[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Parameter Identification in Photothermal Imaging

  • Published:
Journal of Mathematical Imaging and Vision Aims and scope Submit manuscript

Abstract

We propose a technique to reconstruct the geometry of inclusions and their material parameters in thermal scattering near surfaces. The imaging problem is reformulated as a constrained optimization problem with a finite number of stationary constraints. The unknown domains and their parameters are the design variables. A descent method combining topological derivative analysis to find improved guesses of the objects and gradient iterations to correct their material parameters provides reasonable reconstructions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Allaire, G., de Gournay, F., Jouve, F., Toader, A.M.: Structural optimization using topological and shape sensitivity via a level-set method. Control Cybern. 34, 59–80 (2005)

    MATH  Google Scholar 

  2. Almond, D.P., Patel, P.M.: Photothermal Science and Techniques. Chapman and Hall, London (1996)

    Google Scholar 

  3. Banks, H.T., Kojima, F.: Boundary shape identification problems in two-dimensional domains related to thermal testing of materials. Q. Appl. Math. 47, 273–293 (1989)

    MATH  MathSciNet  Google Scholar 

  4. Banks, H.T., Kojima, F., Winfree, W.P.: Boundary estimation problems arising in thermal tomography. Inverse Probl. 6, 897–921 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cakoni, F., Colton, D., Monk, P.: The determination of the surface conductivity of a partially coated dielectric. SIAM J. Appl. Math. 65, 767–789 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Carpio, A., Rapún, M.-L.: Solving inverse inhomogeneous problems by topological derivative methods. Inverse Probl. 24, 045014 (2008)

    Article  Google Scholar 

  7. Carpio, A., Rapún, M.-L.: Domain reconstruction by photothermal techniques. J. Comput. Phys. 227, 8083–8106 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Carpio, A., Rapún, M.-L.: Hybrid topological derivative and gradient based methods for electrical impedance tomography. Inverse Probl. 28, 095010 (2012)

    Article  Google Scholar 

  9. Costabel, M., Stephan, E.: A direct boundary integral equation method for transmission problems. J. Math. Anal. Appl. 106, 367–413 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  10. Elden, L., Berntsson, F., Reginska, T.: Wavelet and Fourier methods for solving the sideways heat equation. SIAM J. Sci. Comput. 21, 2187–2205 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  11. Feijoo, G.R.: A new method in inverse scattering based on the topological derivative. Inverse Probl. 20, 1819–1840 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  12. Garrido, F., Salazar, A.: Thermal wave scattering from spheres. J. Appl. Phys. 95, 140–149 (2004)

    Article  Google Scholar 

  13. Guzina, B.B., Bonnet, M.: Small-inclusion asymptotic of misfit functionals for inverse problems in acoustics. Inverse Probl. 22, 1761–1785 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  14. Guzina, B.B., Chikichev, I.: From imaging to material identification: a generalized concept of topological sensitivity. J. Mech. Phys. Solids 55, 245–279 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  15. Heath, D.M., Welch, C.S., Winfree, W.P.: Quantitative thermal diffusivity measurements of composites. In: Review of Progress in Quantitative Non-Destructive Evaluation, vol. 5B, pp. 1125–1132. Plenum, New York (1986)

    Google Scholar 

  16. Hohage, T., Rapún, M.-L., Sayas, F.-J.: Detecting corrosion using thermal measurements. Inverse Probl. 23, 53–72 (2007)

    Article  MATH  Google Scholar 

  17. Hohage, T., Sayas, F.-J.: Numerical approximation of a heat diffusion problem by boundary element methods using the Laplace transform. Numer. Math. 102, 67–92 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  18. Isakov, V.: Inverse Problems for Partial Differential Equations. Springer, New York (1998)

    Book  MATH  Google Scholar 

  19. López-Fernández, M., Palencia, C.: On the numerical inversion of the Laplace transform of certain holomorphic mappings. Appl. Numer. Math. 51, 289–303 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  20. Mandelis, A.: Diffusion-Wave Fields. Mathematical Methods and Green Functions. Springer, New York (2001)

    Book  MATH  Google Scholar 

  21. Mandelis, A.: Diffusion waves and their uses. Phys. Today 53, 29–34 (2000)

    Article  Google Scholar 

  22. Nicolaides, L., Mandelis, A.: Image-enhanced thermal-wave slice diffraction tomography with numerically simulated reconstructions. Inverse Probl. 13, 1393–1412 (1997)

    Article  MATH  Google Scholar 

  23. Ocáriz, A., Sánchez-Lavega, A., Salazar, A.: Photothermal study of subsurface cylindrical structures II. Experimental results. J. Appl. Phys. 81, 7561–7566 (1997)

    Article  Google Scholar 

  24. Rapún, M.-L., Sayas, F.-J.: Boundary integral approximation of a heat diffusion problem in time-harmonic regime. Numer. Algorithms 41, 127–160 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  25. Rapún, M.-L., Sayas, F.-J.: Boundary element simulation of thermal waves. Arch. Comput. Methods Eng. 14, 3–46 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  26. Salazar, A., Sánchez-Lavega, A., Celorrio, R.: Scattering of cylindrical thermal waves in fiber composites: in-plane thermal diffusivity. J. Appl. Phys. 93, 4536–4542 (2003)

    Article  Google Scholar 

  27. Terrón, J.M., Salazar, A., Sánchez-Lavega, A.: General solution for the thermal wave scattering in fiber composites. J. Appl. Phys. 91, 1087–1098 (2002)

    Article  Google Scholar 

Download references

Acknowledgements

The authors are partially supported by the Spanish Government research project TRA2010–18054 and the Spanish Ministerio de Economia y Competitividad Grants No. FIS2011-28838-C02-02, and No. FIS2010-22438-E.

Author information

Authors and Affiliations

  1. Dept. Matemática Aplicada, Universidad Complutense de Madrid, Madrid, Spain

    A. Carpio

  2. Dept. Fundamentos Matemáticos, ETSI Aeronáuticos, Universidad Politécnica de Madrid, Madrid, Spain

    M.-L. Rapún

Authors
  1. A. Carpio
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M.-L. Rapún
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M.-L. Rapún.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Carpio, A., Rapún, ML. Parameter Identification in Photothermal Imaging. J Math Imaging Vis 49, 273–288 (2014). https://doi.org/10.1007/s10851-013-0459-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10851-013-0459-y

Keywords

Search

Navigation