Atmospheric
Photonics Research, Volume. 4, Issue 2, 0074(2016)
Wavelet modulus maxima method for on-line wavelength location of pulsed lidar in CO2 differential absorption lidar detection
Differential absorption lidar (DIAL) is an excellent technology for atmospheric CO2 detection. However, the accuracy and stability of a transmitted on-line wavelength are strictly required in a DIAL system. The fluctuation of a tunable pulsed laser system is relatively more serious than that of other laser sources, and this condition leads to a large measurement error for the lidar signal. These concerns pose a significant challenge in on-line wavelength calibration. This study proposes an alternative method based on wavelet modulus maxima for the accurate on-line wavelength calibration of a pulsed laser. Because of the different propagation characteristics of the wavelet transform modulus maxima between signal and noise, the singularities of a signal can be obtained by detection of the local modulus maxima in the wavelet transform maximum at fine scales. Simulated analysis shows that the method is more accurate than the general method such as quintic polynomial fitting and can steadily maintain high calibration precision at different signal-to-noise ratios (SNRs). Last, 16 groups of real experiments were conducted to verify the simulated analysis, which shows that the proposed method is an alternative for accurately calibrating an on-line wavelength. In addition, the proposed method is able to suppress noises in the process of wavelength calibration, which gives it an advantage in accurate on-line wavelength calibration with a low SNR.Research Funds for the Central Universities (2042015kf0015).
1. INTRODUCTION
Atmospheric
To address these issues, several systems have been developed to explore atmospheric
Numerous groups have focused on the calibration of on-line wavelengths, and a series of on-line wavelength calibration systems that significantly improve the detection precision of DIAL have been designed [
Sign up for Photonics Research TOC Get the latest issue of Advanced Photonics delivered right to you!Sign up now
Dye laser, characterized by its mature mechanics and high stability to obtain infrared laser with a narrow linewidth, is a good choice for tunable laser sources of pulsed lidar to build global multipoint networks. With future development of laser technology, an optical parametric oscillator (OPO) with seed injection may be a better choice to obtain an infrared laser with a narrow linewidth. However, at present, a dye laser is a more feasible and reasonable scheme [
Figure 1.Fluctuation of the dye laser emission system at around 1.6 μm region.
In this study, a method for the accurate on-line wavelength calibration of a pulsed lidar is proposed. The method is based on wavelet modulus maxima and achieved by wavelet packet analysis. As an important parameter of wavelet transform, a wavelet modulus maxima plays a vital role in the detection of singular points [
The principle and laser emission system of DIAL is described in Section
2. METHODOLOGY
A. DIAL Principle
DIAL is an attractive means for detecting
Figure 2.Diagram of the ground-based DIAL.
The lidar equations of two wavelengths in the DIAL system can be written as [
Dividing Eq. (
Equation (
B. Emission System of DIAL
The simultaneous measurement system of the dual-wavelength laser is shown in Fig.
Figure 3.Simultaneous emission system of the dual-wavelength laser.
In the DIAL system, the high-precision frequency calibration of the on-line wavelength has a significant influence on inversion precision. The wavelet modulus maxima described in Section
3. WAVELET MODULUS MAXIMA
With the characteristics of multiresolution analysis, wavelet transform can represent a signal by localizing it in both time and frequency domains [
A. Lipchitz Index and Wavelet Modulus Maxima
Suppose
The process of singularity detection based on wavelet modulus maxima includes two main concepts. First is the Lipchitz index, which is used to measure the local regularity of function
Generally, the Lipchitz index of a function implies its singularity size. A function with a high
The second concept is modulus maxima. If Eq. (
The singularities of signal and noise have remarkable differences, which diversify the wavelet transform modulus maxima, thus making their wavelet transform modulus maxima completely different at different scales. The Lipchitz index of signal is greater than zero, and the modulus maxima increases with the decomposition scale. By contrast, the Lipchitz index of noise is less than zero, and the modulus maxima decreases with the decomposition scale.
B. Singularity Detection Through the Wavelet Modulus Maxima
The wavelet transform modulus maxima of various scales have different propagation characteristics between the signal and noise. Based on function singularity theory and the differences in the singularities between signal and noise, singularity detection can be performed through different propagation characteristics along the scale direction of the wavelet transform modulus maxima [
If
Notably,
4. SIMULATION ANALYSIS
A. On-Line Wavelength Calibration Through the Wavelet Modulus Maxima
The simulated signals obtained from the HITRAN 2012 database are used to prove that the method we proposed is useful in the calibration of on-line wavelength. Most spectroscopic parameters of
|
Figure 4.Calculated absorption cross sections of
According to the HITRAN 2012 molecular spectroscopic database, three absorption peaks exist in this range of the 30012/00001 carbon dioxide band: R14, R16, and R18 [
Figure 5.Calculated absorption cross sections of the
The process of on-line wavelength calibration with the simulated signals consists of two stages. The wavelength of the output pulsed laser was first stepped around the peak area by the monitor of a wave meter whose accuracy is less than
Figure
Figure 6.Simulated result of on-line wavelength calibration through the wavelet modulus maxima in R16.
