Abstract

We determine a set of experimental parameters through the application of an evolutionary inversion procedure. The input to the algorithm is experimental apertureless scanning near-field optical microscope data. The performance of our inversion procedure is assessed by means of a comparison with a nonevolutionary technique.

© 2005 Optical Society of America

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References

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  1. D. Macías, A. Vial, and D. Barchiesi, J. Opt. Soc. Am. A 21, 1465 (2004).
    [CrossRef]
  2. S. Aubert, A. Bruyant, S. Blaize, R. Bachelot, G. Lerondel, S. Hudlet, and P. Royer, J. Opt. Soc. Am. B 20, 2117 (2003).
    [CrossRef]
  3. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, 1972).
  4. M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).
  5. R. Fikri, D. Barchiesi, F. H’Dhili, R. Bachelot, A. Vial, and P. Royer, Opt. Commun. 221, 13 (2003).
    [CrossRef]
  6. J. Nelder and R. Mead, Comput. J. 7, 308 (1965).
    [CrossRef]
  7. M. Wright, in Numerical Analysis 1995, D. F. Griffiths and G. A. Watson, eds. (Addison-Wesley, 1996), pp. 191–208.
  8. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77:?The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992).

2004 (1)

2003 (2)

S. Aubert, A. Bruyant, S. Blaize, R. Bachelot, G. Lerondel, S. Hudlet, and P. Royer, J. Opt. Soc. Am. B 20, 2117 (2003).
[CrossRef]

R. Fikri, D. Barchiesi, F. H’Dhili, R. Bachelot, A. Vial, and P. Royer, Opt. Commun. 221, 13 (2003).
[CrossRef]

1965 (1)

J. Nelder and R. Mead, Comput. J. 7, 308 (1965).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, 1972).

Aubert, S.

Bachelot, R.

S. Aubert, A. Bruyant, S. Blaize, R. Bachelot, G. Lerondel, S. Hudlet, and P. Royer, J. Opt. Soc. Am. B 20, 2117 (2003).
[CrossRef]

R. Fikri, D. Barchiesi, F. H’Dhili, R. Bachelot, A. Vial, and P. Royer, Opt. Commun. 221, 13 (2003).
[CrossRef]

Barchiesi, D.

D. Macías, A. Vial, and D. Barchiesi, J. Opt. Soc. Am. A 21, 1465 (2004).
[CrossRef]

R. Fikri, D. Barchiesi, F. H’Dhili, R. Bachelot, A. Vial, and P. Royer, Opt. Commun. 221, 13 (2003).
[CrossRef]

Blaize, S.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

Bruyant, A.

Fikri, R.

R. Fikri, D. Barchiesi, F. H’Dhili, R. Bachelot, A. Vial, and P. Royer, Opt. Commun. 221, 13 (2003).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77:?The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992).

H’Dhili, F.

R. Fikri, D. Barchiesi, F. H’Dhili, R. Bachelot, A. Vial, and P. Royer, Opt. Commun. 221, 13 (2003).
[CrossRef]

Hudlet, S.

Lerondel, G.

Macías, D.

Mead, R.

J. Nelder and R. Mead, Comput. J. 7, 308 (1965).
[CrossRef]

Nelder, J.

J. Nelder and R. Mead, Comput. J. 7, 308 (1965).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77:?The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992).

Royer, P.

R. Fikri, D. Barchiesi, F. H’Dhili, R. Bachelot, A. Vial, and P. Royer, Opt. Commun. 221, 13 (2003).
[CrossRef]

S. Aubert, A. Bruyant, S. Blaize, R. Bachelot, G. Lerondel, S. Hudlet, and P. Royer, J. Opt. Soc. Am. B 20, 2117 (2003).
[CrossRef]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, 1972).

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77:?The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77:?The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992).

Vial, A.

D. Macías, A. Vial, and D. Barchiesi, J. Opt. Soc. Am. A 21, 1465 (2004).
[CrossRef]

R. Fikri, D. Barchiesi, F. H’Dhili, R. Bachelot, A. Vial, and P. Royer, Opt. Commun. 221, 13 (2003).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

Wright, M.

M. Wright, in Numerical Analysis 1995, D. F. Griffiths and G. A. Watson, eds. (Addison-Wesley, 1996), pp. 191–208.

Comput. J. (1)

J. Nelder and R. Mead, Comput. J. 7, 308 (1965).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

R. Fikri, D. Barchiesi, F. H’Dhili, R. Bachelot, A. Vial, and P. Royer, Opt. Commun. 221, 13 (2003).
[CrossRef]

Other (4)

M. Wright, in Numerical Analysis 1995, D. F. Griffiths and G. A. Watson, eds. (Addison-Wesley, 1996), pp. 191–208.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77:?The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, 1972).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

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Figures (2)

Fig. 1
Fig. 1

(a) Experimental data from Ref. [2] (gray solid curve) and predicted approach curves (solid, dashed, and dotted curves) obtained through Eq. (3) (see text for details). Histograms corresponding to the frequency of convergence to an optimal solution when (b) the termination criterion is the maximum number of iterations g = 100 , (c) the termination criterion is the relative difference Δ e = 10 6 , (d) the inverse problem is solved by means of the Simplex algorithm.

Fig. 2
Fig. 2

Fitness functional as a function of the amplitude of vibration A and the angle of incidence θ i . The local minimum shows the uniqueness of the solution and the performance of the evolutionary approach.

Tables (1)

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Table 1 Parameters Retrieved from the Experimental Approach Curve Above a Dark Fringe a

Equations (4)

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min s ( e ) s ( t ) ( p ( 0 ) ) 2 2 ,
subject to l < p ( 0 ) < u ,
s ( z 0 , p ( 0 ) ) = α exp ( 2 z D p ) I 1 ( 2 ζ D p ) + 2 β cos ( ϕ t ) exp ( z D p ) I 1 ( ζ D p ) + d ,
ζ = { A if z 0 A , z 0 otherwise }

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