Laser absorption spectroscopy data processing method based on co-frequency and dual-wavelength and its application

TANG Qi-xing; ZHANG Yu-jun; CHEN Dong; ZHANG Kai; HE Ying; YOU Kun; LIU Guo-hua; LU Yi-bing; FAN Bo-qiang; YU Dong-qi

doi:10.1364/OE.26.004459

1. Introduction

During the detection process of atmosphere in open space, the transmitted beam is inevitably affected by atmospheric turbulence, resulting in fluctuation noise superimposed in the received optical signal. Atmospheric turbulence mainly result in the laser's scintillation effect with the refractivity change of the atmospheric molecular cluster, which causes the intensity fluctuation, the phase fluctuation, the beam expansion, the beam drift and the image point jitter of the light beam, finally resulting in a linear variation of the gas absorption spectrum [1–5]. Therefore, it’s important to effectively reduce the influence of atmospheric turbulence on the laser absorption spectrometer [6–11] for the stability and accuracy of the measurement.

A method with increasing the receiving aperture is proposed in literature [12,13], using a sufficiently large receiver aperture to collect the total light intensity in most of the beams. The method of increasing the laser wavelength scanning frequency is adopted in literature [14] to overcome the influence of the low-frequency component [15] on the laser absorption spectrum signal. The researches above has focused on reducing the light intensity loss and shortening the scanning time to solve the affection of atmospheric turbulence, but there are not many researches on the two-wavelength differential absorption technique. Literature [16] and [17] are mainly devoted to the experimental research of two-wavelength differential absorption technology, while there is not much research on the algorithm to eliminate the effects of atmospheric turbulence on the detection of the atmosphere. Based on this, the correction method of atmospheric turbulence is theoretically analyzed at first. In order to reduce the error influence factors and the error transfer coefficient, the atmospheric turbulence noise in open space is reduced with the spectral data processing algorithm based on the co-frequency and dual-wave. And then an atmospheric detection system in open space based on the algorithm above is established to verify its validity and applicability.

2. Theoretical analysis of atmospheric turbulence modification

2.1 Two-wavelength differential absorption method

The two-wavelength differential absorption technique is based on the assumption that the atmosphere is solidified during a very short interval in the open space atmosphere detection process. That is, the statistical characteristics of the information carried in the received signal along the same atmospheric path and transmitted at the two beams of wavelengths λ₁ and λ₂ (one containing the absorption line and one not containing the absorption line) are highly correlated (Fig. 1), and the two received signals are processed differentially to reduce the affection of atmospheric noise [16,17].

Fig. 1 Schematic of two-wavelength differential absorption technique at λ₁ and λ₂.

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According to Beer-Lambert's law:

I_{1} (λ_{1}, t) = I_{01} (λ_{1}, t) \exp (- S^{*} Φ P c (λ_{1}, t) L) \exp (- σ_{1} (λ_{1}, t) L)

I_{2} (λ_{2}, t + Δ) = I_{02} (λ_{2}, t + Δ) \exp (- σ_{2} (λ_{2}, t + Δ) L)

where I₀₁(λ₁, t)and I₀₂(λ₂, t + Δ) denote the two beams incident light intensities, I₁(λ₁, t) and I₂(λ₂, t + Δ) denote the two beams transmitted light intensities, S* (cm⁻²atm⁻¹) is the absorption line intensity, Φ (cm) is the normalized linear function, P (atm) is the total gas pressure, c (%) is the component concentration of the absorbed gas, σ₁ and σ₂ represent scattering and absorption losses at two beams, L (cm) is the optical absorbing path length. Δ is the a very short interval, suppose σ₁(λ₁,t) = σ₂(λ₂,t + Δ). Then Eq. (1) changes to:

\frac{I_{1} (λ_{1}, t)}{I_{01} (λ_{1}, t)} = \exp (- S^{*} Φ P c (λ_{1}, t) L) \frac{I_{2} (λ_{2}, t + Δ)}{I_{02} (λ_{2}, t + Δ)}

c can be obtained from Eq. (3):

c (λ_{1}, t) = \frac{1}{S^{*} Φ P L} (\ln \frac{I_{2} (λ_{2}, t + Δ)}{I_{02} (λ_{2}, t + Δ)} - \ln \frac{I_{1} (λ_{1}, t)}{I_{01} (λ_{1}, t)})

