Abstract

We introduce an inversion procedure for the characterization of a nanostructure from near-field intensity data. The method proposed is based on heuristic arguments and makes use of evolution strategies for the solution of the inverse problem as a nonlinear constrained-optimization problem. By means of some examples we illustrate the performance of our inversion method. We also discuss its possibilities and potential applications.

© 2004 Optical Society of America

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References

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  1. J.-J. Greffet, R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).
    [CrossRef]
  2. C. Girard, C. Joachim, S. Gauthier, “The physics of the near field,” Rep. Prog. Phys. 63, 893–938 (2000).
    [CrossRef]
  3. D. Courjon, C. Bainier, “Near-field microscopy and nearfield optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
    [CrossRef]
  4. A. Dereux, C. Girard, J.-C. Weeber, “Theoretical principles of near-field optical microscopies and spectroscopies,” J. Chem. Phys. 112, 7775–7789 (2000).
    [CrossRef]
  5. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
    [CrossRef]
  6. A. Taflove, M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. 23, 623–630 (1975).
    [CrossRef]
  7. J. Jin, The Finite Element Method in Electromagnetics (Wiley, New York, 1993).
  8. D. A. Christensen, “Analysis of near-field tip patterns including object interaction using finite-difference time-domain calculations,” Ultramicroscopy 57, 189–195 (1995).
    [CrossRef]
  9. H. Furukawa, S. Kawata, “Analysis of image formation in a near-field scanning optical microscope: effects of multiple scattering,” Opt. Commun. 132, 170–178 (1996).
    [CrossRef]
  10. J. P. Kottman, O. J. F. Martin, “Accurate solution of the volume-integral equation for high-permittivity scatterers,” IEEE Trans. Antennas Propag. 48, 1719–1726 (2000).
    [CrossRef]
  11. R. Fikri, Th. Grosges, D. Barchiesi, “Apertureless scanning near-field optical microscopy: the need for probe-vibration modeling,” Opt. Lett. 28, 2147–2149 (2003).
    [CrossRef] [PubMed]
  12. F. de Fornel, P. M. Adam, L. Salomon, J. P. Goudonnet, A. Sentenac, R. Carminati, J.-J. Greffet, “Analysis of image formation with a photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 35–45 (1996).
    [CrossRef]
  13. O. J. F. Martin, C. Girard, D. Dereux, “Dielectric versus topographic contrast in near-field microscopy,” J. Opt. Soc. Am. A 13, 1801–1808 (1996).
    [CrossRef]
  14. R. Carminati, J.-J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope. Concept of transfer function,” Opt. Commun. 116, 316–321 (1995).
    [CrossRef]
  15. J.-J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
    [CrossRef]
  16. R. Carminati, J.-J. Greffet, “Reconstruction of the dielectric contrast profile from near-field data,” Ultramicroscopy 61, 11–16 (1995).
    [CrossRef]
  17. D. Macı́as, G. Olague, E. R. Méndez, “Surface profile reconstruction from scattered-intensity data using evolutionary strategies,” in Applications of Evolutionary Computing, S. Cagnoni, J. Gottlieb, E. Hart, M. Middendorf, G. R. Raidl, eds. (Springer-Verlag, Berlin, 2002), pp. 233–244.
  18. R. Wehrens, M. B. Lutgarde, “Classical and nonclassical optimization methods,” in Encyclopedia of Analytical Chemistry, R. A. Meyers, ed. (Wiley, New York, 2000).
  19. J. H. Holland, Adaptation in Natural and Artificial Systems (MIT Press, Cambridge, Mass., 1992).
  20. D. S. Weile, E. Michielssen, “Genetic algorithm optimization applied to electromagnetics: a review,” IEEE Trans. Antennas Propag. 45, 343–353 (1997).
    [CrossRef]
  21. H. P. Schwefel, Evolution and Optimum Seeking (Wiley, New York, 1995).
  22. L. J. Fogel, “Autonomous automata,” Ind. Res. 4, 14–19 (1962).
  23. R. Salomon, “Evolutionary algorithms and gradient search: similarities and differences,” IEEE Trans. Evolutionary Comput. 2, 45–55 (1997).
    [CrossRef]
  24. Z. Michalewicz, Genetic Algorithms+Data Structures=Evolution Programs (Springer-Verlag, Berlin, 1996).
  25. H. G. Beyer, The Theory of Evolution Strategies (Springer-Verlag, Berlin, 2001).
  26. Th. Bäck, U. Hammel, H.-P. Schwefel, “Evolutionary computation: comments on the history and current state,” IEEE Trans. Evolutionary Computation. 1, 3–17 (1997).
    [CrossRef]
  27. D. Van Labeke, D. Barchiesi, “Scanning tunneling optical microscopy: a theoretical macroscopic approach,” J. Opt. Soc. Am. A 9, 732–739 (1992).
    [CrossRef]
  28. J. Sjibers, P. Scheunders, N. Bonnet, D. Van Dyck, E. Raman, “Quantification and improvement of the signal-to-noise ratio in a magnetic resonance,” Magn. Reson. Imaging 14, 1157–1163 (1996).
    [CrossRef]

