Multipass cell (MPC), with a long effective optical path length (OPL), is an effective method to improve measurement sensitivity in laser absorption spectroscopy for trace gas sensing. We present a space equation (SE) method to design MPC, which can solve inaccuracy caused by using paraxial-matrix (PM) method. The location and dimension of light spot pattern can be calculated accurately and intuitively through SE method. Meanwhile, actual effective OPL can be accurately calculated, SE method can reduce the interference effect, the direction of each ray can be obtained accurately, and, hence, designing the angle of outgoing ray is simple. By adjusting the mirror curvature, mirror space, incident angle, and incident position, we realized four dense spot patterns with different multiple reflections in MATLAB simulation. We calculated the shape changes of light spot after multiple reflection and its influence on the design of outgoing ray hole size accurately. We also considered the evolution of dense pattern and found a method easy to obtain multiple ring pattern. We verified the validity of the proposed model and built a compact MPC with seven rings dense spot pattern. Such MPC offers an effective OPL of 36.48 m with 198 times of reflection. We verified the tunable diode laser absorption spectroscopy (TDLAS) technology to measure 610-ppmv standard methane. In contrast to PM method, the improvement of the signal-to-noise ratio (SNR) of 1.36 times is achieved when the volume of MPC is reduced by 3 times. In addition, the SNR can be improved to 6.6 times, while the volume of MPC is the same. Results validated the ability of the SE method to design MPC.

中文翻译：

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用空间方程法对带有两个球面镜的多通道像元进行光学设计和验证

具有较长有效光程长度（OPL）的多通道样品池（MPC）是一种有效的方法，可提高用于痕量气体感测的激光吸收光谱法中的测量灵敏度。我们提出了一种空间方程（SE）方法来设计MPC，它可以解决由于使用近轴矩阵（PM）方法而引起的误差。通过SE方法可以准确直观地计算出光斑图案的位置和尺寸。同时，可以准确地计算出实际有效的OPL，SE方法可以减少干涉效应，可以准确地获得每条光线的方向，因此，设计出射光线的角度很简单。通过调整反射镜的曲率，反射镜的空间，入射角和入射位置，我们在MATLAB仿真中实现了四个具有不同多次反射的密集光斑图案。我们精确地计算了多次反射后光斑的形状变化及其对出射光孔尺寸设计的影响。我们还考虑了密集图案的演变，找到了一种易于获得多个环形图案的方法。我们验证了所提出模型的有效性，并构建了具有七个环密集斑点图案的紧凑型MPC。这种MPC可提供36.48 m的有效OPL和198倍的反射率。我们验证了可调谐二极管激光吸收光谱（TDLAS）技术可测量610 ppmv标准甲烷。与PM方法相比，当MPC的体积减少3倍时，可实现1.36倍的信噪比（SNR）的提高。此外，在MPC的体积相同的情况下，SNR可以提高到6.6倍。结果证实了SE方法设计MPC的能力。