The gas concentration measurement accuracy is expressed in the form of standard deviation

σ_{c (t)}

, the error transfer formula [18] is applied to the Eq. (4), and the result is expressed as:

\begin{array}{l} σ_{c (t)} = \sqrt{{(\frac{\partial_{c (t)}}{\partial_{I_{2} (λ_{2}, t + Δ)}})}^{2} σ_{I_{2} (λ_{2}, t + Δ)}^{2} + {(\frac{\partial_{c (t)}}{\partial_{I_{02} (λ_{2}, t + Δ)}})}^{2} σ_{I_{02} (λ_{2}, t + Δ)}^{2} + {(\frac{\partial_{c (t)}}{\partial_{I_{1} (λ_{1}, t)}})}^{2} σ_{I_{1} (λ_{1}, t)}^{2} + {(\frac{\partial_{c (t)}}{\partial_{I_{01} (λ_{1}, t)}})}^{2} σ_{I_{01} (λ_{1}, t)}^{2}} \\ = \sqrt{\begin{array}{l} {(\frac{1}{S^{*} Φ P L I_{2} (λ_{2}, t + Δ)})}^{2} σ_{I_{2} (λ_{2}, t + Δ)}^{2} + {(- \frac{1}{S^{*} Φ P L I_{02} (λ_{2}, t + Δ)})}^{2} σ_{I_{02} (λ_{2}, t + Δ)}^{2} \\ + {(- \frac{1}{S^{*} Φ P L I_{1} (λ_{1}, t)})}^{2} σ_{I_{1} (λ_{1}, t)}^{2} + {(\frac{1}{S^{*} Φ P L I_{01} (λ_{1}, t)})}^{2} σ_{I_{01} (λ_{1}, t)}^{2} \end{array}} \\ = \frac{1}{S^{*} Φ P L} \sqrt{\frac{σ_{I_{2} (λ_{2}, t + Δ)}^{2}}{{(I_{2} (λ_{2}, t + Δ))}^{2}} + \frac{σ_{I_{02} (λ_{2}, t + Δ)}^{2}}{{(I_{02} (λ_{2}, t + Δ))}^{2}} + \frac{σ_{I_{1} (λ_{1}, t)}^{2}}{{(I_{1} (λ_{1}, t))}^{2}} + \frac{σ_{I_{01} (λ_{1}, t)}^{2}}{{(I_{01} (λ_{1}, t))}^{2}}} \end{array}

where

σ_{I_{2} (λ_{2}, t + Δ)}

is the standard deviation of I₂(λ₂, t + Δ),

σ_{I_{02} (λ_{2}, t + Δ)}

is the standard deviation of I₀₂(λ₂, t + Δ),

σ_{I_{1} (λ_{1}, t)}

is the standard deviation of I₁(λ₁, t),

σ_{I_{01} (λ_{1}, t)}

is the standard deviation of I₀₁(λ₁, t),

\frac{\partial_{c (t)}}{\partial_{I_{2} (λ_{2}, t + Δ)}}

,

\frac{\partial_{c (t)}}{\partial_{I_{02} (λ_{2}, t + Δ)}}

,

\frac{\partial_{c (t)}}{\partial_{I_{1} (λ_{1}, t)}}

,

\frac{\partial_{c (t)}}{\partial_{I_{01} (λ_{1}, t)}}

is the gas concentration error transfer coefficient of

σ_{I_{2} (λ_{2}, t + Δ)}

,

σ_{I_{02} (λ_{2}, t + Δ)}

,

σ_{I_{1} (λ_{1}, t)}

,

σ_{I_{01} (λ_{1}, t)}

, respectively.

Aimed at the Eq. (5), the following discussion has been made.

