## Accuracy improvement of quantitative analysis in laser-induced breakdown spectroscopy using modified wavelet transform |

Optics Express, Vol. 22, Issue 9, pp. 10233-10238 (2014)

http://dx.doi.org/10.1364/OE.22.010233

Acrobat PDF (1437 KB)

### Abstract

A modified algorithm of background removal based on wavelet transform was developed for spectrum correction in laser-induced breakdown spectroscopy (LIBS). The optimal type of wavelet function, decomposition level and scaling factor γ were determined by the root-mean-square error of calibration (RMSEC) of the univariate regression model of the analysis element, which is considered as the optimization criteria. After background removal by this modified algorithm with RMSEC, the root-mean-square error of cross-validation (RMSECV) and the average relative error (ARE) criteria, the accuracy of quantitative analysis on chromium (Cr), vanadium (V), cuprum (Cu), and manganese (Mn) in the low alloy steel was all improved significantly. The results demonstrated that the algorithm developed is an effective pretreatment method in LIBS to significantly improve the accuracy in the quantitative analysis.

© 2014 Optical Society of America

## 1. Introduction

1. W. B. Lee, J. Y. Wu, Y. I. Lee, and J. Sneddon, “Recent applications of laser-induced breakdown spectrometry: a review of material approaches,” Appl. Spectrosc. Rev. **39**(1), 27–97 (2004). [CrossRef]

5. L. Dudragne, P. Adam, and J. Amouroux, “Time-resolved laser-induced breakdown spectroscopy: application for qualitative and quantitative detection of fluorine, chlorine, sulfur, and carbon in air,” Appl. Spectrosc. **52**(10), 1321–1327 (1998). [CrossRef]

7. Z. Wang, Z. Y. Hou, S. L. Lui, D. Jiang, J. M. Liu, and Z. Li, “Utilization of moderate cylindrical confinement for precision improvement of laser-induced breakdown spectroscopy signal,” Opt. Express **20**(S6), A1011–A1018 (2012). [CrossRef]

9. X. G. Shao, A. K. M. Leung, and F. T. Chau, “Wavelet: a new trend in chemistry,” Acc. Chem. Res. **36**(4), 276–283 (2003). [CrossRef] [PubMed]

10. C. M. Galloway, E. C. Le Ru, and P. G. Etchegoin, “An iterative algorithm for background removal in spectroscopy by wavelet transforms,” Appl. Spectrosc. **63**(12), 1370–1376 (2009). [CrossRef] [PubMed]

11. X. G. Ma and Z. X. Zhang, “Application of wavelet transform to background correction in inductively coupled plasma atomic emission spectrometry,” Anal. Chim. Acta **485**(2), 233–239 (2003). [CrossRef]

12. C. X. Ma and X. G. Shao, “Continuous wavelet transform applied to removing the fluctuating background in near-infrared spectra,” J. Chem. Inf. Comput. Sci. **44**(3), 907–911 (2004). [CrossRef] [PubMed]

*et al.*adopted stationary WT via adaptive variable threshold for noise reduction, which successfully achieved noise suppression and signal preservation [13

13. J. Schlenke, L. Hildebrand, J. Moros, and J. J. Laserna, “Adaptive approach for variable noise suppression on laser-induced breakdown spectroscopy responses using stationary wavelet transform,” Anal. Chim. Acta **754**, 8–19 (2012). [CrossRef] [PubMed]

*et al.*established a new double threshold optimization model of wavelet denoising, and demonstrated the performance of the method for both synthetic and actual LIBS signals [14

14. B. Zhang, L. X. Sun, H. B. Yu, Y. Xin, and Z. B. Cong, “Wavelet denoising method for laser-induced breakdown spectroscopy,” J. Anal. At. Spectrom. **28**(12), 1884–1893 (2013). [CrossRef]

*et al.*implemented WT to subtract background for LIBS application by utilizing the wavelet coefficients instead of the spectral information after reconstruction for the first time, and analyzed quantitatively the high-concentration carbon element in coal [15

15. T. B. Yuan, Z. Wang, Z. Li, W. D. Ni, and J. M. Liu, “A partial least squares and wavelet-transform hybrid model to analyze carbon content in coal using Laser-induced breakdown spectroscopy,” Anal. Chim. Acta **807**, 29–35 (2014). [CrossRef] [PubMed]

*et al.*proposed a concept of factor of the low-frequency part of the highest level of wavelet decomposition to amend the estimated background in high performance liquid chromatography (HPLC) [9

