Research on the spectral phase correction method for the atmospheric detection in open space

Qi-Xing Tang; Yu-Jun Zhang; Dong Chen; Kai Zhang; Ying He; Kun You; Guo-hua Liu; Yi-Bing Lu; Bo-Qiang Fan; Dong-Qi Yu

doi:10.1364/OE.26.019328

1. Introduction

The measuring method of the laser absorption spectrum only use the change of the light intensity, especially the high sensitivity method with the second harmonic detection technology for the wavelength modulation, which has high accuracy for the gas concentration inversion in theory. However, during the atmospheric detection process in open space, the transmitted beam [1–8] will be affected by atmospheric turbulence [9–13], which causes the distortion of the laser wavefront and finally results in a linear variation of the gas absorption spectrum [14–18]. Therefore, it is important to study the spectral data correction method.

In the previous study, aiming at the direct absorption method, a spectral data processing method based on co-frequency and dual-wave has been proposed with the theoretical analysis on the error transfer law of the system measurement model. However, there has not been any analysis on the method of wavelength modulation to reduce the turbulence influence. So the further study on the spectral phase correction method for the open space atmospheric detection is demanded.

A method of the light intensity elimination is proposed in literature [19, 20]. The traditional I_2f/I_1f method and light intensity elimination method in wavelength modulation has been analyzed and discussed. The 2f signal is divided by the fitting mean intensity signal to compensate for the intensity change influence on the detection results caused by the turbulence. The research mentioned above has focused on reducing incident light intensities to solve the affection of the atmospheric turbulence, but there has been not any research on the phase correction technique. On the basis of the previous research, the error analysis of the measuring model has been carried out. The atmospheric turbulence noise in open space is reduced with the spectral phase correction method. And then an atmospheric detection system for phase correction in open space based on co-frequency and dual-wave has been established to verify its validity and applicability.

2. Classical light intensity elimination method

Due to the interference form the channel and system noise, the random fluctuation of the transmitted light intensities signal is received by the detector during the atmospheric detection process in open space, which affects the detection accuracy of the harmonic signal. The channel noise interference mainly refers to that of the atmospheric turbulence on the transmission laser beam.

According to Beer-Lambert's law, it can be represented by a sine fourier series:

I (v) = I_{0} (v) \exp (- S^{*} Φ (v) P c L) = \sum_{n = 0}^{n = + \infty} A_{n} (v) \sin (n 2 π f t),

where I₀ is the beam incident light intensities, I is the beam transmitted light intensities, S* (cm⁻²atm⁻¹) is the absorption line intensity, Φ(υ) is the normalized linear function, P (atm) is the total gas pressure, c (%) is the component concentration of the absorbed gas, and L (cm) is the optical absorbing path length. The instantaneous frequency is:

v = v_{c} + a \cos (2 π f t) .

Where υ_c is the center frequency of the laser, a is the modulation amplitude, and f is the modulation frequency.

During the atmospheric detection process in open space, Δt is a very short interval, and ψ [21–24] is the corresponding phase fluctuation. Then:

\begin{array}{l} I (v) = \sum_{n = 0}^{n = + \infty} A_{n} (v) \sin (n (2 π f (t + Δ t))) = \sum_{n = 0}^{n = + \infty} A_{n} (v) \sin (n (2 π f t + 2 π f Δ t)) \\ = \sum_{n = 0}^{n = + \infty} A_{n} (v) \sin (n (2 π f t + Ψ)) \end{array}

I_{2 f} = A_{2} (v) \sin (2 (2 π f t + Ψ)) .

With the light intensity elimination method [19], the 2f signal is divided by the fitting mean intensity signal to compensate for the intensity change influence on the detection results caused by the turbulence.

{\begin{cases} I_{f} = \frac{I_{2 f}}{\bar{I_{0}}} = \frac{A_{2} (v) \sin (2 (2 π f t + Ψ))}{\bar{I_{0}}} \\ = A \sin (2 (2 π f t + Ψ)) \\ A = \frac{A_{2} (v)}{\bar{I_{0}}} \end{cases},

where

\bar{I_{0}}

is the fitted mean intensity signal.

The standard deviation $σ_{I_{f}}$ can be expressed as:

σ_{I_{f}} = \sqrt{{(\frac{\partial_{I_{f}}}{\partial_{A}})}^{2} σ_{A}^{2} + {(\frac{\partial_{I_{f}}}{\partial_{Ψ}})}^{2} σ_{Ψ}^{2}} .

Aimed at the Eq. (6), the following discussion has been made.