The gas concentration measurement accuracy of the two-wavelength differential absorption technique are related to $σ_{I_{2} (λ_{2}, t + Δ)}^{2}$ , $σ_{I_{02} (λ_{2}, t + Δ)}^{2}$ , $σ_{I_{1} (λ_{1}, t)}^{2}$ and $σ_{I_{01} (λ_{1}, t)}^{2}$ and affected by the different error transfer coefficient such as I₂(λ₂, t + Δ), I₀₂(λ₂, t + Δ), I₁(λ₁, t) and I₀₁(λ₁, t).

2.2 Method of spectral data processing based on the co-frequency and dual-wave

In order to reduce the error influence factors and the error transfer coefficient, a method of spectral data processing based on the co-frequency and dual-wave is proposed. It’s assumed that the same laser is used to alternately operate one semiconductor laser in two scanning states. One scanning cycle passes through the absorption line of the gas to be measured and the other does not pass through the absorption line of the gas to be measured (Fig. 2). The atmospheric turbulence law in a single cycle is analyzed by using different scanning states.

Fig. 2 Schematic of co-frequency and dual-wave.

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Note: The center wavelength at λ₂ ∈ (λ_c, λ_d)not passes through the absorption line, and the beam is the same from the same laser. Then Eqs. (1) and (2) changes to:

In P - wave : I_{1} (λ_{1}, t) = I_{01} (λ_{1}, t) \exp (- S^{*} Φ P c (λ_{1}, t) L) \exp (- σ_{1} (λ_{1}, t) L)

In Q - wave : I_{1} (λ_{2}, t + Δ) = I_{01} (λ_{2}, t + Δ) \exp (- σ_{2} (λ_{2}, t + Δ) L)

Similarly:

\begin{array}{l} c (λ_{1}, t) = \frac{1}{S^{*} Φ P L} (\ln \frac{I_{1} (λ_{2}, t + Δ)}{I_{01} (λ_{2}, t + Δ)} - \ln \frac{I_{1} (λ_{1}, t)}{I_{01} (λ_{1}, t)}) \\ = \frac{1}{S^{*} Φ P L} \ln \frac{I_{1} (λ_{2}, t + Δ)}{I_{1} (λ_{1}, t)} \end{array}

Similarly, the gas concentration measuring accuracy is expressed in the form of standard deviation, the error transfer formula [18] is applied to the Eq. (8), and the result is expressed as:

\begin{array}{l} σ_{c (t)} = \sqrt{{(\frac{\partial_{c (t)}}{\partial_{I_{1} (λ_{2}, t + Δ)}})}^{2} σ_{I_{1} (λ_{2}, t + Δ)}^{2} + {(\frac{\partial_{c (t)}}{\partial_{I_{1} (λ_{1}, t)}})}^{2} σ_{I_{1} (λ_{1}, t)}^{2}} \\ = \sqrt{{(\frac{1}{S^{*} Φ P L I_{1} (λ_{2}, t + Δ)})}^{2} σ_{I_{1} (λ_{2}, t + Δ)}^{2} + {(- \frac{1}{S^{*} Φ P L I_{1} (λ_{1}, t)})}^{2} σ_{I_{1} (λ_{1}, t)}^{2}} \\ = \frac{1}{S^{*} Φ P L} \sqrt{\frac{σ_{I_{1} (λ_{2}, t + Δ)}^{2}}{{(I_{1} (λ_{2}, t + Δ))}^{2}} + \frac{σ_{I_{1} (λ_{1}, t)}^{2}}{{(I_{1} (λ_{1}, t))}^{2}}} \end{array}

Aimed at the Eq. (9), the following discussion has been made.

The concentration measuring accuracy of the proposed method is related to $σ_{I_{1} (λ_{2}, t + Δ)}^{2}$ and $σ_{I_{1} (λ_{1}, t)}^{2}$ and affected by error transfer coefficients such as I₁(λ₂, t + Δ) and I₁(λ₁, t). Compared with the two-wavelength differential absorption technique, the influence factors and error transfer coefficient of the gas concentration measuring error are reduced with the method of spectral data processing based on the co-frequency and dual-wave.