2003 (1)

2000 (3)

C. Girard, C. Joachim, S. Gauthier, “The physics of the near field,” Rep. Prog. Phys. 63, 893–938 (2000).
[CrossRef]

A. Dereux, C. Girard, J.-C. Weeber, “Theoretical principles of near-field optical microscopies and spectroscopies,” J. Chem. Phys. 112, 7775–7789 (2000).
[CrossRef]

J. P. Kottman, O. J. F. Martin, “Accurate solution of the volume-integral equation for high-permittivity scatterers,” IEEE Trans. Antennas Propag. 48, 1719–1726 (2000).
[CrossRef]

1997 (4)

R. Salomon, “Evolutionary algorithms and gradient search: similarities and differences,” IEEE Trans. Evolutionary Comput. 2, 45–55 (1997).
[CrossRef]

Th. Bäck, U. Hammel, H.-P. Schwefel, “Evolutionary computation: comments on the history and current state,” IEEE Trans. Evolutionary Computation. 1, 3–17 (1997).
[CrossRef]

J.-J. Greffet, R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).
[CrossRef]

D. S. Weile, E. Michielssen, “Genetic algorithm optimization applied to electromagnetics: a review,” IEEE Trans. Antennas Propag. 45, 343–353 (1997).
[CrossRef]

1996 (4)

F. de Fornel, P. M. Adam, L. Salomon, J. P. Goudonnet, A. Sentenac, R. Carminati, J.-J. Greffet, “Analysis of image formation with a photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 35–45 (1996).
[CrossRef]

O. J. F. Martin, C. Girard, D. Dereux, “Dielectric versus topographic contrast in near-field microscopy,” J. Opt. Soc. Am. A 13, 1801–1808 (1996).
[CrossRef]

H. Furukawa, S. Kawata, “Analysis of image formation in a near-field scanning optical microscope: effects of multiple scattering,” Opt. Commun. 132, 170–178 (1996).
[CrossRef]

J. Sjibers, P. Scheunders, N. Bonnet, D. Van Dyck, E. Raman, “Quantification and improvement of the signal-to-noise ratio in a magnetic resonance,” Magn. Reson. Imaging 14, 1157–1163 (1996).
[CrossRef]

1995 (4)

R. Carminati, J.-J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope. Concept of transfer function,” Opt. Commun. 116, 316–321 (1995).
[CrossRef]

J.-J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
[CrossRef]

R. Carminati, J.-J. Greffet, “Reconstruction of the dielectric contrast profile from near-field data,” Ultramicroscopy 61, 11–16 (1995).
[CrossRef]

D. A. Christensen, “Analysis of near-field tip patterns including object interaction using finite-difference time-domain calculations,” Ultramicroscopy 57, 189–195 (1995).
[CrossRef]

1994 (1)

D. Courjon, C. Bainier, “Near-field microscopy and nearfield optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
[CrossRef]

1992 (1)

1975 (1)

A. Taflove, M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. 23, 623–630 (1975).
[CrossRef]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

1962 (1)

L. J. Fogel, “Autonomous automata,” Ind. Res. 4, 14–19 (1962).

Adam, P. M.

