Applied Physics B

, 124:55 | Cite as

Non-destructive testing of ceramic materials using mid-infrared ultrashort-pulse laser

  • S. C. Sun
  • Hong Qi
  • X. Y. An
  • Y. T. Ren
  • Y. B. Qiao
  • Liming M. Ruan
Part of the following topical collections:
  1. Mid-infrared and THz Laser Sources and Applications


The non-destructive testing (NDT) of ceramic materials using mid-infrared ultrashort-pulse laser is investigated in this study. The discrete ordinate method is applied to solve the transient radiative transfer equation in 2D semitransparent medium and the emerging radiative intensity on boundary serves as input for the inverse analysis. The sequential quadratic programming algorithm is employed as the inverse technique to optimize objective function, in which the gradient of objective function with respect to reconstruction parameters is calculated using the adjoint model. Two reticulated porous ceramics including partially stabilized zirconia and oxide-bonded silicon carbide are tested. The retrieval results show that the main characteristics of defects such as optical properties, geometric shapes and positions can be accurately reconstructed by the present model. The proposed technique is effective and robust in NDT of ceramics even with measurement errors.

List of symbols


Set of all restriction


Weight coefficient


Speed of light (m/s)




Search direction


Parameter of DRIFD phase function


Set of equality restriction


Objective function


Parameter of H–G phase function


Heaviside step function or approximation of the Hessian


Radiative intensity, W/(m2 sr)


Iteration number


Size of medium


Number of restriction


Number of equality restriction




Refractive index


Normal vector


Number of grid or set of all neighboring pixel pairs


Total number of the parameter to be reconstructed

Number of discretized direction


Sharpness parameter


Penalty factor




Emerging radiative intensity


Transmission distance of the collimated intensity


Subject to


Source term (W/m3)


Time (s)


Pulse width of laser (s)


Lagrangian multiplier in SQP


Directional weight


Parameter to be reconstructed or coordinate in x direction (m)


Coordinate in y direction (m)

Greeks symbols


Search step size


A positive value


Extinction coefficient (m−1)


Dirac’s delta function


Convergence accuracy


Time step (s)


Grid size in x direction


Grid size in y direction


Directional cosines of y direction


Scale parameter


Absorption coefficient (m−1)


Scattering coefficient (m−1)


Lagrangian multiplier in adjoint model


Scattering direction

\({\varvec{\Omega}^\prime }\)

Incident direction


A small positive value


Directional cosines in x direction


Regularization term



Back scattering


Estimated value


Exact value


Collimated value or central point


Diffused value


Computational domain




Diffusely reflective




Isotropically scattering


lth discretized direction


Boundary of computational domain


mth discretized direction


The maximum value


Penalty function




Neighboring position


Neighboring position


x direction


y direction


Upstream position in x direction


Upstream position in y direction



The supports of this work by the National Natural Science Foundation of China (No. 51576053) is gratefully acknowledged. A very special acknowledgement also to the editors and referees who made important comments to improve this paper.


