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Fourier and wavelet transform analysis of wavelength modulation spectroscopy signal

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Abstract

In the present paper, the performances of an approach based on continuous wavelet transform to demodulate wavelength modulation spectroscopy harmonic signal (CWT-WMS) have been compared to the conventional approach using digital lock-in amplifier (DLI-WMS) based on classic Fourier transform analysis. For both methods, consistent results were obtained and good agreement between the experimental and simulated results was observed. The CWT method does not require the use of a reference signal and the phase-insensitive harmonic signals are directly obtained. The CWT method also demonstrates higher signal-to-noise ratio (SNR) and better temporal coherence than the DLI-WMS approach. The results obtained in the present study for \(\text{CO}_{{2}}\) in a gas cell and in a previous study for \(\text{H}_{{2}}\)O in a laminar flame tend to indicate that the parameters of the CWT-WMS method could be used for a large variety of experimental conditions and target species without requiring important adjustment. On the other hand, the DLI-WMS method presents a benefit in term of computational time which is \(47.9\%\) shorter than for the CWT-WMS.

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Notes

  1. The harmonic wavelet is one type of wavelet which was created by Newland [51].

References

  1. X. Chao, Development of laser absorption sensors for combustion gases. Ph.D. thesis, Stanford University (2012)

  2. X. Chao, J. Jeffries, R. Hanson, Appl. Phys. B 110(3), 359–365 (2013)

    Article  ADS  Google Scholar 

  3. D. Robichaud, L. Yeung, D. Long, M. Okumura, D. Havey, J. Hodges, C. Miller, L. Brown, J. Phys. Chem. A 113(47), 13089–13099 (2009)

    Article  Google Scholar 

  4. C. Liu, L. Xu, Appl. Spectrosc. Rev. 54(1), 1–44 (2019)

    Article  ADS  Google Scholar 

  5. H. Li, G.B. Rieker, X. Liu, J.B. Jeffries, R.K. Hanson, Appl. Opt. 45(5), 1052–1061 (2006)

    Article  ADS  Google Scholar 

  6. J. Silver, Appl. Opt. 31(6), 707–717 (1992)

    Article  ADS  Google Scholar 

  7. A. Farooq, J. Jeffries, R. Hanson, Appl. Opt. 48, 6740–6753 (2009)

    Article  ADS  Google Scholar 

  8. P. Lundin, L. Cocola, M. Lewander, A. Olsson, S. Svanberg, J. Food Eng. 111(4), 612–617 (2012)

    Article  Google Scholar 

  9. S. Basu, D. Lambe, R. Kumar, Int. J. Heat Mass Transf. 53(4), 703–714 (2010)

    Article  Google Scholar 

  10. W.-Q. Wang, L. Zhang, W.-H. Zhang, Procedia Eng. 52, 401–407 (2013)

    Article  Google Scholar 

  11. A. Lucchesini, S. Gozzini, Spectrochim. Acta Part A Mol. Biomol. Spectrosc. 60(14), 3381–3386 (2004)

    Article  ADS  Google Scholar 

  12. B. Shaw, J. Quant. Spectrosc. Radiat. Transf. 109(17–18), 2891–2894 (2008)

    Article  ADS  Google Scholar 

  13. K. Tanaka, K. Miyamura, K. Akishima, K. Tonokura, M. Konno, Infrared Phys. Technol. 79, 1–5 (2016)

    Article  ADS  Google Scholar 

  14. W. Ren, L. Luo, F. Tittel, Sens. Actuators B Chem. 221, 1062–1068 (2015)

    Article  Google Scholar 

  15. G. Zhao, W. Tan, J. Hou, X. Qiu, W. Ma, Z. Li, L. Dong, L. Zhang, W. Yin, L. Xiao, O. Axner, S. Jia, Opt. Express 24(2), 1723–1733 (2016)

