近日，来自安徽大学、安庆师范大学、复旦大学、皖西学院的联合研究团队发表了《参数调谐随机共振作为增强波长调制光谱学的工具，使用密集重叠斑点模式多程吸收池》论文。

Recently, the joint research team from Anhui Key Laboratory of Mine Intelligent Equipment and Technology, School of Electronic Engineering and Intelligent Manufacturing, Department of Atmospheric and Oceanic Sciences, School of Electrical and Photoelectronic Engineering, West Anhui University published an academic papers Parameter-tuning stochastic resonance as a tool to enhance wavelength modulation spectroscopy using a dense overlapped spot pattern multi-pass cell.

背景

激光吸收光谱技术已在许多应用中得到证明，如空气质量监测、工业过程控制和医学诊断。测量的精度对这些应用非常重要。尽管激光吸收光谱在敏感检测方面具有许多优点，但仍需要很长的光学路径长度和特殊的测量技术来检测极微量的物质，以实现高检测灵敏度。为了实现这些目的，通常采用具有长光学路径的多程吸收池来增强吸收信号。然而，在吸收信号中经常出现意想不到的干扰光束、热噪声、射频噪声、电噪声和白噪声，严重影响了检测的精度。当使用密集重叠斑点模式的多程吸收池时，这些问题在激光吸收光谱中很常见。因此，从强噪声背景中有效提取弱光电吸收信号具有重要意义。

已提出了几种方法来消除噪声的负面影响。传统的弱周期信号处理方法主要包括时间平均法、滤波法和相关分析法。

① 时间平均法可以获得信噪比（SNR）较高的信号，因此可以降低噪声的标准差并提高信号质量。然而，这种方法无法消除强噪声背景。

② 基于硬件和软件的信号滤波广泛用于降噪，其特点是带宽较窄。在实际应用中，期望的信号和噪声通常具有连续的功率谱和宽带宽，但制造与信号带宽相匹配以去除噪声的滤波器相对较困难。如果滤波器的带宽非常小，噪声将大幅衰减。然而，这可能会破坏期望的信号。

③ 相关检测方法是通过周期信号的自相关来去除噪声的。其本质是建立一个非常窄的带宽滤波器，以滤除与信号频率不同的噪声。与上述其他弱周期信号检测方法相比，参数调谐随机共振（SR）方法的优势显而易见。即使噪声和信号具有相同的频率，只要它们达到最佳的共振匹配，SR方法就可以将部分噪声能量转化为信号能量，以抑制噪声并增强信号。

在这项工作中，我们将SR方法应用于波长调制光谱学（WMS），并使用密集重叠斑点模式的多程吸收池。首先，将进行数值计算以找到合适的参数并评估最佳SR系统的性能，然后通过实验验证SR方法可以有效增强WMS信号。

Introduction

The laser absorption spectroscopy technology has been demonstrated in many applications, such as air quality monitoring, industrial process control, and medical diagnostic. The precision

of the measurement is important to those applications. Although laser absorption spectroscopy has many advantages in sensitive detection, it still needs a long optical path length and special

measurement technology for detecting a very trace substance, with a high detection sensitivity . For those purposes, a multi-pass cell with a long optical path is usually applied to enhance the absorption signal. However, the unexpected interference fringe, thermal noise, shot noise, electrical noise and white noise, often occur in absorption signals and seriously spoil the detection precision. Those problems are common for laser absorption spectroscopy when using dense overlapped spot pattern multi-pass cell. Therefore, it is of great significance to effectively extract weak photoelectric absorption signals from a strong noise background.

Several methods are proposed to eliminate the negative influence of the noise. The traditional weak periodic signal processing methods mainly include time average method, filtering method,

and correlation analysis method.

①The signal with a high signal-to-noise ratio (SNR) can be obtained by time average method, so the standard deviation of noise can be reduced and the signal quality can be improved. Nevertheless, the strong noise background cannot be fully eliminated by this method.

