Advertisement

Journal of Materials Science

, Volume 41, Issue 1, pp 147–153 | Cite as

Fredholm integral equation of the Laser Intensity Modulation Method (LIMM): Solution with the polynomial regularization and L-curve methods

  • Sidney B. LangEmail author
Article

Abstract

The Laser Intensity Modulation Method (LIMM) is widely used for the determination of the spatial distribution of polarization in polar ceramics and polymers, and space charge in non-polar polymers. The analysis of experimental data requires a solution of a Fredholm integral equation of the 1st kind. This is an ill-posed problem that has multiple and very different solutions. One of the more frequently used methods of solution is based upon Tikhonov regularization. A new method, the Polynomial Regularization Method (PRM), was developed for solving the LIMM equation with an 8th degree polynomial using smoothing to achieve a stable and optimal solution. An algorithm based upon the L-curve method (LCM) was used for the prediction of the best regularization parameter. LIMM data were simulated for an arbitrary polarization distribution and were analyzed using PRM and LCM. The calculated distribution function was in good agreement with the simulated polarization distribution. Experimental polarization distributions in a poorly poled sample of polyvinylidene fluoride (PVDF) and in a LiNbO3 bimorph, and space charge in polyethylene were analyzed. The new techniques were applied to the analysis of 3-dimensional polarization distributions.

Keywords

Space Charge Regularization Parameter Lithium Niobate Fredholm Integral Equation Polarization Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. B. LANG and D. K. DAS-GUPTA, Ferroelectrics 39 (1981) 1249.Google Scholar
  2. 2.
    Idem., J. Appl. Phys. 59 (1986) 2151.CrossRefGoogle Scholar
  3. 3.
    S. B. LANG, IEEE Trans. Dielectr. Electr. Insul. 11 (2004) 3.CrossRefGoogle Scholar
  4. 4.
    B. PLOSS, R. EMMERICH and S. BAUER, J. Appl. Phys. 72 (1992) 5363.CrossRefGoogle Scholar
  5. 5.
    S. BAUER and S. BAUER-GOGONEA, IEEE Trans. Dielec. Elec. Insul. 10 (2003) 883.CrossRefGoogle Scholar
  6. 6.
    B. L. PHILLIPS, J. Assoc. Comput. Mach. 9 (1962) 84.Google Scholar
  7. 7.
    S. B. LANG, Ferroelectrics 118 (1991) 343.Google Scholar
  8. 8.
    P. BLOβ, M. STEFFEN, H. SCHAFER, Y. GUO MAO and G. M. SESSLER, IEEE Trans. Dielec. Elec. Insul. 3 (1996) 182.CrossRefGoogle Scholar
  9. 9.
    P. BLOβ, M. STEFFEN, H. SCHAFER, G. EBERLE and W. EISENMENGER, ibid. 3 (1996) 417.CrossRefGoogle Scholar
  10. 10.
    S. B. LANG, ibid. 5 (1998) 70.CrossRefGoogle Scholar
  11. 11.
    T. SANDNER, G. SUCHANECK, R. KOEHLER, A. SUCHANECK and G. GERLACH, Integr. Ferroelectr. 46 (2002) 243.CrossRefGoogle Scholar
  12. 12.
    WOLFRAM RESEARCH, Inc., Mathematica, Version 5.0, Champaign, IL, USA (2003).Google Scholar
  13. 13.
    C. ALQUIE, C. LABURTHE TOLRA, J. LEWINER and S. B. LANG, IEEE Trans. Electr. Insul. 27 (1992) 751.CrossRefGoogle Scholar
  14. 14.
    A. MELLINGER, Meas. Sci. Technol. 15 (2004) 1347.CrossRefGoogle Scholar
  15. 15.
    P. C. HANSEN and D. P. O'LEARY, SIAM J. Sci. Comput. 14 (1993) 1487.Google Scholar
  16. 16.
    H. AHLFELDT, J. WEBJORN and G. ARVIDSSON, IEEE Photon. Tech. Lett. 3 (1991) 638.CrossRefGoogle Scholar
  17. 17.
    V. D. KUGEL and G. ROSENMAN, App. Phys. Lett. 23 (1993) 2902.CrossRefGoogle Scholar
  18. 18.
    S. B. LANG, V. D. KUGEL and G. ROSENMAN, Ferroelectrics 157 (1994) 69.Google Scholar
  19. 19.
    T. PAWLOWSKI, S. B. LANG and R. FLEMING, in Proceedings of the 2004 Conference on Electrical Insulation and Dielectric Phenonema, Boulder, CO, USA (IEEE Service Center, Piscataway, NJ, USA, 2004) p. 93.Google Scholar
  20. 20.
    A. MELLINGER, R. SINGH, M. WEGENER, W. WIRGES, R. GERHARD-MULTHAUPT and S. B. LANG, Appl. Phys. Lett. 86 (2005) 82903.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Chemical EngineeringBen-Gurion University of the NegevBeer ShevaIsrael

Personalised recommendations