Bäck, Th.

Th. Bäck, U. Hammel, H.-P. Schwefel, “Evolutionary computation: comments on the history and current state,” IEEE Trans. Evolutionary Computation. 1, 3–17 (1997).
[CrossRef]

Bainier, C.

D. Courjon, C. Bainier, “Near-field microscopy and nearfield optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
[CrossRef]

Barchiesi, D.

Beyer, H. G.

H. G. Beyer, The Theory of Evolution Strategies (Springer-Verlag, Berlin, 2001).

Bonnet, N.

J. Sjibers, P. Scheunders, N. Bonnet, D. Van Dyck, E. Raman, “Quantification and improvement of the signal-to-noise ratio in a magnetic resonance,” Magn. Reson. Imaging 14, 1157–1163 (1996).
[CrossRef]

Brodwin, M. E.

A. Taflove, M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. 23, 623–630 (1975).
[CrossRef]

Carminati, R.

J.-J. Greffet, R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).
[CrossRef]

F. de Fornel, P. M. Adam, L. Salomon, J. P. Goudonnet, A. Sentenac, R. Carminati, J.-J. Greffet, “Analysis of image formation with a photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 35–45 (1996).
[CrossRef]

R. Carminati, J.-J. Greffet, “Reconstruction of the dielectric contrast profile from near-field data,” Ultramicroscopy 61, 11–16 (1995).
[CrossRef]

R. Carminati, J.-J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope. Concept of transfer function,” Opt. Commun. 116, 316–321 (1995).
[CrossRef]

J.-J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
[CrossRef]

Christensen, D. A.

D. A. Christensen, “Analysis of near-field tip patterns including object interaction using finite-difference time-domain calculations,” Ultramicroscopy 57, 189–195 (1995).
[CrossRef]

Courjon, D.

D. Courjon, C. Bainier, “Near-field microscopy and nearfield optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
[CrossRef]

de Fornel, F.

Dereux, A.

A. Dereux, C. Girard, J.-C. Weeber, “Theoretical principles of near-field optical microscopies and spectroscopies,” J. Chem. Phys. 112, 7775–7789 (2000).
[CrossRef]

Dereux, D.

Fikri, R.

Fogel, L. J.

L. J. Fogel, “Autonomous automata,” Ind. Res. 4, 14–19 (1962).

Furukawa, H.

H. Furukawa, S. Kawata, “Analysis of image formation in a near-field scanning optical microscope: effects of multiple scattering,” Opt. Commun. 132, 170–178 (1996).
[CrossRef]

Gauthier, S.

C. Girard, C. Joachim, S. Gauthier, “The physics of the near field,” Rep. Prog. Phys. 63, 893–938 (2000).
[CrossRef]

Girard, C.

C. Girard, C. Joachim, S. Gauthier, “The physics of the near field,” Rep. Prog. Phys. 63, 893–938 (2000).
[CrossRef]

A. Dereux, C. Girard, J.-C. Weeber, “Theoretical principles of near-field optical microscopies and spectroscopies,” J. Chem. Phys. 112, 7775–7789 (2000).
[CrossRef]

O. J. F. Martin, C. Girard, D. Dereux, “Dielectric versus topographic contrast in near-field microscopy,” J. Opt. Soc. Am. A 13, 1801–1808 (1996).
[CrossRef]

Goudonnet, J. P.

Greffet, J.-J.

J.-J. Greffet, R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).
[CrossRef]

F. de Fornel, P. M. Adam, L. Salomon, J. P. Goudonnet, A. Sentenac, R. Carminati, J.-J. Greffet, “Analysis of image formation with a photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 35–45 (1996).
[CrossRef]

R. Carminati, J.-J. Greffet, “Reconstruction of the dielectric contrast profile from near-field data,” Ultramicroscopy 61, 11–16 (1995).
[CrossRef]

R. Carminati, J.-J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope. Concept of transfer function,” Opt. Commun. 116, 316–321 (1995).
[CrossRef]

J.-J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
[CrossRef]

Grosges, Th.