    Article  ADS  Google Scholar 

  16. G.B. Rieker, J.B. Jeffries, R.K. Hanson, Appl. Opt. 48(29), 5546–5560 (2009)

    Article  ADS  Google Scholar 

  17. R.M. Spearrin, C.S. Goldenstein, J. Jeffries, R. Hanson, Appl. Opt. 53(9), 1938–1946 (2014)

    Article  ADS  Google Scholar 

  18. R. Sur, K. Sun, J. Jeffries, J. Socha, R. Hanson, Fuel 150, 102–111 (2015)

    Article  Google Scholar 

  19. Z. Qu, R. Ghorbani, D. Valiev, F. Schmidt, Opt. Express 23(12), 16492–16499(2015)

  20. P.A. Boettcher, R. Mével, V. Thomas, J.E. Shepherd, Fuel 96, 392–403 (2012)

    Article  Google Scholar 

  21. R. Mével, K. Chatelain, P.A. Boettcher, J.E. Shepherd, Fuel 126, 282–293 (2014)

    Article  Google Scholar 

  22. R. Mevel, F. Rostand, D. Lemarie, L. Breyton, J. Shepherd, Fuel 236, 373–381 (2019)

    Article  Google Scholar 

  23. S. Gersen, A. Mokhov, H. Levinsky, Combust. Flame 155(1–2), 267–276 (2008)

    Article  Google Scholar 

  24. A. Hangauer, A. Spitznas, J. Chen, R. Strzoda, H. Link, M. Fleischer, Procedia Chem. 1(1), 955–958 (2009)

    Article  Google Scholar 

  25. S. Wagner, B. Fisher, J. Fleming, V. Ebert, Proc. Combust. Inst. 32(1), 839–846 (2009)

    Article  Google Scholar 

  26. T. Cai, G. Wang, W. Zhang, X. Gao, Measurement 45(8), 2089–2095 (2012)

    Article  ADS  Google Scholar 

  27. F. Wang, K. Cen, N. Li, Q. Huang, X. Chao, J. Yan, Y. Chi, Flow Meas. Instrum. 21(3), 382–387 (2010). Special Issue: Validation and data fusion for process tomographic flow measurements validation and data fusion for process tomographic flow measurements

  28. Z. Wang, P. Fu, X. Chao, Appl. Sci. 9, # 2723 (2019)

  29. G. Rieker, J. Liu, J. Jeffries, R. Hanson, T. Mathur, M. Gruber, C. Carter, Diode laser sensor for gas temperature and \({{\rm H}}_{2}{{\rm O}}\) concentration in a scramjet combustor using wavelength modulation spectroscopy. In: 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2005–3710 (2005)

  30. H. Duan, A. Gautam, B.D. Shaw, H.H. Cheng, Appl. Opt. 48(2), 401–407 (2009)

    Article  ADS  Google Scholar 

  31. X. Zhou, X. Jin, Infrared Laser Eng. 43(6), 1722–1727 (2014)

    Google Scholar 

  32. C. Torrence, G.P. Compo, Bull. Am. Meteorol. Soc. 79(1), 61–78 (1998)

    Article  ADS  Google Scholar 

  33. A.K. Sen, G. Litak, R. Taccani, R. Radu, Chaos Solitons Fractals 38(3), 886–893 (2008)

  34. P. Goupillaud, A. Grossmann, J. Morlet, Geoexploration 23(1), 85–102 (1984)

    Article  Google Scholar 

  35. M. Farge, Annu. Rev. Fluid Mech. 24, 395–457 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  36. C.-T. Zheng, W.-L. Ye, J.-Q. Huang, T.-S. Cao, M. Lv, J.-M. Dang, Y.-D. Wang, Sens. Actuators B Chem. 190, 249–258 (2014)