The flow chart of the comparison between the two methods is shown in Fig. 3.

Fig. 3 The flow chart of the comparison between the two methods.

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3. Method of spectral data processing based on the co-frequency and dual-wave

The absorption spectrum signals D_P(n) is for the detected optical path and R_P(n) is for the reference optical path in the P-wave scanning state, as well as the non-absorption spectrum signals D_Q(m) is for the detected optical path and R_Q(m) is for the reference optical path in the Q-wave scanning state, where m and n are the positions of the signal corresponding sequence.

3.1 Scintillation noise correction

The scintillation noise is corrected with piecewise fitting and the weighted average value of the superimposed region, as shown in Fig. 4. It is shown that the dots in the TQ1, TP1, and TQ2 segments respectively represent the difference between the reference signal and the detected signal at the same time. Polynomial fitting is performed on the data of TQ1 and TP1, and then the data of TP1 and TQ2. Then overlay appears in the TP1 segment fitting data, so the weighted average of the fitting value of the two TP1 segments is calculated as the final value.

Fig. 4 The diagram of the scintillation noise correction algorithm.

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The difference D(m) between signals D_Q(m) and R_Q(m), the difference between the first 30% D_P(n) and R_P(n) also with the difference between the last 10% D_P(n) and R_P(n) are fitted by the Eq. (10) to obtain the scintillation noise signals E(n) of D_P(n) and E(m) of D_Q(m).Then the residual standard deviation σ_x1 of the difference signal used for fitting is calculated.

{\begin{cases} E (k) = b_{0} + b_{1} k + b_{2} k^{2} + b_{3} k^{3} + b_{4} k^{4} \\ E (m) = E (k); 1 \leq k \leq \max (m) \\ E (n) = E (k) \\ \max (m) \leq k \leq \max (n) + \max (m); \\ a n d n = k - \max (m) \end{cases}

where b₀, b₁, b₂, b₃ and b₄ are the fitting coefficients, k is the position of the signal corresponding sequence and max(k) = max(n) + max(m).

Similarly, the difference between the first 30% D_P(n) and R_P(n), the difference between the last 10% D_P(n) and R_P(n) also with the difference between D_Q1(m) and R_Q1(m) for the next cycle are fitted by the Eq. (11) to obtain the scintillation noise signals E^’(n) of D_P(n) and E^’(m) of D_Q1(m) for the next cycle. Then the residual standard deviation σ_x2 of the difference signal used for fitting is calculated.

{\begin{cases} E^{'} (s) = {b^{'}}_{0} + {b^{'}}_{1} s + {b^{'}}_{2} s^{2} + {b^{'}}_{3} s^{3} + {b^{'}}_{4} s^{4} \\ E^{'} (n) = E (s); 1 \leq s \leq \max (n) \\ E^{'} (m) = E (s) \\ \max (n) \leq s \leq \max (n) + \max (m); \\ a n d m = s - \max (n) \end{cases}

where b^’₀, b^’₁, b^’₂, b^’₃ and b^’₄ are the fitting coefficients, s is the position of the signal corresponding sequence and max(s) = max(n) + max(m).

According to the method mentioned above, it is known that the scintillation noise signal of the absorption spectrum signal D_P(n) is the weighted average $\bar{E (n)}$ of E(n) and E^’(n).

{\begin{cases} σ_{\bar{x 1}} = \frac{σ_{x 1}}{\sqrt{n + m}} \\ σ_{\bar{x 2}} = \frac{σ_{x 2}}{\sqrt{n + m}} \\ p : p^{'} = \frac{1}{σ_{_{\bar{x 1}}}^{2}} : \frac{1}{σ_{_{\bar{x 2}}}^{2}} \\ \bar{E (n)} = \frac{E (n) + E^{'} (n)}{p + p^{'}} \end{cases}

The scintillation noise correction is performed on the signal D_P(n) and D_Q(m) to obtain a corrected absorption spectrum signal D^’_P(n) and a non-absorption spectrum signal D^’_Q(m):