(1) The measuring accuracy of the light intensity elimination method is related to $σ_{A}^{2}$ , which is the intensity fluctuation.
(2) The measuring accuracy of the light intensity elimination method is related to $σ_{Ψ}^{2}$ , which is the phase fluctuation.

3. Spectral phase correction method for the atmospheric detection in open space

During the atmospheric detection process in open space, the excessive phase noise is introduced into the signal due to the atmospheric turbulence. The error analysis of the light intensity elimination method has been carried out, which shows this method is also affected by $σ_{A}^{2}$ and $σ_{Ψ}^{2}$ . Therefore, in order to improve the stability during the transmission, the spectral phase correction method for the atmospheric detection in open space is proposed based on the previous study. According to the paper [25], the dual-waves has been superimposed with the modulation signal, as shown in Fig. 1, between which there are following relations. One scanning cycle (P-wave) passes through the absorption line of the gas to be measured and the other (Q-wave) does not pass through the same absorption, meanwhile the center wavelength at λ₂ ∈ (λ_c, λ_d)does not pass through the absorption line.

Fig. 1 The dual-waves superimposed with the modulation signal. One scanning cycle (P-wave) passes through the absorption line of the gas to be measured and the other (Q-wave) does not pass through the same absorption,

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The instantaneous harmonics intensity of P-wave and Q-wave is known from Eq. (3). And the same phase noise is generated in P-wave compared with Q-wave by superimposing a modulating signal m times father than that in Q-wave (m ≥2) based on the assumption that the atmosphere is solidified during a very short interval during the atmospheric detection process.

P - w a v e {\begin{cases} I_{1 f} (v_{1}) = A_{1} (v_{1}) \sin (2 π f t + m Ψ) \\ I_{2 f} (v_{1}) = A_{2} (v_{1}) \sin (2 π 2 f t + 2 m Ψ) \\ I_{3 f} (v_{1}) = A_{3} (v_{1}) \sin (2 π 3 f t + 3 m Ψ) \end{cases}

Q - w a v e {\begin{cases} {I^{'}}_{1 f} (v_{2}) = A_{1}^{'} (v_{2}) \sin (2 π f t + Ψ) \\ {I^{'}}_{2 f} (v_{2}) = A_{2}^{'} (v_{2}) \sin (2 π 2 f t + 2 Ψ) \\ {I^{'}}_{3 f} (v_{2}) = A_{3}^{'} (v_{2}) \sin (2 π 3 f t + 3 Ψ) \end{cases}

The second harmonic signal is proportional to the gas concentration [26–31], so that of P-wave is taken. In order to eliminate the phase fluctuation caused by the atmospheric turbulence, the harmonic signals, which have the same phase fluctuation of the dual-waves (P-wave and Q-wave) based on the assumption that the atmosphere is solidified during a very short interval during the atmospheric detection process, should be taken. It is also known that m≥2, so the maximum of Q-wave is the fourth harmonic signal. To solve this problem, I_f(υ₁) is obtained by Eq. (9), and the m-partial harmonic signal of Q-wave is taken at that time. I_f’(υ’) can be obtained by Eq. (10).

I_{f} (v_{1}) = \frac{I_{2 f} (v_{1})}{I_{1 f} (v_{1})} = \frac{A_{2} (v_{1})}{A_{1} (v_{1})} \cos (2 π f t + m Ψ)

\begin{array}{l} I_{f}^{'} (v^{'}) = I_{f} (v_{1}) I_{m f}^{'} (v_{2}) \\ = \frac{A_{2} (v_{1})}{A_{1} (v_{1})} \cos (2 π f t + m Ψ) A_{m}^{'} (v_{2}) \sin (2 π m f t + m Ψ) \\ = \frac{A_{2} (v_{1}) A_{m}^{'} (v_{2})}{2 A_{1} (v_{1})} [\sin (2 π t (1 + m) f + 2 m Ψ) \\ + \sin (2 π t (m - 1) f)] . \end{array}

In order to obtain the highly sensitive I_f’(υ’) signal, when m = 2, |I_f’(υ’)| obtains the maximum value.

| I_{f}^{'} (v^{'}) | ⩽ \frac{| A_{2} (v_{1}) | | A_{m}^{'} (v_{2}) |}{2 | A_{1} (v_{1}) |} ⩽ \frac{| A_{2} (v_{1}) | | A_{2}^{'} (v_{2}) |}{2 | A_{1} (v_{1}) |} .