9. X. G. Shao, A. K. M. Leung, and F. T. Chau, “Wavelet: a new trend in chemistry,” Acc. Chem. Res. **36**(4), 276–283 (2003). [CrossRef] [PubMed]

16. X. G. Shao, W. S. Cai, and Z. X. Pan, “Wavelet transform and its applications in high performance liquid chromatography (HPLC) analysis,” Chemom. Intell. Lab. Syst. **45**(1–2), 249–256 (1999). [CrossRef]

## 2. Algorithm description

15. T. B. Yuan, Z. Wang, Z. Li, W. D. Ni, and J. M. Liu, “A partial least squares and wavelet-transform hybrid model to analyze carbon content in coal using Laser-induced breakdown spectroscopy,” Anal. Chim. Acta **807**, 29–35 (2014). [CrossRef] [PubMed]

19. X. G. Shao, L. M. Shao, and G. W. Zhao, “Extraction of extended X-ray absorption fine structure information from the experimental data using the wavelet transform,” Anal. Commun. **35**(4), 135–137 (1998). [CrossRef]

- (1) Select the wavelet function which varies from db1 to db10, and choose the decomposition level which ranges between 4 and 13.
- (2) Set the approximation coefficients
*c*to zero, which is equivalent to γ_{J,k}= 1. Then reconstruct the spectra. Extract the intensity information of analysis element to build the calibration regression model, and calculate the RMSEC._{ini} - (3) Determine the optimum values of the wavelet function (
*W*) and decomposition level (*L*) which make the RMSEC achieve the minimum. - (4) Perform wavelet decomposition again using the wavelet function (
*W*) and decomposition level (*L*) for the spectra. Then solve the optimum γby the least squares method, and the RMSEC is still considered as the optimization goal. That is, γ_{opt}satisfies Eq. (2)_{opt} - (5) Multiply
*c*by (1-γ_{J,k}) for the spectra and then reconstruct the spectral signal according to Eq. (1). Finally, the background-corrected spectra are obtained._{opt}

## 3. Experimental

## 4. Results and discussions

22. A. E. Kramida Y. Ralchenko, J. Reader, and NIST ASD Team, “NIST Atomic Spectra Database (version 5.1)” (National Institute of Standards and Technology, 2013), http://physics.nist.gov/asd.

**γ**influence the RMSEC.

### 4.1 Optimization of the wavelet function and decomposition level

### 4.2 Optimization of the scaling factor γ

### 4.3 Comparison of quantitative analysis

*et al.*[23

23. L. X. Sun and H. B. Yu, “Automatic estimation of varying continuum background emission in laser-induced breakdown spectroscopy,” Spectrochim. Acta, B At. Spectrosc. **64**(3), 278–287 (2009). [CrossRef]

^{2}and lower ARE. The above analysis revealed that the proposed method can effectively improve the accuracy of the regression model.

## 5. Conclusions

^{2}and ARE are all significantly improved, successfully proving the validity of the background correction algorithm. This method can effectively improve the quality of the signals and the accuracy of the regression model. Accordingly, the proposed method can be used as a competitive preprocessing tool for LIBS and other spectral analysis.

## Acknowledgments

## References and links

1. | W. B. Lee, J. Y. Wu, Y. I. Lee, and J. Sneddon, “Recent applications of laser-induced breakdown spectrometry: a review of material approaches,” Appl. Spectrosc. Rev. |

2. | Z. Wang, T. B. Yuan, Z. Y. Hou, W. D. Zhou, J. D. Lu, H. B. Ding, and X. Y. Zeng, “Laser-induced breakdown spectroscopy in China,” Front. Phys. (2014). |

3. | L. B. Guo, Z. Q. Hao, M. Shen, W. Xiong, X. N. He, Z. Q. Xie, M. Gao, X. Y. Li, X. Y. Zeng, and Y. F. Lu, “Accuracy improvement of quantitative analysis by spatial confinement in laser-induced breakdown spectroscopy,” Opt. Express |

4. | P. Fichet, P. Mauchien, J. F. Wagner, and C. Moulin, “Quantitative elemental determination in water and oil by laser induced breakdown spectroscopy,” Anal. Chim. Acta |

5. | L. Dudragne, P. Adam, and J. Amouroux, “Time-resolved laser-induced breakdown spectroscopy: application for qualitative and quantitative detection of fluorine, chlorine, sulfur, and carbon in air,” Appl. Spectrosc. |