Hammel, U.

Th. Bäck, U. Hammel, H.-P. Schwefel, “Evolutionary computation: comments on the history and current state,” IEEE Trans. Evolutionary Computation. 1, 3–17 (1997).
[CrossRef]

Holland, J. H.

J. H. Holland, Adaptation in Natural and Artificial Systems (MIT Press, Cambridge, Mass., 1992).

Jin, J.

J. Jin, The Finite Element Method in Electromagnetics (Wiley, New York, 1993).

Joachim, C.

C. Girard, C. Joachim, S. Gauthier, “The physics of the near field,” Rep. Prog. Phys. 63, 893–938 (2000).
[CrossRef]

Kawata, S.

H. Furukawa, S. Kawata, “Analysis of image formation in a near-field scanning optical microscope: effects of multiple scattering,” Opt. Commun. 132, 170–178 (1996).
[CrossRef]

Kottman, J. P.

J. P. Kottman, O. J. F. Martin, “Accurate solution of the volume-integral equation for high-permittivity scatterers,” IEEE Trans. Antennas Propag. 48, 1719–1726 (2000).
[CrossRef]

Lutgarde, M. B.

R. Wehrens, M. B. Lutgarde, “Classical and nonclassical optimization methods,” in Encyclopedia of Analytical Chemistry, R. A. Meyers, ed. (Wiley, New York, 2000).

Maci´as, D.

D. Macı́as, G. Olague, E. R. Méndez, “Surface profile reconstruction from scattered-intensity data using evolutionary strategies,” in Applications of Evolutionary Computing, S. Cagnoni, J. Gottlieb, E. Hart, M. Middendorf, G. R. Raidl, eds. (Springer-Verlag, Berlin, 2002), pp. 233–244.

Martin, O. J. F.

J. P. Kottman, O. J. F. Martin, “Accurate solution of the volume-integral equation for high-permittivity scatterers,” IEEE Trans. Antennas Propag. 48, 1719–1726 (2000).
[CrossRef]

O. J. F. Martin, C. Girard, D. Dereux, “Dielectric versus topographic contrast in near-field microscopy,” J. Opt. Soc. Am. A 13, 1801–1808 (1996).
[CrossRef]

Méndez, E. R.

D. Macı́as, G. Olague, E. R. Méndez, “Surface profile reconstruction from scattered-intensity data using evolutionary strategies,” in Applications of Evolutionary Computing, S. Cagnoni, J. Gottlieb, E. Hart, M. Middendorf, G. R. Raidl, eds. (Springer-Verlag, Berlin, 2002), pp. 233–244.

Michalewicz, Z.

Z. Michalewicz, Genetic Algorithms+Data Structures=Evolution Programs (Springer-Verlag, Berlin, 1996).

Michielssen, E.

D. S. Weile, E. Michielssen, “Genetic algorithm optimization applied to electromagnetics: a review,” IEEE Trans. Antennas Propag. 45, 343–353 (1997).
[CrossRef]

Olague, G.

D. Macı́as, G. Olague, E. R. Méndez, “Surface profile reconstruction from scattered-intensity data using evolutionary strategies,” in Applications of Evolutionary Computing, S. Cagnoni, J. Gottlieb, E. Hart, M. Middendorf, G. R. Raidl, eds. (Springer-Verlag, Berlin, 2002), pp. 233–244.

Raman, E.

J. Sjibers, P. Scheunders, N. Bonnet, D. Van Dyck, E. Raman, “Quantification and improvement of the signal-to-noise ratio in a magnetic resonance,” Magn. Reson. Imaging 14, 1157–1163 (1996).
[CrossRef]

Salomon, L.

Salomon, R.

R. Salomon, “Evolutionary algorithms and gradient search: similarities and differences,” IEEE Trans. Evolutionary Comput. 2, 45–55 (1997).
[CrossRef]

Scheunders, P.

J. Sjibers, P. Scheunders, N. Bonnet, D. Van Dyck, E. Raman, “Quantification and improvement of the signal-to-noise ratio in a magnetic resonance,” Magn. Reson. Imaging 14, 1157–1163 (1996).
[CrossRef]

Schwefel, H. P.