Because the scan lengths of P-wave and Q-wave are different, the data lengths of P-wave and Q-wave are different. According to the length of P-wave, the I_2f’(υ₂) signal of Q-wave is fitted by Eq. (12) to obtain a signal with the same length as P-wave. Then the I_2f’(υ₂) signal is calculated by Eq. (13).

{I^{'}}_{2 f} (v_{2}_{n}) = a_{0} + a_{1} f (v_{2}_{n}) + a_{2} f (v_{2} {_{n}}^{2}) + a_{3} f (v_{2} {_{n}}^{3}) + a_{4} f (v_{2} {_{n}}^{4}),

where a₀, a₁, a₂, a₃ and a₄ are fitting coefficients, n is the position of the signal corresponding sequence, f(x) is the modulation function.

{\begin{cases} I_{f}^{'} (v^{'}) = \frac{A_{2} (v_{1}) A_{2}^{'} (v_{2})}{2 A_{1} (v_{1})} [\sin (2 π t (3 f) + 4 Ψ) + \sin (2 π t f)] \\ = A^{'} [\sin (2 π t (3 f) + 4 Ψ) + \sin (2 π t f)] \\ A^{'} = \frac{A_{2} (v_{1}) A_{2}^{'} (v_{2})}{2 A_{1} (v_{1})} \end{cases}

From Eq. (13), it can be seen that the phase fluctuation caused by the atmospheric turbulence is completely eliminated at the first harmonic of the signal I_f’(υ’).

At the first harmonic, the standard deviation $σ_{I_{f}}$ can be expressed as:

σ_{{I^{'}}_{f} (v^{'})} = \sqrt{{(\frac{\partial_{{I^{'}}_{f} (v^{'})}}{\partial_{A^{'}}})}^{2} σ_{A^{'}}^{2}} .

Aimed at the Eq. (14), it can be known that:

The measuring accuracy of the spectral phase correction method for the atmospheric detection is related to $σ_{A^{'}}^{2}$ , so the method can eliminate the phase fluctuation caused by the atmospheric turbulence.

4. The atmospheric detection system for the phase correction in open space based on co-frequency and dual-wave

The system structure is shown in Fig. 2, which mainly includes the laser and its control section, the optical element part and the data processing section. The laser and its control section consist of a tunable semiconductor laser, a laser control module and a signal generator. The optical element part consists of a reference optical path and a detecting optical path. The data processing section is integrated with the data acquisition, signal processing and display modules.

Fig. 2 System construction. Scanning signal: the co-frequency and dual-wave, Reference cell: 20 cm.

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The detection light source uses a DFB laser with the center wavelength at 1653nm which is the near-infrared single absorption line of CH4. And the light from the laser is coupled into a single-mode fiber. The laser control module can control the temperature and current to change the output wavelength of the laser, and adjust the center wavelength of the laser to the absorption line of CH₄ at 1653.7 nm. The co-frequency and dual-wave scanning signal and a sine wave modulation signal are generated by the signal generator and superimposed on the laser controller to make the laser alternately work in two scanning states. The single-mode beam output from the laser is divided half to half into the reference and detecting optical path. The reference light can be collimated by the collimator and reach the InGaAs photodetector 1 through the standard reference 5% gas pool of 20cm optical length. The beam of the detecting optical path can be collimated by the collimator and emit through a telescope. After going through the atmosphere telemetry, the beam is reflected by the target mirror. The Fresnel lens, placed in the front section of the telescope, is used to receive the reflected light beam. And then the beam is focused on the InGaAs photodetector 2 with the Fresnel lens. After the signals of the detecting and reference light path have passed through the data acquisition module, the collected data is sent to the signal processing unit.

The flow chart of the signal processing unit is shown in Fig. 3. The first and second harmonic signal of P-wave and Q-wave for the reference and detecting optical path are respectively extracted with digital lock-in, so the I_f(υ₁) signals of the reference and detecting optical path can be obtained respectively. Then, fitting their corresponding Q-wave to obtain complete two harmonic signal, the I_f(υ₁) signal of the reference and detecting path and the obtained complete two harmonic signal are substituted into the Eq. (10) to calculate I_f’(υ’). After the digital filtering, a standard spectral signal is obtained for the reference optical path, and the spectral signal to be measured is obtained for the detection optical path. The detection optical path signal is fitted with the reference optical path signal, and then the final CH₄ concentration can be inverted.

Fig. 3 Flow chart of signal processing unit. a standard spectral signal is obtained for the reference optical path, and the spectral signal to be measured is obtained for the detection optical path.