6. | J. P. Singh and S. N. Thakur, |

7. | Z. Wang, Z. Y. Hou, S. L. Lui, D. Jiang, J. M. Liu, and Z. Li, “Utilization of moderate cylindrical confinement for precision improvement of laser-induced breakdown spectroscopy signal,” Opt. Express |

8. | T. Fujimoto, |

9. | X. G. Shao, A. K. M. Leung, and F. T. Chau, “Wavelet: a new trend in chemistry,” Acc. Chem. Res. |

10. | C. M. Galloway, E. C. Le Ru, and P. G. Etchegoin, “An iterative algorithm for background removal in spectroscopy by wavelet transforms,” Appl. Spectrosc. |

11. | X. G. Ma and Z. X. Zhang, “Application of wavelet transform to background correction in inductively coupled plasma atomic emission spectrometry,” Anal. Chim. Acta |

12. | C. X. Ma and X. G. Shao, “Continuous wavelet transform applied to removing the fluctuating background in near-infrared spectra,” J. Chem. Inf. Comput. Sci. |

13. | J. Schlenke, L. Hildebrand, J. Moros, and J. J. Laserna, “Adaptive approach for variable noise suppression on laser-induced breakdown spectroscopy responses using stationary wavelet transform,” Anal. Chim. Acta |

14. | B. Zhang, L. X. Sun, H. B. Yu, Y. Xin, and Z. B. Cong, “Wavelet denoising method for laser-induced breakdown spectroscopy,” J. Anal. At. Spectrom. |

15. | T. B. Yuan, Z. Wang, Z. Li, W. D. Ni, and J. M. Liu, “A partial least squares and wavelet-transform hybrid model to analyze carbon content in coal using Laser-induced breakdown spectroscopy,” Anal. Chim. Acta |

16. | X. G. Shao, W. S. Cai, and Z. X. Pan, “Wavelet transform and its applications in high performance liquid chromatography (HPLC) analysis,” Chemom. Intell. Lab. Syst. |

17. | S. G. Mallat, “A theory of multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. |

18. | S. G. Mallat, |

19. | X. G. Shao, L. M. Shao, and G. W. Zhao, “Extraction of extended X-ray absorption fine structure information from the experimental data using the wavelet transform,” Anal. Commun. |

20. | D. Chen, X. G. Shao, B. Hu, and Q. D. Su, “A background and noise elimination method for quantitative calibration of near infrared spectra,” Anal. Chim. Acta |

21. | I. Daubechies, |

22. | A. E. Kramida Y. Ralchenko, J. Reader, and NIST ASD Team, “NIST Atomic Spectra Database (version 5.1)” (National Institute of Standards and Technology, 2013), http://physics.nist.gov/asd. |

23. | L. X. Sun and H. B. Yu, “Automatic estimation of varying continuum background emission in laser-induced breakdown spectroscopy,” Spectrochim. Acta, B At. Spectrosc. |

**OCIS Codes**

(100.7410) Image processing : Wavelets

(160.3900) Materials : Metals

(300.6365) Spectroscopy : Spectroscopy, laser induced breakdown

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: March 3, 2014

Revised Manuscript: April 11, 2014

Manuscript Accepted: April 14, 2014

Published: April 21, 2014

**Citation**

X. H. Zou, L. B. Guo, M. Shen, X. Y. Li, Z. Q. Hao, Q. D. Zeng, Y. F. Lu, Z. M. Wang, and X. Y. Zeng, "Accuracy improvement of quantitative analysis in laser-induced breakdown spectroscopy using modified wavelet transform," Opt. Express **22**, 10233-10238 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-9-10233