H. P. Schwefel, Evolution and Optimum Seeking (Wiley, New York, 1995).

Schwefel, H.-P.

Th. Bäck, U. Hammel, H.-P. Schwefel, “Evolutionary computation: comments on the history and current state,” IEEE Trans. Evolutionary Computation. 1, 3–17 (1997).
[CrossRef]

Sentenac, A.

Sjibers, J.

J. Sjibers, P. Scheunders, N. Bonnet, D. Van Dyck, E. Raman, “Quantification and improvement of the signal-to-noise ratio in a magnetic resonance,” Magn. Reson. Imaging 14, 1157–1163 (1996).
[CrossRef]

Taflove, A.

A. Taflove, M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. 23, 623–630 (1975).
[CrossRef]

Van Dyck, D.

J. Sjibers, P. Scheunders, N. Bonnet, D. Van Dyck, E. Raman, “Quantification and improvement of the signal-to-noise ratio in a magnetic resonance,” Magn. Reson. Imaging 14, 1157–1163 (1996).
[CrossRef]

Van Labeke, D.

Weeber, J.-C.

A. Dereux, C. Girard, J.-C. Weeber, “Theoretical principles of near-field optical microscopies and spectroscopies,” J. Chem. Phys. 112, 7775–7789 (2000).
[CrossRef]

Wehrens, R.

R. Wehrens, M. B. Lutgarde, “Classical and nonclassical optimization methods,” in Encyclopedia of Analytical Chemistry, R. A. Meyers, ed. (Wiley, New York, 2000).

Weile, D. S.

D. S. Weile, E. Michielssen, “Genetic algorithm optimization applied to electromagnetics: a review,” IEEE Trans. Antennas Propag. 45, 343–353 (1997).
[CrossRef]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

IEEE Trans. Antennas Propag. (3)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

J. P. Kottman, O. J. F. Martin, “Accurate solution of the volume-integral equation for high-permittivity scatterers,” IEEE Trans. Antennas Propag. 48, 1719–1726 (2000).
[CrossRef]

D. S. Weile, E. Michielssen, “Genetic algorithm optimization applied to electromagnetics: a review,” IEEE Trans. Antennas Propag. 45, 343–353 (1997).
[CrossRef]

IEEE Trans. Evolutionary Comput. (1)

R. Salomon, “Evolutionary algorithms and gradient search: similarities and differences,” IEEE Trans. Evolutionary Comput. 2, 45–55 (1997).
[CrossRef]

IEEE Trans. Evolutionary Computation. (1)

Th. Bäck, U. Hammel, H.-P. Schwefel, “Evolutionary computation: comments on the history and current state,” IEEE Trans. Evolutionary Computation. 1, 3–17 (1997).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

A. Taflove, M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. 23, 623–630 (1975).
[CrossRef]

Ind. Res. (1)

L. J. Fogel, “Autonomous automata,” Ind. Res. 4, 14–19 (1962).

J. Chem. Phys. (1)

A. Dereux, C. Girard, J.-C. Weeber, “Theoretical principles of near-field optical microscopies and spectroscopies,” J. Chem. Phys. 112, 7775–7789 (2000).
[CrossRef]

J. Opt. Soc. Am. A (3)

Magn. Reson. Imaging (1)

J. Sjibers, P. Scheunders, N. Bonnet, D. Van Dyck, E. Raman, “Quantification and improvement of the signal-to-noise ratio in a magnetic resonance,” Magn. Reson. Imaging 14, 1157–1163 (1996).
[CrossRef]

Opt. Commun. (3)

H. Furukawa, S. Kawata, “Analysis of image formation in a near-field scanning optical microscope: effects of multiple scattering,” Opt. Commun. 132, 170–178 (1996).
[CrossRef]

R. Carminati, J.-J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope. Concept of transfer function,” Opt. Commun. 116, 316–321 (1995).
[CrossRef]

J.-J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
[CrossRef]

Opt. Lett. (1)

Prog. Surf. Sci. (1)

