近日，來自安徽大學、安慶師范大學、復旦大學、皖西學院的聯合研究團隊發表了《參數調諧隨機共振作為增強波長調制光譜學的工具，使用密集重疊斑點模式多程吸收池》論文。

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

激光吸收光譜技術已在許多應用中得到證明，如空氣質量監測、工業過程控制和醫學診斷。測量的精度對這些應用非常重要。盡管激光吸收光譜在敏感檢測方面具有許多優點，但仍需要很長的光學路徑長度和特殊的測量技術來檢測極微量的物質，以實現高檢測靈敏度。為了實現這些目的，通常采用具有長光學路徑的多程吸收池來增強吸收信號。然而，在吸收信號中經常出現意想不到的干擾光束、熱噪聲、射頻噪聲、電噪聲和白噪聲，嚴重影響了檢測的精度。當使用密集重疊斑點模式的多程吸收池時，這些問題在激光吸收光譜中很常見。因此，從強噪聲背景中有效提取弱光電吸收信號具有重要意義。

已提出了幾種方法來消除噪聲的負面影響。傳統的弱周期信號處理方法主要包括時間平均法、濾波法和相關分析法。

① 時間平均法可以獲得信噪比（SNR）較高的信號，因此可以降低噪聲的標準差并提高信號質量。然而，這種方法無法消除強噪聲背景。

② 基于硬件和軟件的信號濾波廣泛用于降噪，其特點是帶寬較窄。在實際應用中，期望的信號和噪聲通常具有連續的功率譜和寬帶寬，但制造與信號帶寬相匹配以去除噪聲的濾波器相對較困難。如果濾波器的帶寬非常小，噪聲將大幅衰減。然而，這可能會破壞期望的信號。

③ 相關檢測方法是通過周期信號的自相關來去除噪聲的。其本質是建立一個非常窄的帶寬濾波器，以濾除與信號頻率不同的噪聲。與上述其他弱周期信號檢測方法相比，參數調諧隨機共振（SR）方法的優勢顯而易見。即使噪聲和信號具有相同的頻率，只要它們達到最佳的共振匹配，SR方法就可以將部分噪聲能量轉化為信號能量，以抑制噪聲并增強信號。

在這項工作中，我們將SR方法應用于波長調制光譜學（WMS），并使用密集重疊斑點模式的多程吸收池。首先，將進行數值計算以找到合適的參數并評估最佳SR系統的性能，然后通過實驗驗證SR方法可以有效增強WMS信號。

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.

實驗裝置的示意圖如圖1所示。海爾欣光電科技有限公司為此研究提供了鎖相放大器（Healthy Photon，HPLIA），用于解調來自光電探測器的吸收信號，解調頻率為第二諧波信號2f的頻率（其中f = 6千赫茲是正弦波的調制頻率）。鎖相放大器的時間常數設置為1毫秒。解調后的信號隨后由一個數據采集卡數字化，并顯示在計算機上。

 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.

結論

參數調諧隨機共振（SR）方法可以將部分噪聲能量轉化為信號能量，以抑制噪聲并放大信號，與傳統的弱周期信號檢測方法（例如，時間平均法、濾波法和相關分析法）相比。本研究進行了數值計算，以找到將SR方法應用于波長調制光譜學（WMS）的最佳共振參數。在隨機共振狀態下，2f信號的峰值（CH4濃度恒定在約20 ppm）有效放大到約0.0863 V，比4000次時間平均信號的峰值（約0.0231 V）高3.8倍。盡管標準差也從約0.0015 V（1σ）增加到約0.003 V（1σ），但信噪比相應提高了1.83倍（從約25.9提高到約15.8）。獲得了SR 2f信號峰值與原始2f信號峰值的線性光譜響應。這表明在強噪聲背景下，SR方法對增強光電信號是有效的。

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.

參考：

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