  1. 1.
    T.J. Hendricks, J.R. Howell, Absorption/scattering coefficients and scattering phase functions in reticulated porous ceramics. ASME J. Heat Transf. 118(1), 79–87 (1996)CrossRefGoogle Scholar
  2. 2.
    J. Rebelo Kornmeier, M. Hofmann, S. Schmidt, Non-destructive testing of satellite nozzles made of carbon fibre ceramic matrix composite, C/SiC. Mater. Charact. 58(10), 922–927 (2007)CrossRefGoogle Scholar
  3. 3.
    S. Petit, M. Duquennoy, M. Ouaftouh, F. Deneuville, M. Ourak, S. Desvaux, Non-destructive testing of ceramic balls using high frequency ultrasonic resonance spectroscopy. Ultrasonics 43(10), 802–810 (2005)CrossRefGoogle Scholar
  4. 4.
    B. Zhang, C.L. Xu, S.M. Wang, An inverse method for flue gas shielded metal surface temperature measurement based on infrared radiation. Meas. Sci. Technol. 27(7), 074002 (2016)ADSCrossRefGoogle Scholar
  5. 5.
    J.L. Gong, J.Y. Liu, L. Qin, Y. Wang, Investigation of carbon fiber reinforced polymer (CFRP) sheet with subsurface defects inspection using thermal-wave radar imaging (TWRI) based on the multi-transform technique. NDT&E Int. 62, 130–136 (2014)CrossRefGoogle Scholar
  6. 6.
    D.J.W. Klunder, E. Krioukov, F.S. Tan, T. van der Veen, H.F. Bulthuis, G. Sengo, C. Otto, H.J.W.M. Hoekstra, A. Driessen, Vertically and laterally waveguide-coupled cylindrical microresonators in Si3N4 on SiO2 technology. Appl. Phys. B 73(5–6), 603–608 (2014)ADSGoogle Scholar
  7. 7.
    G.L. Yuan, S.W. Or, J.M. Liu, Z.G. Liu, Structural transformation and ferroelectromagnetic behavior in single-phase Bi1–xNdxFeO3 multiferroic ceramics. Appl. Phys. Lett. 89(5), 052905 (2006)ADSCrossRefGoogle Scholar
  8. 8.
    Y.K. Zhu, G.Y. Tian, R.S. Lu, H. Zhang, A review of optical NDT technologies. Sensors 11(8), 7773–7798 (2011)CrossRefGoogle Scholar
  9. 9.
    J.Y. Liu, L. Qin, Q.J. Tang, Y. Wang, Experimental study of inspection on a metal plate with defect using ultrasound lock-in thermographic technique. Infrared Phys. Technol. 55(4), 284–291 (2012)ADSCrossRefGoogle Scholar
  10. 10.
    R. Dsouza, H.M. Subhash, K. Neuhaus, J. Hogan, C. Wilson, M. Leahy, 3D nondestructive testing system with an affordable multiple reference optical-delay-based optical coherence tomography. Appl. Opt. 54(18), 5634–5638 (2015)ADSCrossRefGoogle Scholar
  11. 11.
    T.H. Wei, D.J. Hagan, M.J. Sence, E.W. Van Stryland, J.W. Perry, D.R. Coulter, Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines. Appl. Phys. B 54(1), 46–51 (1992)ADSCrossRefGoogle Scholar
  12. 12.
    R.E. Alvarez, A. Macovski, Energy-selective reconstructions in X-ray computerised tomography. Phys. Med. Biol. 21(5), 733–744 (1976)CrossRefGoogle Scholar
  13. 13.
    L.-S. Chang, T.-H. Chuang, Ultrasonic testing of artificial defects in alumina ceramic. Ceram. Int. 23(4), 367–373 (1997)CrossRefGoogle Scholar
  14. 14.
    M. Ohtsu, M. Shigeishi, H. Iwase, W. Koyanagit, No access determination of crack location, type and orientation in a concrete structures by acoustic emission. Mag. Concrete Res. 43(155), 127–134 (1991)CrossRefGoogle Scholar
  15. 15.
    K.F. Schmidt, R.M. Goitia, W.A. Ellingson, W. Green, Correlation of scanning microwave interferometry and digital X-ray images for damage detection in ceramic composite armor. AIP Conf. Proc. 1430(1), 1129–1136 (2012)ADSCrossRefGoogle Scholar
  16. 16.
    S. Sfarra, D. Ambrosini, A. Paoletti, D. Paoletti, C. Ibarra-Castanedo, A. Bendada, X. Maldague, Quantitative infrared thermography (IRT) and holographic interferometry (HI): nondestructive testing (NDT) for defects detection in the silicate ceramics industry. Adv. Sci. Technol. Res. J. 68, 102–107 (2010)CrossRefGoogle Scholar
  17. 17.
    S. Pangraz, H. Simon, R. Herzer, W. Arnold, Non-destructive Evaluation of Engineering Ceramics by High-Frequency Acoustic Techniques. (Springer, Boston, 1991)CrossRefGoogle Scholar
  18. 18.
    J.Y. Liu, J.L. Gong, L. Qin, H.M. Wang, Y. Wang, Study of inspection on metal sheet with subsurface defects using linear frequency modulated ultrasound excitation thermal-wave imaging (LFM-UTWI). Infrared Phys. Technol. 62, 136–142 (2014)ADSCrossRefGoogle Scholar
  19. 19.
    D. Balageas, X. Maldague, D. Burleigh, V.P. Vavilov, B. Oswald-Tranta, J.M. Roche, C. Pradere, G.M. Carlomagno, Thermal (IR) and other NDT techniques for improved material inspection. J. Nondestr. Eval. 35(1), 18 (2016)CrossRefGoogle Scholar
  20. 20.
    J.M. Milne, P. Carter, A transient thermal method of measuring the depths of sub-surface flaws in metals. Br. J. Non-Destr. Test. 30(5), 333–336 (1988)Google Scholar
  21. 21.
    J.G. Sun, S. Erdman, L. Connolly, Measurement of delamination size and depth in ceramic matrix composites using pulsed thermal imaging, in 27th International cocoa beach conference on advanced ceramics and composites: B: ceramic engineering and science proceedings, vol. 24, no. 4 (Wiley, Hoboken, 2003), pp. 201–206Google Scholar
  22. 22.
    J.Y. Liu, Q.J. Tang, X. Liu, Y. Wang, Research on the quantitative analysis of subsurface defects for non-destructive testing by lock-in thermography. NDT&E Int. 45(1), 104–110 (2012)CrossRefGoogle Scholar
