Applied Physics B

, 124:190 | Cite as

Optimal selection of spectral lines for multispectral absorption tomography

  • Qianwei Qu
  • Zhang Cao
  • Lijun XuEmail author
  • Weiwei Cai


Multispectral absorption tomography (MAT) is evolving into a mature imaging technique for flow diagnostics due to recent progress in both laser sources and nonlinear tomography. For the absorption-based technique, how to determine and utilize the most informative spectral lines are critical for successful implementation of the technique. In this work, we propose a method to select the optimal combination of spectral lines from the candidate set for MAT. We select the Gram determinant of selected spectral lines in given temperature interval as the cost function of the optimization problem, which can then be maximized by enumerating all the possible combinations of the candidate spectral lines. The numerical studies performed in this work verified the effectiveness of the proposed method, whose purpose was to achieve the best performance for the reconstruction of temperature distribution.



This work was supported by the National Natural Science Foundation of China (no. 61620106004, no. 61522102), Ministry of Science and Technology of the People’s Republic of China (no. 2016YFF0100600) and Chinese government “Thousand Talented Youth Program”. We are indebted to Mr. Tao Yu (Department of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China) for valuable discussions and suggestions.

Supplementary material

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Supplementary material 1 (MP4 353 KB)
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Supplementary material 4 (MP4 15312 KB)