    Article  Google Scholar 

  37. C. Li, X. Guo, W. Ji, J. Wei, X. Qiu, W. Ma, Opt. Quantum Electron. 50(7), 1–11 (2018)

    Google Scholar 

  38. J. Li, U. Parchatka, H. Fischer, Anal. Methods 6(15), 5483–5488 (2014)

    Article  Google Scholar 

  39. Z. Gao, W. Ye, C. Zheng, Y. Wang, Optoelectron. Lett. 10(4), 299–303 (2014)

    Article  ADS  Google Scholar 

  40. J. Dang, H. Yu, C. Zheng, L. Wang, Y. Sui, Y. Wang, Opt. Laser Technol. 101, 57–67 (2018)

    Article  ADS  Google Scholar 

  41. K. Zheng, C. Zheng, H. Zhang, J. Li, Z. Liu, Z. Chang, Y. Zhang, Y. Wang, F. Tittel, IEEE Sens. J. 21(5), 6830–6838 (2021)

    Article  ADS  Google Scholar 

  42. J. Xia, C. Feng, F. Zhu, S. Ye, S. Zhang, A. Kolomenskii, Q. Wang, J. Dong, Z. Wang, W. Jin, Sens. Actuators B Chem. 334, # 129641 (2021)

  43. G. Zhu, H. Zhu, C. Yang, W. Gui, J. Opt. Technol. 84(5), 355–359 (2017)

    Article  Google Scholar 

  44. Q. Luo, C. Song, C. Yang, W. Gui, Y. Sun, Z. Jeffrey, IEEE Trans. Instrum. Meas. 69(8), 5828–5842 (2020)

    Article  Google Scholar 

  45. Y. Meng, T. Liu, K. Liu, J. Jiang, R. Wang, T. Wang, H. Hu, IEEE Photonics J. 6(6), # 6803209 (2014)

  46. L. Zhang, F. Wang, H. Wei, J. Wang, H. Cui, G. Zhao, Laser Optoelectron. Prog. 58(7), 8 (2021)

    Google Scholar 

  47. Y. Zhou, S. Miao, D. Yao, M. Dong, C. Zheng, Y. Wang, Chin. J. Lasers 47(6), 9 (2020)

    Google Scholar 

  48. M. Sun, H. Ma, Q. Liu, Z. Cao, G. Wang, K. Liu, Y. Huang, X. Gao, R. Rao, Acta Opt. Sin. 38(5), 344–350 (2018)

    Google Scholar 

  49. L. Zhang, F. Wang, L. Yu, J. Yan, K. Cen, Spectrosc. Spectr. Anal. 36(6), 1794–1798 (2016)

    Google Scholar 

  50. H. Cui, K. Yang, L. Zhang, X. Wu, Y. Liu, A. Wang, H. Li, M. Ji, Spectrosc. Spectr. Anal. 36(9), 2997–3002 (2016)

    Google Scholar 

  51. D.E. Newland, Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 443(1917), 203–225 (1993)

  52. R.K. Hanson, R.M. Spearrin, C.S. Goldenstein, Spectroscopy and Optical Diagnostics for Gases (Springer, Berlin, 2016)