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### References

- W. B. Lee, J. Y. Wu, Y. I. Lee, J. Sneddon, “Recent applications of laser-induced breakdown spectrometry: a review of material approaches,” Appl. Spectrosc. Rev. 39(1), 27–97 (2004). [CrossRef]
- Z. Wang, T. B. Yuan, Z. Y. Hou, W. D. Zhou, J. D. Lu, H. B. Ding, and X. Y. Zeng, “Laser-induced breakdown spectroscopy in China,” Front. Phys. (2014).
- L. B. Guo, Z. Q. Hao, M. Shen, W. Xiong, X. N. He, Z. Q. Xie, M. Gao, X. Y. Li, X. Y. Zeng, Y. F. Lu, “Accuracy improvement of quantitative analysis by spatial confinement in laser-induced breakdown spectroscopy,” Opt. Express 21(15), 18188–18195 (2013). [CrossRef] [PubMed]
- P. Fichet, P. Mauchien, J. F. Wagner, C. Moulin, “Quantitative elemental determination in water and oil by laser induced breakdown spectroscopy,” Anal. Chim. Acta 429(2), 269–278 (2001). [CrossRef]
- L. Dudragne, P. Adam, J. Amouroux, “Time-resolved laser-induced breakdown spectroscopy: application for qualitative and quantitative detection of fluorine, chlorine, sulfur, and carbon in air,” Appl. Spectrosc. 52(10), 1321–1327 (1998). [CrossRef]
- J. P. Singh and S. N. Thakur, Laser-Induced Breakdown Spectroscopy (Elsevier Science, 2007).
- Z. Wang, Z. Y. Hou, S. L. Lui, D. Jiang, J. M. Liu, Z. Li, “Utilization of moderate cylindrical confinement for precision improvement of laser-induced breakdown spectroscopy signal,” Opt. Express 20(S6), A1011–A1018 (2012). [CrossRef]
- T. Fujimoto, Plasma Spectroscopy (Clarendon, 2004).
- X. G. Shao, A. K. M. Leung, F. T. Chau, “Wavelet: a new trend in chemistry,” Acc. Chem. Res. 36(4), 276–283 (2003). [CrossRef] [PubMed]
- C. M. Galloway, E. C. Le Ru, P. G. Etchegoin, “An iterative algorithm for background removal in spectroscopy by wavelet transforms,” Appl. Spectrosc. 63(12), 1370–1376 (2009). [CrossRef] [PubMed]
- X. G. Ma, Z. X. Zhang, “Application of wavelet transform to background correction in inductively coupled plasma atomic emission spectrometry,” Anal. Chim. Acta 485(2), 233–239 (2003). [CrossRef]
- C. X. Ma, X. G. Shao, “Continuous wavelet transform applied to removing the fluctuating background in near-infrared spectra,” J. Chem. Inf. Comput. Sci. 44(3), 907–911 (2004). [CrossRef] [PubMed]
- J. Schlenke, L. Hildebrand, J. Moros, J. J. Laserna, “Adaptive approach for variable noise suppression on laser-induced breakdown spectroscopy responses using stationary wavelet transform,” Anal. Chim. Acta 754, 8–19 (2012). [CrossRef] [PubMed]
- B. Zhang, L. X. Sun, H. B. Yu, Y. Xin, Z. B. Cong, “Wavelet denoising method for laser-induced breakdown spectroscopy,” J. Anal. At. Spectrom. 28(12), 1884–1893 (2013). [CrossRef]
- T. B. Yuan, Z. Wang, Z. Li, W. D. Ni, J. M. Liu, “A partial least squares and wavelet-transform hybrid model to analyze carbon content in coal using Laser-induced breakdown spectroscopy,” Anal. Chim. Acta 807, 29–35 (2014). [CrossRef] [PubMed]
- X. G. Shao, W. S. Cai, Z. X. Pan, “Wavelet transform and its applications in high performance liquid chromatography (HPLC) analysis,” Chemom. Intell. Lab. Syst. 45(1–2), 249–256 (1999). [CrossRef]
- S. G. Mallat, “A theory of multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. 11(7), 674–693 (1989). [CrossRef]
- S. G. Mallat, A Wavelet Tour of Signal Processing: The Sparse Way (Academic, 2008).
- X. G. Shao, L. M. Shao, G. W. Zhao, “Extraction of extended X-ray absorption fine structure information from the experimental data using the wavelet transform,” Anal. Commun. 35(4), 135–137 (1998). [CrossRef]
- D. Chen, X. G. Shao, B. Hu, Q. D. Su, “A background and noise elimination method for quantitative calibration of near infrared spectra,” Anal. Chim. Acta 511(1), 37–45 (2004). [CrossRef]
- I. Daubechies, Ten Lectures on Wavelets (Society for Industrial and Applied Mathematics, 1992).
- A. E. Kramida Y. Ralchenko, J. Reader, and NIST ASD Team, “NIST Atomic Spectra Database (version 5.1)” (National Institute of Standards and Technology, 2013), http://physics.nist.gov/asd .
- L. X. Sun, H. B. Yu, “Automatic estimation of varying continuum background emission in laser-induced breakdown spectroscopy,” Spectrochim. Acta, B At. Spectrosc. 64(3), 278–287 (2009). [CrossRef]

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