## 3 System Configuration  
Using the above detection principle, the schematic block diagram and physical image of the sensing system are shown in Figure 2a,b, respectively.  
The sensing system mainly includes an optical part and an electrical part. In the optical part, a continuous-wave ICL with a thermoelectric cooling function produced by Nanoplus was used as a luminous source. In order to meet the compact requirements of the sensing system, the physical size of the MPGC was \(20\times 7.6\times 10.5\) cm\({}^{3}\), and the effective optical path was 24 m. The emitting light of the ICL enters into the MPGC (custom design multi-pass White type absorption cell) with correct position and angle, and exits to the mid-infrared MCT detector after 215 reflections in the interior of the MPGC. The mid-infrared detector (PVI-4 TE-5, VIGO, Ozarow Mazowiecki, Poland) with a thermoelectric cooling function was manufactured by VIGO Systems.  
In the electrical part, a self-fabricated ICL driver and temperature controller were used to replace commercial instruments, thereby reducing the size and cost of the proposed sensor. A low-power, high-performance, floating-point digital signal processor (DSP, Texas Instruments, Dallas, TX, USA) was used as the controller for the sensing system. Under the control of the DSP processor, a triangular wave signal and a sine wave signal are superimposed by an adder and supplied to a current source for scanning and modulating the ICL. The signal output from the mid-infrared MCT is demodulated using a self-developed lock-in amplifier (LIA). The DSP processor uses an analog-to-digital converter (ADC) to acquire the peak of secondary harmonic signal pairs, and then obtains the \({}^{13}\)CO\({}_{2}\)/\({}^{12}\)CO\({}_{2}\) isotope ratio according to the calibration curve. A pressure controller (model IQ + Flow, \(4\times 3\times 1\) cm\({}^{3}\)) manufactured by Bronkhorst was used to control the pressure of the MPGC at 20 Torr, while the micro-DC pump (TOPSFLO, Changsha, China) manufactured by Knf Neuberger was used to extract the separated gas into the MPGC.  
As the absorption coefficient of the selected absorption line pairs to be measured can be affected by the temperature of CO\({}_{2}\), the temperature of CO\({}_{2}\) directly affects the accuracy and precision of the sensing system. A high-precision temperature control system for the MPGC was designed and developed in this paper. The schematic block diagram and physical image are shown in Figure 3a,b.  
In terms of hardware in the circuit, a polyimide electrothermal film as a heating device and a PT1000 platinum resistor with \(\pm 0.03\)\({}^{\circ}\)C accuracy (1/10 B Class) as a temperature sensor were used to form a closed-loop temperature control system. The precision of the temperature measurement could reach 10 mK. For software, the Ziegler-Nichols method was used to set the values of the three proportional, integral, and difference parameters (P, I, and D) [24]. Aiming to address the temperature overshoot caused by the complex structure and slow response of the controlled object, the integral  
Figure 2: (**a**) Schematic block diagram of the sensing system including an optical part and an electrical part. (**b**) Gas sensor physical image including an optical part and an electrical part. MPGC: multi-pass gas cell; ICL: interband cascade laser; MCT: mercury cadmium telluride.  
separation PID control algorithm was used to rapidly control the temperature and avoid overshoot, resulting in reliable performance for the \({}^{13}\)CO\({}_{2}\)/\({}^{12}\)CO\({}_{2}\) isotope sensing system.