    Book  Google Scholar 

  53. C.S. Goldenstein, R.M. Spearrin, J.B. Jeffries, R.K. Hanson, Prog. Energy Combust. 60, 132–176 (2017)

    Article  Google Scholar 

  54. K. Sun, X. Chao, R. Sur, C. Goldenstein, J. Jeffries, R. Hanson, Meas. Sci. Technol. 24(12), 125203 (2013)

    Article  ADS  Google Scholar 

  55. A. Grinsted, J.C. Moore, S. Jevrejeva, Nonlinear Process. Geophys. 11(5/6), 561–566 (2004)

    Article  ADS  Google Scholar 

  56. J. Lin, L. Qu, J. Sound Vib. 234(1), 135–148 (2000)

    Article  ADS  Google Scholar 

  57. I. Gordon, L. Rothman, R. Hargreaves, R. Hashemi, E. Karlovets, F. Skinner, E. Conway, C. Hill, R. Kochanov, Y. Tan, P. Wcisło, A. Finenko, K. Nelson, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. Chance, A. Coustenis, B. Drouin, J. Flaud, R. Gamache, J. Hodges, D. Jacquemart, E. Mlawer, A. Nikitin, V. Perevalov, M. Rotger, J. Tennyson, G. Toon, H. Tran, V. Tyuterev, E. Adkins, A. Baker, A. Barbe, E. Can., A. Cs.sz.r, A. Dudaryonok, O. Egorov, A. Fleisher, H. Fleurbaey, A. Foltynowicz, T. Furtenbacher, J. Harrison, J. Hartmann, V. Horneman, X. Huang, T. Karman, J. Karns, S. Kassi, I. Kleiner, V. Kofman, F. Kwabia-Tchana, N. Lavrentieva, T. Lee, D. Long, A. Lukashevskaya, O. Lyulin, V. Makhnev, W. Matt, S. Massie, M. Melosso, S. Mikhailenko, D. Mondelain, H. Müller, O. Naumenko, A. Perrin, O. Polyansky, E. Raddaoui, P. Raston, Z. Reed, M. Rey, C. Richard, R. T.bi.s, I. Sadiek, D. Schwenke, E. Starikova, K. Sung, F. Tamassia, S. Tashkun, J. V. Auwera, I. Vasilenko, A. Vigasin, G. Villanueva, B. Vispoel, G. Wagner, A. Yachmenev, S. Yurchenko, J. Quant. Spectrosc. Radiat. Transf. 107949 (2021)

  58. Z. Li, TDL-WMS laser calibration helper for manually etalon peaks counting (2021). https://github.com/lzt66666/TDL-WMS-laser-calibration-helper.git

  59. H. Li, A. Farooq, J. Jeffries, R. Hanson, Appl. Phys. B 89(2), 407–416 (2007)

    Article  ADS  Google Scholar 

  60. A. Farooq, J. Jeffries, R. Hanson, Appl. Phys. B 96(1), 161–173 (2009)

    Article  ADS  Google Scholar 

  61. J.X. Rodrigues, K. Pai, Modified linear phase frequency response masking fir filter, in ISPA 2005. Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis, 2005. IEEE (2005), pp. 434–439

  62. Z. Wang, P. Fu, X. Chao, Meas. Sci. Technol. 31(3), 035202 (2019)

    Article  ADS  Google Scholar 

  63. Z. Wang, P. Fu, L. Hou, X. Chao, Meas. Sci. Technol. 31(10), 105202 (2020)

    Article  ADS  Google Scholar 

  64. W.J. Williams, M.L. Brown, A.O. Hero III, Uncertainty, information, and time-frequency distributions, in Advanced Signal Processing Algorithms, Architectures, and Implementations II, vol. 1566 (International Society for Optics and Photonics, 1991), pp. 144–156

  65. A. Klein, O. Witzel, V. Ebert, Sensors 14(11), 21497–21513 (2014)

    Article  ADS  Google Scholar 

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Acknowledgements

Funding for this research was provided by Tsinghua-Foshan Innovation Special Fund (TFISF), Grant number 2020THFS0108, and National Natural Science Foundation of China (NSFC), Grant number 51976105. Wavelet software was provided by C. Torrence and G. Compo, and is available at URL: http://paos.colorado.edu/research/wavelets/.

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Authors and Affiliations

  1. Center for Combustion Energy, School of Vehicle and Mobility, and State Key Laboratory for Automotive Safety and Energy, Tsinghua University, Beijing, 100084, China

    Zongtai Li & Rémy Mével

  2. Center for Combustion Energy, Department of Energy and Power Engineering, and Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Tsinghua University, Beijing, 100084, China

    Zhenhai Wang & Xing Chao

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  1. Zongtai Li
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Li, Z., Wang, Z., Mével, R. et al. Fourier and wavelet transform analysis of wavelength modulation spectroscopy signal. Appl. Phys. B 128, 109 (2022). https://doi.org/10.1007/s00340-022-07834-7

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