{\begin{cases} {D^{'}}_{P} (n) = D_{P} (n) + \bar{E (n)} \\ {D^{'}}_{Q} (m) = D_{Q} (m) + E (m) \end{cases}

3.2 Background noise correction

Due to the influence of atmospheric turbulence, it is no longer viable that the traditional method of background fitting which relies on finding the unabsorbed spectral region data. However, based on this method, combined with the idea that Q-wave is not absorbed, the first m signals and latter 10%of D^’_P(n) are considered as unabsorbed spectral region data. Then polynomial fitting of the above signals gives a background noise signal B(n).

B (n) = a_{0} + a_{1} n + a_{2} n^{2}

where a₀, a₁ and a₂ are the fitting coefficients, n is the position of the signal corresponding sequence.

The background noise correction is performed on D^’_P(n) to obtain the spectral signal x(n):

x (n) = \frac{{D^{'}}_{P} (n)}{B (n)}

Then the laser wavelength shift correction [19,20] is performed on x(n) to obtain the corrected spectral signal x^’(n), and the average

\bar{x^{'} (n)}

of signals x^’(n) within N periods is obtained to eliminate the random noise. At last the spectral line fitting is performed to obtain the gas concentration.

4. Atmospheric detection system in open space based on co-frequency and dual-wave

The system structure is shown in Fig. 5, mainly including the laser and its control section, the optical structure and the data processing section. The laser and its control section consists of a tunable semiconductor laser, a laser control module and a signal generator. The optical structure consists of a reference optical path and a probing optical path. The data processing section is integrated with amplification filter, data acquisition, signal processing and display modules.

Fig. 5 System construction.

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The DFB laser with the center wavelength at 2333nm which is the near-infrared single absorption line of CO is used as detection light source. The laser control module (LDC3724B) is used to control the temperature and current to change the output wavelength of the laser. The co-frequency and dual-wave scanning signal is generated by the signal generator and put into the laser controller to make the laser alternately work in two scanning states. The single-mode beam output from the laser is divided half and half into the reference and probing optical path. The reference light reaches the InGaAs photodetector 1 through the standard reference 5% gas pool of 20 cm optical length. The beam of the detection light path is collimated by the collimator and emitted by a telescope. After going through telemetry the atmosphere, the beam is reflected by the cooperative target, and then focused on the InGaAs photodetector 2 with the receiving element. After the signals of the probing and reference light path have been rebalanced with the data processing section, the concentration of CO gas can be inversed.

5. Experimental verification and application

Experiments are carried out with the established atmospheric detection system in open space based on co-frequency and dual-wave (L = 700m). The sampling frequency is set to 170Hz and the acquisition card’s sampling rate is 200kHz. Spectral signals from the reference and probing optical path are collected at the same time before the spectral data processing.

First, the scintillation noise correction algorithm above is used for the reference and probing optical signal. It’s shown in Fig. 6(a) that the spectral signal before and after the correction. It can be seen that the fluctuation of the probing spectral signal after scintillation noise correction is obviously suppressed, and the scintillation noise is well eliminated. It is known in Fig. 6(b) that the scintillation fluctuations are great. Based on the reference spectral data at the same time, the maximum fluctuation of the spectral signal after the scintillation noise correction is reduced from 12.854% to 4.635%.

Fig. 6 The spectral signal before and after the scintillation noise correction. (a) The spectral signal before and after the correction. (b) The figure of the scintillation noise.

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Then, the background noise correction algorithm above is used for the background noise of the corrected probing spectral signal. It’s shown in Fig. 7(a) that the Voigt fitting for the single-intensity absorbance with the conventional method of a correlation coefficient 0.5306. It’s shown in Fig. 7(b) that the Voigt fitting for the single-intensity absorbance with the above algorithm of a correlation coefficient 0.9525.

Fig. 7 The background noise correction. (a) The existing method of single absorbance curve. (b) The algorithm of single absorbance curve.