②The signal filters based on hardware and software are widely used for noise reduction, the characteristic of which is narrow bandwidth. In practical application, the desired signal and noise usually have a continuous power spectrum and wide bandwidth, but it is relatively difficult to manufacture a filter that matches the bandwidth of the signal to remove the noise. If the bandwidth of the filter is very small, the noise will be greatly attenuated. However, this may destroy the desired signal.

③The correlation detection method is used to remove the noise by the autocorrelation of the periodic signal. Its essence is to establish a very narrow bandwidth filter to filter out the noise, the frequency of which is different from that of the signal. Compared with other weak periodic signal detection methods mentioned above, the advantage of the parameter-tuning stochastic resonance (SR) method is apparent. Even if the noise and signal have the same frequency, as long as they reach the optimal resonance matching, the SR method can convert part of the noise energy into the signal energy to suppress the noise and enhance the signal.

In this work, the SR method is applied to the wavelength modulation spectroscopy (WMS) by using the dense overlapped spot pattern multi-pass cell. first, the numerical calculation will be implemented to find the suitable parameters and evaluate the performance of the optimal SR system, and then it is verified that the SR method can effectively enhance the WMS signal by the experiments.

实验装置的示意图如图1所示。海尔欣光电科技有限公司为此研究提供了锁相放大器（Healthy Photon，HPLIA），用于解调来自光电探测器的吸收信号，解调频率为第二谐波信号2f的频率（其中f = 6千赫兹是正弦波的调制频率）。锁相放大器的时间常数设置为1毫秒。解调后的信号随后由一个数据采集卡数字化，并显示在计算机上。

 A schematic diagram of the experimental setup is shown in Fig. 1. HealthyPhoton Technology Co., Ltd. provides a lock-in amplifier (HPLIA), which is used for demodulation of absorption signal from the photodetector at the frequency of second harmonic signal 2f (where f =6 KHz is the modulation frequency of the sine wave). The time constant of the lock-in amplifier is set to 1 ms. The demodulated signal is subsequently digitalized by a DAQ card and displayed on a computer.

Fig. 1. Schematic diagram of experimental device of measurement.

Healthy Photon，lock-in amplifier HPLIA

Fig. 2. 2f SR signal and 2f time average signal.

结论

参数调谐随机共振（SR）方法可以将部分噪声能量转化为信号能量，以抑制噪声并放大信号，与传统的弱周期信号检测方法（例如，时间平均法、滤波法和相关分析法）相比。本研究进行了数值计算，以找到将SR方法应用于波长调制光谱学（WMS）的最佳共振参数。在随机共振状态下，2f信号的峰值（CH4浓度恒定在约20 ppm）有效放大到约0.0863 V，比4000次时间平均信号的峰值（约0.0231 V）高3.8倍。尽管标准差也从约0.0015 V（1σ）增加到约0.003 V（1σ），但信噪比相应提高了1.83倍（从约25.9提高到约15.8）。获得了SR 2f信号峰值与原始2f信号峰值的线性光谱响应。这表明在强噪声背景下，SR方法对增强光电信号是有效的。

Conclusion

The parameter-tuning stochastic resonance (SR) method can convert part of the noise energy into the signal energy to suppress the noise and amplify the signal, comparing with traditional weak periodic signal detection methods (e.g., time average method, filtering method, and correlation analysis method). In this work, the numerical calculation is conducted to find the optimal resonance parameters for applying the SR method to the wavelength modulation spectroscopy (WMS). Under the stochastic resonance state, the peak value of 2f signal (a constant concentration of CH4∼20 ppm) is effectively amplified to ∼0.0863 V, which is 3.8 times as much as the peak value of 4000-time average signal (∼0.0231 V). Although the standard deviation also increases from ∼0.0015 V(1σ) to ∼0.003 V(1σ), the SNR can be improved by 1.83 times (from ∼25.9 to ∼15.8) correspondingly. A linear spectral response of SR 2f signal peak value to raw 2f signal peak value is obtained. It suggests that the SR method is effective for enhancing photoelectric signal under strong noise background.

参考：

Reference:

Parameter-tuning stochastic resonance as a tool to enhance wavelength modulation spectroscopy using a dense overlapped spot pattern multi-pass cell, Optics Express 32010