A total of 100 simulated experiments were conducted to evaluate the accuracy of on-line wavelength calibration. The statistical result of the on-line wavelength calibration through the wavelet modulus maxima is shown in Table
|
The statistical result shows that around 99% of the calibration results can be better than 0.8 pm, and 93% can be better than 0.5 pm when the SNR is 20. This result indicates that the calibration of on-line wavelength through wavelet modulus maxima is accurate and stable.
B. Comparison Between the Two Methods of On-Line Wavelength Calibration
The calibration of on-line wavelength by general method was compared with that by the wavelet modulus maxima with the same simulated signals and SNR to evaluate the effect of on-line wavelength calibration using wavelet modulus maxima.
The general method for on-line wavelength calibration of a pulsed laser is mainly via quintic polynomial fitting [
Figure 7.Simulated result of on-line wavelength calibration through quintic polynomial fitting in R16.
|
Both the accuracy and stability of on-line wavelength calibration with the quintic polynomial fitting are worse than those with the wavelet modulus maxima. Approximately 42% of the calibration results cannot attain 0.5 pm when the SNR is 20. To obtain an intuitive comparison result, the statistical results of the 100 simulated experiments on on-line wavelength calibration with the two methods are drawn into a scatter plot, which is shown in Fig.
Figure 8.Calibration result of the wavelet modulus maxima and polynomial fitting method with an SNR of 20.
A total of 100 simulated experiments on on-line wavelength calibration with different SNRs were performed through two methods to assess the applicability of the proposed method at different noise levels. The results are shown in Figs.
Figure 9.Calibration result of the wavelet modulus maxima and polynomial fitting method with an SNR of 80.
Figure 10.Calibration result of the wavelet modulus maxima and polynomial fitting method with an SNR of 50.
Figure 11.Calibration result of the wavelet modulus maxima and polynomial fitting method with an SNR of 30.
Figure 12.Calibration result of the wavelet modulus maxima and polynomial fitting method with an SNR of 10.
Figure 13.Calibration result of the wavelet modulus maxima and polynomial fitting method with an SNR of 5.
Figure 14.Calibration result of the wavelet modulus maxima and polynomial fitting method with an SNR of 1.
The statistical results of the simulated signals with different SNRs for on-line wavelength calibration conducted through the quintic polynomial fitting and the wavelet modulus maxima method are shown in Table
|
The conclusion that can be drawn from the statistical calibration results of the simulated signals is as follows: accuracy and stability of on-line calibration through the quintic polynomial fitting method worsens with the decrease in SNR; this method cannot even be used when the SNR is less than 5. By contrast, although the wavelet modulus maxima method is subject to the effect of low SNR, it has strong noise immunity and consistently good accuracy and stability for on-line wavelength in the case of any SNR. When the SNR of signal is 1, about 91 out of 100 calibrated results through the wavelet modulus maxima method are better than 0.8 pm. However, only 48 out of 100 calibrated results through the quintic polynomial fitting method are better than 0.8 pm. In summary, the wavelet modulus-based method proposed in this study has a better effect in on-line calibration than general methods, both in terms of accuracy and stability, and it has distinct advantage especially in the calibration of signals with low SNRs.
Furthermore, as shown in Figs.
5. EXPERIMENTS WITH REAL MEASURED SIGNALS
On the basis of the simulated signal analysis, the proposed method is tested by examination of real measurement data acquired by a 16 m gas absorption cell in our wavelength control unit. The result shows that the method is effective in calibrating the on-line wavelength of our DIAL system.
The system configuration of the wavelength control unit is shown in Fig.
Figure 15.Wavelength control unit of the ground-based DIAL.
The absorption line of
Figure 16.Result of on-line wavelength calibration with real measured signals through the wavelet modulus maxima at the R16 region.
Sixteen groups of on-line wavelength calibration experiments are performed at the R16 and R18 regions with the use of a gas cell with a step size of 3 pm. The spanned wavelength range is set from 1571.93 to 1572.72 nm to obtain two absorption peaks in the scanning experiments. Sampling 260 wavelengths in the span range for each group takes 260 s. The result of the on-line wavelength calibration of the real measured experiments was analyzed; these experiments focused on the R16 and R18 regions and applied the wavelet modulus maxima method. The distance between the two absorption peaks in the 16 experiments is shown in Table
|
The difference between the results obtained through the proposed method and the theoretical one is approximately 2.12 pm. Compared with the calibrated accuracy of the simulated signals, that of the real measured signals is worse, which is caused by the fluctuation of the pulsed laser. The wavelength of the same absorption peak will be different each time because the wavelength of the pulsed laser is always fluctuating, which is the main reason for a difficult pulse laser wavelength calibration; the evaluation error will also considerably increase as the two peaks are synchronously calibrated. The calibration effect will improve if a single absorption peak is calibrated.