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5. Experimental verification and application

In order to verify the feasibility and versatility of the proposed phase correction method, experiments are carried out with the established atmospheric detection system for the phase correction in open space based on co-frequency and dual-wave. The sampling frequency is set to 100Hz, the modulation frequency is 50kHz, the values of modulation depth of the laser is 2.2, the sampling rate of the acquisition card is 200kHz, and the length of the detecting optical path is 700m.

5.1 Calibrate analog experiment with the optical path length to 20m

In the experiment, a 20m multi-reflection cell is placed on the detecting optical path to measure the fixed CH₄ concentration 30ppm. So the optical path length is 20m. In order to verify the accuracy of the proposed phase correction method, the fixed concentration is measured for 1h without the atmospheric turbulence at first. In the measuring process, after the gas is injected into the partition, the inlet and outlet of the gas multi-reflection cell are closed. Therefore, it can be considered that the concentration does not change during the measurement. It is shown in Fig. 4 that the standard deviation is 0.018, which shows its accuracy.

Fig. 4 Successive measurements in the absence of atmospheric turbulence. A 20m multi-reflection cell is placed on the detecting optical path to measure the fixed CH4 concentration 30ppm. At this time, the optical path length is 20m.

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Then, the influence of turbulence is simulated using a rotatable thin phase screen plate, with a pseudo-random phase distribution obeying Kolmogorov spectrum statistics, and keep the CH₄ 30ppm unchanged. After the data acquisition module, the second harmonic absorption spectrum signal of P-wave for the detecting optical path is directly obtained with the digital lock-in, as shown in Fig. 5. Although the gas concentration is constant in the multi-reflection cell, it can be seen that the signal is fluctuating due to atmospheric turbulence. The signal is respectively processed with the proposed phase correction method and the traditional concentration inversion method with the 2f-wavelength modulation for 50 times averaging to invert the concentration. It’s shown in Fig. 6 that the standard deviation of the traditional concentration inversion method with the 2f-wavelength modulation is 0.2038, while that of the proposed phase correction method is 0.0476, which can prove its validity and the effects of reducing the atmospheric turbulence.

Fig. 5 Two harmonic absorption spectrum signal of P-wave. The influence of turbulence is simulated by a rotatable thin phase screen plate, with a pseudo-random phase distribution obeying Kolmogorov spectrum statistics, and kept the CH4 30ppm unchanged.

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Fig. 6 The diagram of the concentration. The black line is the concentration before correction, the red line is the concentration after correction.

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5.2 Three methods actual comparison experiment with detecting optical path length to 700 m

In order to further verify the proposed spectral phase correction method, it is compared with the traditional concentration inversion method using the 2f-wavelength modulation and the classical light intensity elimination method. Using the established atmospheric detection system for the phase correction in open space based on co-frequency and dual-wave, the spectral signal is analyzed in three methods.

Method one: the standard spectral signal of the reference optical path and that of the detecting optical path I_f’(υ’) are obtained by the signal processing unit.

Method two: After the data acquisition module, the second harmonic absorption spectral signals of P-wave for the reference and detecting optical path are obtained with digital lock-in to invert the concentration directly.

Method three: The signals based on co-frequency and dual-wave are recorded simultaneously, and then the corresponding P-wave light intensity of the detecting optical path are fitted. The standard spectral signal is shown in Fig. 7(a), which provides the basis for the central wavelength alignment and inversion concentration to be measured with the spectral signal. It is shown in Fig. 7(b) that the second harmonic absorption spectral signal of P-wave for the detecting optical path.

Fig. 7 (a) Standard spectrum, which provides the basis for the central wavelength alignment and inversion concentration to be measured with the spectral signal; (b) Two harmonic absorption spectral signal of P-wave in the open path.

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Method one is the proposed phase correction method. Method two is the traditional concentration inversion method with the 2f-wavelength modulation [20,26,28,30,31]. Method three is the classical light intensity elimination method for the single-measuring concentration inversion [19]. It is shown in Fig. 8 that the spectral signal fluctuation by Method one is obviously suppressed. Taking the average concentration signal at the same time as the benchmark, the maximum fluctuation by Method one is 1.06%, the maximum fluctuation by Method two is 12.4%, and the maximum fluctuation by Method three is 4%. It can be seen that the proposed phase correction method can effectively improve the quality of the spectral signal and reduce the noise fluctuation of the atmospheric turbulence.

Fig. 8 The concentrations of three methods. Method one is the proposed phase correction method, Method two is traditional concentration inversion method with the 2f-wavelength modulation, Method three is classical light intensity elimination method.