  1. 1.
    H.P. Zappe, M. Hess, M. Moser, R. Hövel, K. Gulden, H.P. Gauggel, F. Monti di Sopra, Appl. Opt. 39, 2475 (2000)ADSCrossRefGoogle Scholar
  2. 2.
    E. Normand, G. Duxbury, N. Langford, Opt. Commun. 197, 115 (2001)ADSCrossRefGoogle Scholar
  3. 3.
    C. Liu, L. Xu, Z. Cao, H. McCann, IEEE Trans. Instrum. Meas. 63, 3067 (2014)CrossRefGoogle Scholar
  4. 4.
    C.T. Mems-vcsel, B. Kögel, H. Halbritter, S. Jatta, M. Maute, G. Böhm, M. Amann, M. Lackner, M. Schwarzott, F. Winter, P. Meissner, Sensors (Peterborough, NH) 7, 1483 (2007)Google Scholar
  5. 5.
    J.A. Nwaboh, O. Werhahn, D. Schiel, Appl. Phys. B Lasers Opt. 103, 947 (2011)ADSCrossRefGoogle Scholar
  6. 6.
    O. Witzel, A. Klein, C. Meffert, S. Wagner, S. Kaiser, C. Schulz, V. Ebert, Opt. Express 21, 19951 (2013)ADSCrossRefGoogle Scholar
  7. 7.
    R.S.M. Chrystie, E.F. Nasir, A. Farooq, Appl. Phys. B Lasers Opt. 120, 317 (2015)ADSCrossRefGoogle Scholar
  8. 8.
    K.G.P. Sulzmann, J.E.L. Lowder, S.S. Penner, Combust. Flame 20, 177 (1973)CrossRefGoogle Scholar
  9. 9.
    R.K. Hanson, P.A. Kuntz, C.H. Kruger, Appl. Opt. 16, 8 (1977)Google Scholar
  10. 10.
    R.K. Hanson, P.K. Falcone, Appl. Opt. 17, 2477 (1978)ADSCrossRefGoogle Scholar
  11. 11.
    S.T. Sanders, J. Wang, J.B. Jeffries, R.K. Hanson, Appl. Opt. 40, 4404 (2001)ADSCrossRefGoogle Scholar
  12. 12.
    L. Xu, C. Liu, W. Jing, Z. Cao, X. Xue, Y. Lin, Rev. Sci. Instrum. 87, 013101 (2016)ADSCrossRefGoogle Scholar
  13. 13.
    C. Liu, L. Xu, F. Li, Z. Cao, S.A. Tsekenis, H. McCann, Appl. Phys. B Lasers Opt. 120, 407 (2015)ADSCrossRefGoogle Scholar
  14. 14.
    R.S.M. Chrystie, E.F. Nasir, A. Farooq, Opt. Lett. 35, 3757 (2015)Google Scholar
  15. 15.
    J.H. Northern, S. O’Hagan, B. Fletcher, B. Gras, P. Ewart, C.S. Kim, M. Kim, C.D. Merritt, W.W. Bewley, C.L. Canedy, J. Abell, I. Vurgaftman, J.R. Meyer, S.O.H. Agan, B.F. Letcher, B.G. Ras, P.E. Wart, C.S.K. Im, M.K. Im, C.D.M. Erritt, W.W.B. Ewley, C.L.C. Anedy, J.A. Bell, J.R.M. Eyer, Opt. Lett. 40, 4186 (2015)ADSCrossRefGoogle Scholar
  16. 16.
    E.J. Barton, S.N. Yurchenko, J. Tennyson, S. Clausen, A. Fateev, J. Quant. Spectrosc. Radiat. Transf. 189, 60 (2017)ADSCrossRefGoogle Scholar
  17. 17.
    X. Liu, J.B. Jeffries, R.K. Hanson, K.M. Hinckley, M.A. Woodmansee, Appl. Phys. B 82, 469 (2006)ADSCrossRefGoogle Scholar
  18. 18.
    G. Zhang, J. Liu, Z. Xu, Y. He, R. Kan, Appl. Phys. B 122, 3 (2016)ADSCrossRefGoogle Scholar
  19. 19.
    C. Liu, L. Xu, Z. Cao, Appl. Opt. 52, 4827 (2013)ADSCrossRefGoogle Scholar
  20. 20.
    S.J. Carey, H. McCann, F.P. Hindle, K.B. Ozanyan, D.E. Winterbone, E. Clough, Chem. Eng. J. 77, 111 (2000)CrossRefGoogle Scholar
  21. 21.
    F.P. Hindle, S.J. Carey, K. Ozanyan, D.E. Winterbone, E. Clough, H. McCann, J. Electron. Imaging 10, 593 (2001)ADSCrossRefGoogle Scholar
  22. 22.
    P. Wright, C. Garcia-Stewart, S.J. Carey, F.P. Hindle, S.H. Pegrum, S.M. Colbourne, P.J. Turner, W.J. Hurr, T.J. Litt, S.C. Murray, S.D. Crossley, K.B. Ozanyan, H. McCann, Appl. Opt. 44, 6578 (2005)ADSCrossRefGoogle Scholar
  23. 23.
    L. Ma, X. Li, S.T. Sanders, A.W. Caswell, S. Roy, D.H. Plemmons, J.R. Gord, Opt. Express 21, 1152 (2013)ADSCrossRefGoogle Scholar
  24. 24.
    M.P. Wood, K.B. Ozanyan, IEEE Sens. J. 15, 545 (2015)ADSCrossRefGoogle Scholar
  25. 25.
    C. Liu, L. Xu, J. Chen, Z. Cao, Y. Lin, W. Cai, Opt. Express 23, 22494 (2015)ADSCrossRefGoogle Scholar
  26. 26.
    W. Cai, C.F. Kaminski, Prog. Energy Combust. Sci. 59, 1 (2017)CrossRefGoogle Scholar
  27. 27.
    T. Yu, H. Liu, W. Cai, Opt. Express 25, 24093 (2017)ADSCrossRefGoogle Scholar
  28. 28.