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The data collected in 3 minutes with the experimental system has been processed respectively by using the method of spectral data processing based on the co-frequency and dual-wave also with the existing data processing method for 50 times averaging to invert the concentration, and then the standard deviation distribution chart is obtained as shown in Fig. 8. The mean value of the standard deviation of the existing algorithm is 0.6928, while the mean of the standard deviation of the algorithm mentioned above is 0.1370, and the its standard deviations are all above 0.3211, which proves its validity and the effects of reducing the atmospheric turbulence.

Fig. 8 The diagram of the standard deviation.

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In order to further verify the spectral data processing method based on co-frequency and dual-wave, it’s compared the existing data processing techniques of two-wavelength differential absorption by comparative experiments. System 1 is the experimental system for laser absorption spectrum in open space mentioned above. System 2 is based on the same structure, but another laser 2 is added, wavelength of which doesn’t cover the detection of absorption line. The signal generator of System 2 can generate a single sawtooth signal, the frequency of which is 170Hz unchanged, making laser CO and laser 2 alternately working in two states. The method of spectral data processing based on the co-frequency and dual-wave is adopted in system 1 while the existing method with two-wavelength differential absorption is adopted in system 2 both for 50 times averaging to invert the concentration. Then the concentration distribution chart is obtained as shown in Fig. 9. It can be seen that the standard deviation of the existing method is 0.2974, while the standard deviation of the method proposed is 0.1038, which proves that the proposed method can improve the measurement accuracy better than the existing method. In addition, the Allan analysis corresponding to the above concentration results is also carried out, and the results are shown in Fig. 10. It can be seen that the scintillation and background noise is less with the proposed method than the existing method.

Fig. 9 The diagram of the concentration distribution.

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Fig. 10 The diagram of allan deviation.

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Finally, in order to study the practical application of the proposed method, the atmospheric CO concentrations in open space have been continuously recorded for 70 hours with System 1, as shown in Fig. 11. It can be seen the peak concentration appears at about 22 hours, because the detection time is the rush hour on Friday and the rising concentration of vehicle emission leads to the peak. At the weekend, it can be seen that the concentration drops first and then a trend of stability. It is proved that there is good engineering practical value of the proposed method, such as detecting vehicle exhaust emissions, detecting environmental gas in hazard zone, detecting leakage of natural gas pipeline.

Fig. 11 The diagram of the measured concentration.

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6. Conclusions

The transmitted beam is inevitably affected by atmospheric turbulence, resulting in superimposed fluctuation noise in the received optical signal. Aimed at the problem, a new method for spectral data processing based on the co-frequency and dual-wave has been proposed. Then an atmospheric detection system in open space based on co-frequency and dual-wave has been established. It’s shown that the maximum fluctuation of the spectral signal processed by the proposed method is reduced from 12.854% to 4.635%, and the single-intensity absorbance is fitted by Voigt with its correlation coefficient of 0.9525. The mean of the standard deviation of the algorithm is 0.1370, while the mean value of the standard deviation of the existing algorithm in a short time is 0.6928. And through the comparative experiments, the standard deviation of the existing data processing techniques of two-wavelength differential absorption is 0.2974, while the standard deviation of the proposed method is 0.1038. It can be concluded that the proposed method can effectively reduce the effects of atmospheric turbulence noise and laser flashing to improve the stability of concentration measurement, and also has practical engineering value.

Funding

National Key R & D Program of China (2016YFC0201003); Anhui Provincial major projects of Science and Technology (15czz04124).

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Laser absorption spectroscopy data processing method based on co-frequency and dual-wavelength and its application

Abstract

1. Introduction

2. Theoretical analysis of atmospheric turbulence modification

2.1 Two-wavelength differential absorption method

2.2 Method of spectral data processing based on the co-frequency and dual-wave

3. Method of spectral data processing based on the co-frequency and dual-wave

3.1 Scintillation noise correction

3.2 Background noise correction

4. Atmospheric detection system in open space based on co-frequency and dual-wave

5. Experimental verification and application

6. Conclusions

Funding

References and links

Cited By

Figures (11)

Equations (15)

Optics Express