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From Eq. (14), it can be seen the proposed correction method can suppress the phase fluctuation caused by the atmospheric turbulence. Therefore, it can be concluded that compared with Methods two and three, the quality of the frequency transmission should be significantly improved. The data collected in 3 minutes has been respectively processed by using three methods for 50 times averaging to invert the concentration, and then the power spectral density distribution of the concentration [see inset in Fig. 9] is obtained, as shown in Fig. 9. When the frequency is above 50Hz, the power spectral density of concentration fluctuation with Method one is significantly reduced, while that with Method two and three is still relatively high above 50Hz, especially within the range of 50Hz-150Hz, which indicates that the proposed phase correction method can reduce the short-time fluctuation to 50Hz.

Fig. 9 Power spectral density results for the concentration. Inset: showing the measured concentration. The inset is the concentration collected in 3 minutes

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Then in order to evaluate the effect of phase correction method on system stability better, the Allan analysis results corresponding to the concentration obtained above are given, as shown in Fig. 10. It can be seen that the Allan analysis result by Method one is 8.8 × 10⁻⁸ (1s), Method two is 1 × 10⁻⁴ (1s), and the method three is 7.4 × 10⁻⁶ (1s) and Allan analysis result by method one is 1.8 x 10⁻⁷, method two is 5 × 10⁻⁷, method three is 2.7 × 10⁻⁶ for 10s. Compared with Method two and three, the phase correction method can effectively reduce the random noise fluctuation caused by the short-term atmospheric turbulence. However, from the result for 10s, the improvement is limited, because there are still some other error factors.

Fig. 10 The diagram of Allan deviation. The results are corresponding to the concentration obtained above (see inset in Fig. 9).

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Finally, in order to research the practical application for the proposed method, the atmospheric CH₄ concentration in open space has been recorded continuously for 24 hours with the established detection system. The concentration from 7 o'clock in the morning to 7 of the next morning is shown in Fig. 11. The CH₄ concentration is relatively low during the daytime, showing a growing trend at night and tending to balance at midnight. This is mainly due to the intense photochemical reaction of plants during the day and the strong tropospheric transmission. Diffusion of CH₄ to high altitude results in a relatively low concentration during the day, while the photochemical reactions do not occur at night. The phenomenon of inversion at night leads to CH₄ accumulation in the surface atmosphere. There is a rise in concentration during the day between 11:00 and 13:00. This is mainly due to vehicle emission during peak rush hours, which leads to the increase of the atmospheric CH₄ concentration. So a local peak appears at this time, and then it gradually decreases and tends to be stable. After 17:00, the concentration increases again, because of the common result of peak rush hours and nighttime plant effects. It is proved that the proposed method has practical engineering value.

Fig. 11 The diagram of the measured concentration. It has been recorded for 24 hours with the established detection system, from 7 o'clock in the morning to 7 o'clock the next morning.

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6. Conclusions

Atmospheric detection accuracy is affected by the atmospheric turbulence in open space. In the previous study, a method of spectral data processing based on co-frequency and dual-wave has been used to reduce the scintillation noise influence of the atmospheric turbulence in open space. In this paper, it is focused on the issue of the phase correction. On the basis of the previous research, the wavelength modulated signal is theoretically analyzed. In order to reduce the phase fluctuations caused by the atmospheric turbulence, a new method of the spectral phase correction for the atmospheric detection in open space has been proposed. Then an atmospheric detection system with the method has been established. It is shown that the maximum fluctuation of the spectral signal processed with the proposed method is 1.06%, the power spectral density fluctuation is suppressed below 50Hz, and the Allan analysis result is 8.8 × 10⁻⁸(1s). Compared with the traditional concentration inversion method with the 2f-wavelength modulation and the classical light intensity elimination method, it can be concluded that the proposed method can effectively reduce the noise fluctuation of the atmospheric turbulence and laser flashing and improve the stability of the concentration measurement, which has practical engineering value.

Funding

National Key R&D Program of China (2016YFC0201000); Anhui Natural Science Foundation Project (1808085MD107); Anhui Provincial major projects of Science and Technology (15czz04124); Science and Technology Service Network Initiative (KFJ-STS-ZDTP-002).

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Research on the spectral phase correction method for the atmospheric detection in open space

Abstract

1. Introduction

2. Classical light intensity elimination method

3. Spectral phase correction method for the atmospheric detection in open space

4. The atmospheric detection system for the phase correction in open space based on co-frequency and dual-wave

5. Experimental verification and application

5.1 Calibrate analog experiment with the optical path length to 20m

5.2 Three methods actual comparison experiment with detecting optical path length to 700 m

6. Conclusions

Funding

References

Cited By

Figures (11)

Equations (14)

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