  23. 23.
    J.Y. Liu, Q.J. Tang, Y. Wang, The study of inspection on SiC coated carbon–carbon composite with subsurface defects by lock-in thermography. Compos. Sci. Technol. 72(11), 1240–1250 (2012)CrossRefGoogle Scholar
  24. 24.
    G. Busse, D. Wu, W. Karpen, Thermal wave imaging with phase sensitive modulated thermography. J. Appl. Phys. 71(8), 3962–3965 (1992)ADSCrossRefGoogle Scholar
  25. 25.
    N. Ludwig, P. Teruzzi, Heat losses and 3D diffusion phenomena for defect sizing procedures in video pulse thermography. Infrared Phys. Technol. 43(3), 297–301 (2002)ADSCrossRefGoogle Scholar
  26. 26.
    X. Maldague, A. Ziadi, M. Klein, Double pulse infrared thermography. NDT&E Int. 37(7), 559–564 (2004)CrossRefGoogle Scholar
  27. 27.
    M. Akamatsu, Z.X. Guo, Ultrafast radiative transfer characteristics in multilayer inhomogeneous 3d media subjected to a collimated short square pulse train. Heat Transf. Res. 47(7), 633–651 (2016)CrossRefGoogle Scholar
  28. 28.
    F.Q. Wang, L.X. Ma, J.Y. Tan, Z.N. Guan, L.H. Liu, Optical constant measurements of solar thermochemical reaction catalysts and optical window. Optik. 131, 323–334 (2017)CrossRefGoogle Scholar
  29. 29.
    S.M.H. Sarvari, A new approach to solve the radiative transfer equation in plane-parallel semitransparent media with variable refractive index based on the discrete transfer method. Int. Commun. Heat Mass Transf. 78, 54–59 (2016)CrossRefGoogle Scholar
  30. 30.
    J.C. Hebden, A. Gibson, T. Austin, R.M. Yusof, N. Everdell, D.T. Delpy, S.R. Arridge, J.H. Meek, J.S. Wyatt, Imaging changes in blood volume and oxygenation in the newborn infant brain using three-dimensional optical tomography. Phys. Med. Biol. 49(7), 1117–1130 (2004)CrossRefGoogle Scholar
  31. 31.
    J. Jiao, Z.X. Guo, Thermal interaction of short-pulsed laser focused beams with skin tissues. Phys. Med. Biol. 54(13), 4225–4241 (2009)CrossRefGoogle Scholar
  32. 32.
    K.Y. Li, S.L. Liu, Functional imaging of breast tissue and clinical application. Wuhan Univ. J. Nat. Sci. 11(2), 373–376 (2006)CrossRefGoogle Scholar
  33. 33.
    S.K. Wan, Z.X. Guo, Correlative studies in optical reflectance measurements of cerebral blood oxygenation. J. Quant. Spectrosc. Radiat. Transf. 98(2), 189–201 (2006)ADSCrossRefGoogle Scholar
  34. 34.
    A. Vogel, J. Noack, G. Hüttman, G. Paltauf, Mechanisms of femtosecond laser nanosurgery of cells and tissues. Appl. Phys. B 81(8), 1015–1047 (2005)ADSCrossRefGoogle Scholar
  35. 35.
    M.F. Modest, Radiative Heat Transfer. (McGraw-Hill, New York, 2003)zbMATHGoogle Scholar
  36. 36.
    B. Hunter, Z.X. Guo, Improved treatment of anisotropic scattering for ultrafast radiative transfer analysis. ASME J. Heat Transf. 137(9), 091004 (2015)CrossRefGoogle Scholar
  37. 37.
    R. Siegel, J.R. Howell, Thermal Radiation Heat Transfer, 3rd edn. (Hemisphere Publishing Corporation, Washington DC, 1992)Google Scholar
  38. 38.
    S.C. Mishra, P. Chugh, P. Kumar, K. Mitra, Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium. Int. J. Heat Mass Trasf. 49(11–12), 1820–1832 (2006)CrossRefzbMATHGoogle Scholar
  39. 39.
    M. Sakami, K. Mitra, P.F. Hsu, Analysis of light pulse transport through two-dimensional scattering and absorbing media. J. Quant. Spectrosc. Radiat. Transf. 73(2), 169–179 (2002)ADSCrossRefGoogle Scholar
  40. 40.
    S.S. Saquib, K.M. Hanson, G.S. Cunningham, Model-based image reconstruction from time-resolved diffusion data, in Proceedings of SPIE, (1997), pp. 369–380Google Scholar
  41. 41.
    J. Boulanger, A. Charette, Numerical developments for short-pulsed near infra-red laser spectroscopy. Part II: inverse treatment. J. Quant. Spectrosc. Radiat. Transf. 91(3), 297–318 (2005)ADSCrossRefGoogle Scholar
  42. 42.
    S.P. Han, A globally convergent method for nonlinear programming. J. Optim. Theory Appl. 22(3), 297–309 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    M.J.D. Powell, The Convergence of Variable Metric methods for Non-linearly Constrained Optimization Calculations. (Elsevier Inc, Academic Press Inc, University of Wisconsin, Madison, 1978), pp. 27–63Google Scholar
  44. 44.
    K. Schittkowski, The nonlinear programming method of Wilson, Han, and Powell with an augmented Lagrangian type line search function. Numer. Math. 38(1), 83–114 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    M. Fukushima, A successive quadratic programming algorithm with global and superlinear convergence properties. Math. Program. 35(3), 253–264 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    J.C. Ye, K.J. Webb, C.A. Bouman, R.P. Millane, Optical diffusion tomography by iterative-coordinate-descent optimization in a Bayesian framework. J. Opt. Soc. Am. A 16(10), 2400–2412 (1999)ADSCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.School of Energy Science and EngineeringHarbin Institute of TechnologyHarbinPeople’s Republic of China

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