J.-J. Greffet, R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).
[CrossRef]

Rep. Prog. Phys. (2)

C. Girard, C. Joachim, S. Gauthier, “The physics of the near field,” Rep. Prog. Phys. 63, 893–938 (2000).
[CrossRef]

D. Courjon, C. Bainier, “Near-field microscopy and nearfield optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
[CrossRef]

Ultramicroscopy (2)

R. Carminati, J.-J. Greffet, “Reconstruction of the dielectric contrast profile from near-field data,” Ultramicroscopy 61, 11–16 (1995).
[CrossRef]

D. A. Christensen, “Analysis of near-field tip patterns including object interaction using finite-difference time-domain calculations,” Ultramicroscopy 57, 189–195 (1995).
[CrossRef]

Other (7)

H. P. Schwefel, Evolution and Optimum Seeking (Wiley, New York, 1995).

Z. Michalewicz, Genetic Algorithms+Data Structures=Evolution Programs (Springer-Verlag, Berlin, 1996).

H. G. Beyer, The Theory of Evolution Strategies (Springer-Verlag, Berlin, 2001).

D. Macı́as, G. Olague, E. R. Méndez, “Surface profile reconstruction from scattered-intensity data using evolutionary strategies,” in Applications of Evolutionary Computing, S. Cagnoni, J. Gottlieb, E. Hart, M. Middendorf, G. R. Raidl, eds. (Springer-Verlag, Berlin, 2002), pp. 233–244.

R. Wehrens, M. B. Lutgarde, “Classical and nonclassical optimization methods,” in Encyclopedia of Analytical Chemistry, R. A. Meyers, ed. (Wiley, New York, 2000).

J. H. Holland, Adaptation in Natural and Artificial Systems (MIT Press, Cambridge, Mass., 1992).

J. Jin, The Finite Element Method in Electromagnetics (Wiley, New York, 1993).

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Figures (6)

Fig. 1
Fig. 1

Flux diagram of an evolution strategy.

Fig. 2
Fig. 2

Geometry of the near-field problem.

Fig. 3
Fig. 3

Near-field scattered intensity that serves as the input data for the inversion algorithm: (a) p polarization, (b) s polarization. The crosses correspond to the image generated with the retrieved parameters shown in Table 1.

Fig. 4
Fig. 4

Convergence behavior for one realization of the ES (μ/ρ, λ) when the refractive index of the sample is n(d)=1.51+i0.1.

Fig. 5
Fig. 5

Intensity distribution generated with recovered parameters when the index of refraction of the sample is n(d)=1.51+i0.01. The original scattered intensity is depicted by a solid curve. The crosses correspond to the parameters obtained with the ES (μ/ρ, λ). (a) p polarization, (b) s polarization.

Fig. 6
Fig. 6

(a) Noisy image IN(p)(x1), (b) images Ie(p)(x1) (dotted curve) and I(p)(x1) (solid curve), (c) noisy image IN(s)(x1), (d) images Ie(s)(x1) (dotted curve) and I(s)(x1) (solid curve). The images Ie(p,s)(x1) and I(p,s)(x1) are respectively generated with the estimated and the target parameters shown in Tables 3 and 1.

Tables (3)

Tables Icon

Table 1 Retrieved Parameters Corresponding to Sample 1

Tables Icon

Table 2 Retrieved Parameters Corresponding to Sample 2

Tables Icon

Table 3 Parameters Estimated from Noisy Input Data (Sample 1)

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

f(p(c))=-[I(x1)-I(c)(x1|p(c))]2dx1.
Pμ(g)={e1(g), e2(g),, eμ(g)},
P˜λ(g)={e˜1(g), e˜2(g),, e˜λ(g)},
pl,i(g)ρ=1ρr=1ρpr,i(g),
σ˜l,i=σl,iexp[τNl(0)(0, 1)+τNi(1)(0, 1)],
p˜l,i=pl,i+σ˜l,iNi(2)(0, 1),
τ(2n)-1,τ(2n)-1,
IN(p,s)(x1)=I(p,s)(x1)+N(x1),
P(N)=12πσN2exp-N22σN2,

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