Objective  The effect of thermal blooming in the laser propagation experiment is an important factor affecting the propagation evaluation. The thermal blooming is due to the absorption of gas, which causes the local air to be heated, causing the air to form a density gradient, resulting in refraction and scattering during laser transmission, thus causing the distortion of the laser spot and affecting the experimental results. In the inner channel of the laser propagation, because the laser energy density is high and the air velocity is slow, the thermal blooming is more obvious. Even the trace greenhouse gases will affect the laser propagation. CO₂ is the greenhouse gases of highest concentration and the most difficult to completely remove in the inner channel of laser propagation. Therefore, high-precision detection of CO₂ in the propagation channel is of great significance for propagation evaluation. The inner channel of the laser propagation is characterized by small space and low CO₂ concentration, so a miniaturized and highly sensitive detection system is required. Wavelength Modulation-Tunable Diode Laser Absorption Spectroscopy (WM-TDLAS) technology as an effective detection method is widely used in the detection of trace gas. However, WM-TDLAS system has complex structure and large volume. Therefore, the lock-in amplifier as the core device of WM-TDLAS system is studied in this paper to meet the requirements of high-precision detection of CO₂ and make the WM-TDLAS system more miniaturized.

  Methods  The principle of wavelength modulation detection and lock-in amplifier deeply is analyzed, and the key technologies of digital lock-in amplifier are optimized. The reference signal is generated internally based on DDS principle, and the frequency of sine and cosine reference signal is designed to be adjustable which can expand the scope of application (Fig.2). Combined with the characteristics of wavelength modulation, the integral length of CIC filter is improved based on the number of periodic data points of the modulated signal, and the average is achieved by shifting (Fig.3). The narrow-band low-pass filtering is achieved by CIC filter cascaded FIR filter (Fig.4). JPL algorithm and CORDIC algorithm used to calculate root of sum of squares are simulated. According to the simulation results, the CORDIC algorithm is more suitable for lock-in amplifier (Fig.5). The functions of the lock-in amplifier are implemented based on FPGA (Fig.6). In order to make the system more miniaturized, the software is realized based on Qt and serial communication is combined, so that the lock-in amplifier has the function of data acquisition and processing (Fig.7). Relevant hardware circuits are designed (Fig.9). A WM-TDLAS system is built based on multi-pass cell and the experiments are carried out to verify the function of the designed digital lock-in amplifier (Fig.10).

  Results and Discussions   The reference signal frequency of the designed digital lock-in amplifier is 1-40 kHz adjustable and integration time is 200 μs-20 ms adjustable. The high precision ADC module is designed, and the voltage resolution can reach 0.3 mV. The volume of the final hardware circuit is about 150 cm³, which is far smaller than the commercial lock-in amplifier (Tab.1). Under the condition of normal temperature and pressure and optical path of 30 m, absorption spectrum of CO₂ was measured at 2 μm band, the signal-to-noise ratio of the wavelength modulated absorption spectrum is 102.6, which is about 11.7 times of the direct absorption signal-to-noise ratio of 8.8 (Fig.11). Calibration experiment of low concentration CO₂ is designed and carried out to obtain the linear correlation of the second harmonic amplitude and CO₂ concentration of 0.996 (Fig.12). Under the condition of pure nitrogen, Allan variance is used to evaluate the system performance. When the average time is 2 s, the lower limit of system detection is 1.30 ppm, and when the average time is 180 s, the lower limit of system detection is 0.19 ppm (Fig.13). The system response time is analyzed, and the gas concentration can be obtained within 0.5 s (Fig.14).

  Conclusions  A digital lock-in amplifier is designed based on FPGA and Qt. The key algorithms in the lock-in amplifier are analyzed and optimized, and the relevant software and hardware are implemented. Experiments such as harmonic detection of low concentration CO₂, calibration of low concentration CO₂, analysis of detection sensitivity and analysis of system response time were carried out. The experimental results show that the designed digital lock-in amplifier has the characteristics of high sensitivity, adjustable parameters, real-time processing and miniaturization, and can meet the requirements of low concentration CO₂ detection in the inner channel of laser propagation.