    T. Yu, W. Cai, Appl. Opt. 56, 2183 (2017)ADSCrossRefGoogle Scholar
  29. 29.
    P.C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion (Society for Industrial and Applied Mathematics, Philadelphia, 1998)CrossRefGoogle Scholar
  30. 30.
    W. Cai, C.F. Kaminski, Appl. Phys. Lett. 104, 034101 (2014)ADSCrossRefGoogle Scholar
  31. 31.
    L. Ma, W. Cai, A.W. Caswell, T. Kraetschmer, S.T. Sanders, S. Roy, J.R. Gord, Opt. Express 17, 517 (2009)Google Scholar
  32. 32.
    X. An, T. Kraetschmer, K. Takami, S.T. Sanders, L. Ma, W. Cai, X. Li, S. Roy, J.R. Gord, Appl. Opt. 50, A29 (2011)ADSCrossRefGoogle Scholar
  33. 33.
    W. Cai, C.F. Kaminski, Appl. Phys. B 119, 29 (2015)ADSCrossRefGoogle Scholar
  34. 34.
    W. Cai, C.F. Kaminski, Appl. Phys. Lett. 104, 154106 (2014)ADSCrossRefGoogle Scholar
  35. 35.
    L. Ma, X. Li, W. Cai, S. Roy, J.R. Gord, S.T. Sanders, Appl. Spectrosc. 64, 1273 (2010)Google Scholar
  36. 36.
    C.S. Goldenstein, R.M. Spearrin, I.A. Schultz, J.B. Jeffries, R.K. Hanson, Meas. Sci. Technol. 25, 055101 (2014)ADSCrossRefGoogle Scholar
  37. 37.
    L. Ma, W. Cai, Appl. Opt. 47, 13 (2008)Google Scholar
  38. 38.
    W. Cai, Y. Zhao, L. Ma, J. Quant. Spectrosc. Radiat. Transf. 109, 2673 (2008)ADSCrossRefGoogle Scholar
  39. 39.
    X. Zhou, J.B. Jeffries, R.K. Hanson, Appl. Phys. B 81, 711 (2005)ADSCrossRefGoogle Scholar
  40. 40.
    L.S. Rothman, I.E. Gordon, Y. Babikov, A. Barbe, D. Chris Benner, P.F. Bernath, M. Birk, L. Bizzocchi, V. Boudon, L.R. Brown, A. Campargue, K. Chance, E.A. Cohen, L.H. Coudert, V.M. Devi, B.J. Drouin, A. Fayt, J.M. Flaud, R.R. Gamache, J.J. Harrison, J.M. Hartmann, C. Hill, J.T. Hodges, D. Jacquemart, A. Jolly, J. Lamouroux, R.J. Le Roy, G. Li, D.A. Long, O.M. Lyulin, C.J. Mackie, S.T. Massie, S. Mikhailenko, H.S.P. Müller, O.V. Naumenko, A.V. Nikitin, J. Orphal, V. Perevalov, A. Perrin, E.R. Polovtseva, C. Richard, M.A.H. Smith, E. Starikova, K. Sung, S. Tashkun, J. Tennyson, G.C. Toon, V.G. Tyuterev, G. Wagner, J. Quant. Spectrosc. Radiat. Transf. 130, 4 (2016)ADSCrossRefGoogle Scholar
  41. 41.
    L.S. Rothman, D. Jacquemart, A. Barbe, D.C. Benner, M. Birk, L.R. Brown, M.R. Carleer, J.C. Chackerian, K.C. Et Al, J. Quant. Spectrosc. Radiat. Transf. 96, 139 (2005)ADSCrossRefGoogle Scholar
  42. 42.
    C.S. Goldenstein, C.L. Strand, I. a Schultz, K. Sun, J.B. Jeffries, R.K. Hanson, Appl. Opt. 53, 356 (2014)ADSCrossRefGoogle Scholar
  43. 43.
    C.S. Goldenstein, Wavelength-Modulation Spectroscopy for Determination of Gas Properties in Hostile Environments (Stanford University, California, 2014)Google Scholar
  44. 44.
    K. Sun, X. Chao, R. Sur, C.S. Goldenstein, J.B. Jeffries, R.K. Hanson, Meas. Sci. Technol. 24, 125203 (2013)ADSCrossRefGoogle Scholar
  45. 45.
    R.K. Hanson, R.M. Spearrin, C.S. Goldenstein, Spectroscopy and Optical Diagnostics for Gases (Springer, New York, 2016)CrossRefGoogle Scholar
  46. 46.
    R.J. Vanderbei, D.F. Shanno, Comput. Optim. Appl. 13, 231 (1999)MathSciNetCrossRefGoogle Scholar
  47. 47.
    R.H. Byrd, M.E. Hribar, J. Nocedal, SIAM J. Optim. 9, 877 (1998)CrossRefGoogle Scholar
  48. 48.
    Z. Zhang, P. Sun, T. Pang, H. Xia, X. Cui, Z. Li, L. Han, B. Wu, Y. Wang, M.W. Sigrist, F. Dong, Opt. Eng. 55, 076107 (2016)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Ministry of Education’s Key Laboratory of Precision Opto-mechatronics Technology, School of Instrument Science and Opto-Electronic EngineeringBeihang UniversityBeijingChina
  2. 2.Shenyuan Honors CollegeBeihang UniversityBeijingChina
  3. 3.Department of Mechanical EngineeringShanghai Jiao Tong UniversityShanghaiChina

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