In addition, the method proposed in this paper is used for the calibration of the on-line wavelength. As for the wavelength locking, we have proposed an independent criterion for wavelength drift, named the regular accuracy check, with detailed introduction in [
6. CONCLUSIONS
An alternative method based on wavelet modulus maxima is proposed in this study for the accurate on-line wavelength calibration of a pulsed laser, which is helpful to obtain accurate vertical profiles of atmospheric
The statistical results of 100 simulated experiments with an SNR of 20 show that the average of the absolute values and the standard deviation with the wavelet modulus maxima method are 1572.3365 and
One issue about the method proposed is that the parameter setting of fine calibration based on the wavelet modulus maxima varies with the change of signal sources to obtain an accurate result. Both the smooth function and the decomposition scale of the wavelet can be further studied to improve the precision and practicability in the on-line wavelength calibration in the future.
ACKNOWLEDGMENT
Acknowledgment. This research is supported by the National Natural Science Foundation of China (41127901), the Program for Innovative Research Team in University of Ministry of Education of China (IRT1278), the National Science Foundation of Hubei province (2015CFA002), the China Postdoctoral Science Foundation (2015M570667), and the Fundamental Research Funds for the Central Universities (2042015kf0015).
[1] Climate Change. The physical science basis. Working Group I Contribution to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change(2013).
[3] R. Pachauri, Core Writing, A. Reisinger. Climate change 2007: synthesis report. Contribution of Working Groups I, II and III to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change(2007).
[4] M. O. Andreae, C. D. Jones, P. M. Cox. Strong present-day aerosol cooling implies a hot future. Nature, 435, 1187-1190(2005).
[7] C. E. Miller, D. Crisp, P. L. DeCola, S. C. Olsen, J. T. Randerson, A. M. Michalak, A. Alkhaled, P. Rayner, D. J. Jacob, P. Suntharalingam, D. B. A. Jones, A. S. Denning, M. E. Nicholls, S. C. Doney, S. Pawson, H. Boesch, B. J. Connor, I. Y. Fung, D. O’Brien, R. J. Salawitch, S. P. Sander, B. Sen, P. Tans, G. C. Toon, P. O. Wennberg, S. C. Wofsy, Y. L. Yung, R. M. Law. Precision requirements for space-based XCO2 data. J. Geophys. Res., 112, D10314(2007).
[8] F. Chevallier, S. Maksyutov, P. Bousquet, F. M. Bréon, R. Saito, Y. Yoshida, T. Yokota. On the accuracy of the CO2 surface fluxes to be estimated from the GOSAT observations. Geophys. Res. Lett., 36, L19807(2009).
[12] L. Fiorani, W. Saleh, M. Burton, A. Puiu, M. Queißer. Spectroscopic considerations on DIAL measurement of carbon dioxide in volcanic emissions. J. Optoelectron. Adv. Mater., 15, 317-325(2013).
[13] U. N. Singh, J. Yu, M. Petros, T. Refaat, K. Reithmaier. Development of a pulsed 2-micron integrated path differential absorption lidar for CO2 measurement. Proc. SPIE, 8872, 887209(2013).
[16] S. Kameyama, M. Imaki, Y. Hirano, S. Ueno, S. Kawakami, M. Nakajima. Development of 1.6 micron CW modulation ground-based DIAL system for CO2 monitoring. Proc. SPIE, 7153, 71530L(2008).
[17] L. Fiorani, S. Santoro, S. Parracino, G. Maio, M. Del Franco, A. Aiuppa. Lidar detection of carbon dioxide in volcanic plumes. Proc. SPIE, 9535, 95350N(2015).
[20] F. P. Schäfer. Dye Lasers(2013).
[22] X. Chengzhi, G. Wei, M. Xin, C. Xuewu. A method to eliminate the backlash error of tunable laser. Acta Opt. Sin., 34, 161-169(2014).
[25] A. Behrendt, V. Wulfmeyer, A. Riede, G. Wagner, S. Pal, H. Bauer, M. Radlach, F. Späth. Three-dimensional observations of atmospheric humidity with a scanning differential absorption lidar. Proc. SPIE, 7475, 74750L(2009).
[33] C. K. Chui. An Introduction to Wavelets(2014).
[36] Z. Peng, Y. He, Z. Chen, F. Chu. Identification of the shaft orbit for rotating machines using wavelet modulus maxima. Mech. Syst. Signal Process., 16, 623-635(2002).
[39] S. Mallat, A. Wavelet. Tour of Signal Processing(1999).
Get Citation
Copy Citation Text
Wei Gong, Chengzhi Xiang, Feiyue Mao, Xin Ma, Ailin Liang, "Wavelet modulus maxima method for on-line wavelength location of pulsed lidar in CO2 differential absorption lidar detection," Photonics Res. 4, 0074 (2016)
Received: Oct. 20, 2015
Accepted: Dec. 31, 2015
Published Online: Sep. 28, 2016
The Author Email: Chengzhi Xiang (cxiang@whu.edu.cn)