes and gas conditions was performed.

In the experiment, L₃ and L₅ are held constant, while only L₂ is varied by adjusting ∆L₂. The change in L₂ ranges from −20% to 20% relative to L₃ + L₅, resulting in a ratio L₂/(L₃ + L₅) that spans from 0.8 to 1.2. The test gas conditions in the gas cell are the same as in the above verification experiment. Since the pressure outside the test section, P_out, is 100 kPa, the corresponding pressure ratio P_set/P_out has a range of 0.2–1.0.

Figure 5 shows the pressure measurement error with respect to L₂/(L₃ + L₅) at various pressure ratios. The dashed lines represent linear fits to the measurement data to indicate trends. As shown in Fig. 5, it is observed that the pressure measurement accuracy can be affected if L₂/(L₃ + L₅) < 1 or L₂/(L₃ + L₅) > 1. In other words, the measurement error increases as the reference beam path length is shorter or longer compared to L₃ + L₅. This is because if the magnitude of A_ref decreases as the L₂ gets shorter, the output V_meas increases according to Eq. (2), and as a result, the measured pressure can be overestimated. Similarly, if the magnitude of A_ref increases as the L₂ gets longer, the output V_meas decreases, and as a result, the measured pressure is underestimated. Notably, it is observed that the smaller the value of P_set/P_out, the larger the error according to the same reference beam path length change. In other words, the greater the pressure difference between the test section and the pressure outside the test section, the more sensitive it is to the reference beam path length change. Given that A_ref is directly correlated with the pressure outside the test section, it seems that the greater difference between P_set and P_out leads to more underestimation or overestimation at the same reference beam path length change. In the case of P_set/P_out from 0.8 to 1.0, the pressure difference of which is relatively low, even if the change of L₂ compared to L₃ + L₅ differs by up to ±20%, the measurement error is relatively low at about ±5%. However, in the case of P_set/P_out from 0.2 to 0.4, the pressure difference of which is relatively high, even if the change of L₂ compared to L₃ + L₅ differs by up to ±10%, the measurement error is relatively high at about ±15%. This implies that when using the proposed technique, it is recommended to precisely match the condition L₃ + L₅ = L₂ to reduce measurement error if the pressure difference between the test section and outside the test section is large.

Figure 5. Pressure measurement error with respect to L₂/(L₃ + L₅) at various pressure ratios.

In this study, a theoretical approach and experimental verification for eliminating the absorption effect other than in the test section using log-ratio detection in laser absorption spectroscopy are presented. In the theoretical approach, a beam path length condition that could remove the absorption effect external to the test section without purging was derived. To verify that the external absorption effect can be canceled if the derived condition is satisfied, gas pressure measurements for the test conditions were conducted along the changing the beam path length with the increment of ∆L from 0 to 600 mm. Gas conditions with a pressure range of 20 to 100 kPa and a constant temperature of 293 K were created in a gas cell. Using air as the test gas, the absorption feature in the oxygen A-band is used to measure the air pressure. The results show that the measured gas pressures for each test condition were equal regardless of the beam path length increment. The experimental results verified that the external absorption effect could be eliminated if the derived beam path length condition was satisfied in the log-ratio detection system. Because the proposed method in the study can be applied to TDLAS applications that require gas purging due to the presence of the target gas species in the ambient gas, TDLAS systems can be significantly simplified by eliminating components and equipment related to gas purging. This is thought to be useful in situations where implementing the purging system is impractical due to space constraints.

This research was supported by the BK21 FOUR (Fostering Outstanding Universities for Research) funded by the Ministry of Education (MOE, Republic of Korea) and the National Research Foundation of Korea (NRF).

The authors declare no conflicts of interest.

Data underlying the results presented in this paper is not publicly available at this time, but may be obtained from the authors upon reasonable request.