Abstract

We solve the inverse scattering problem for a surface profile by measuring the intensity of the scattered near field. It was shown numerically [Opt. Lett. 20, 949 (1995)] that the image produced by the superposition of different images taken with all possible angles of incidence closely follows the surface profile. We establish a rigorous analysis of this method based on perturbation theory. Furthermore, we prove that the procedure is equivalent to illuminating the surface with incoherent light and thus has broad experimental applications.

© 1996 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Heinzelmann, D. W. Pohl, Appl. Phys. A 59, 89 (1994).
    [CrossRef]
  2. D. Van-Labeke, D. Barchiesi, J. Opt. Soc. Am. A 10, 2193 (1993).
    [CrossRef]
  3. R. Carminati, J.-J. Greffet, Opt. Commun. 116, 316 (1995).
    [CrossRef]
  4. N. García, M. Nieto-Vesperinas, Opt. Lett. 18, 2090 (1993).
    [CrossRef] [PubMed]
  5. J.-J. Greffet, A. Sentenac, R. Carminati, Opt. Commun. 116, 20 (1995).
    [CrossRef]
  6. N. García, M. Nieto-Vesperinas, Opt. Lett. 20, 949 (1995).
    [CrossRef] [PubMed]
  7. J.-J. Greffet, Opt. Commun. 72, 274 (1989).
    [CrossRef]
  8. F. de Fornel, P. M. Adam, L. Salomon, J. P. Goudonnet, A. Sentenac, R. Carminati, J.-J. Greffet, J. Opt. Soc. Am. A 13, 35 (1996).
    [CrossRef]
  9. R. Carminati, J.-J. Greffet, J. Opt. Soc. Am. A 12, 2716 (1995).
    [CrossRef]
  10. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. X.
  11. E. Wolf, J. Opt. Soc. Am. 68, 6 (1978).
    [CrossRef]
  12. G. Chabrier, F. de Fornel, E. Bourillot, L. Salomon, J. P. Goudonnet, Opt. Commun. 107, 347 (1994).
    [CrossRef]

1996 (1)

1995 (4)

R. Carminati, J.-J. Greffet, J. Opt. Soc. Am. A 12, 2716 (1995).
[CrossRef]

J.-J. Greffet, A. Sentenac, R. Carminati, Opt. Commun. 116, 20 (1995).
[CrossRef]

N. García, M. Nieto-Vesperinas, Opt. Lett. 20, 949 (1995).
[CrossRef] [PubMed]

R. Carminati, J.-J. Greffet, Opt. Commun. 116, 316 (1995).
[CrossRef]

1994 (2)

H. Heinzelmann, D. W. Pohl, Appl. Phys. A 59, 89 (1994).
[CrossRef]

G. Chabrier, F. de Fornel, E. Bourillot, L. Salomon, J. P. Goudonnet, Opt. Commun. 107, 347 (1994).
[CrossRef]

1993 (2)

1989 (1)

J.-J. Greffet, Opt. Commun. 72, 274 (1989).
[CrossRef]

1978 (1)

Adam, P. M.

Barchiesi, D.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. X.

Bourillot, E.

G. Chabrier, F. de Fornel, E. Bourillot, L. Salomon, J. P. Goudonnet, Opt. Commun. 107, 347 (1994).
[CrossRef]

Carminati, R.

Chabrier, G.

G. Chabrier, F. de Fornel, E. Bourillot, L. Salomon, J. P. Goudonnet, Opt. Commun. 107, 347 (1994).
[CrossRef]

de Fornel, F.

F. de Fornel, P. M. Adam, L. Salomon, J. P. Goudonnet, A. Sentenac, R. Carminati, J.-J. Greffet, J. Opt. Soc. Am. A 13, 35 (1996).
[CrossRef]

G. Chabrier, F. de Fornel, E. Bourillot, L. Salomon, J. P. Goudonnet, Opt. Commun. 107, 347 (1994).
[CrossRef]

García, N.

Goudonnet, J. P.

F. de Fornel, P. M. Adam, L. Salomon, J. P. Goudonnet, A. Sentenac, R. Carminati, J.-J. Greffet, J. Opt. Soc. Am. A 13, 35 (1996).
[CrossRef]

G. Chabrier, F. de Fornel, E. Bourillot, L. Salomon, J. P. Goudonnet, Opt. Commun. 107, 347 (1994).
[CrossRef]

Greffet, J.-J.

F. de Fornel, P. M. Adam, L. Salomon, J. P. Goudonnet, A. Sentenac, R. Carminati, J.-J. Greffet, J. Opt. Soc. Am. A 13, 35 (1996).
[CrossRef]

R. Carminati, J.-J. Greffet, J. Opt. Soc. Am. A 12, 2716 (1995).
[CrossRef]

J.-J. Greffet, A. Sentenac, R. Carminati, Opt. Commun. 116, 20 (1995).
[CrossRef]

R. Carminati, J.-J. Greffet, Opt. Commun. 116, 316 (1995).
[CrossRef]

J.-J. Greffet, Opt. Commun. 72, 274 (1989).
[CrossRef]

Heinzelmann, H.

H. Heinzelmann, D. W. Pohl, Appl. Phys. A 59, 89 (1994).
[CrossRef]

Nieto-Vesperinas, M.

Pohl, D. W.

H. Heinzelmann, D. W. Pohl, Appl. Phys. A 59, 89 (1994).
[CrossRef]

Salomon, L.

F. de Fornel, P. M. Adam, L. Salomon, J. P. Goudonnet, A. Sentenac, R. Carminati, J.-J. Greffet, J. Opt. Soc. Am. A 13, 35 (1996).
[CrossRef]

G. Chabrier, F. de Fornel, E. Bourillot, L. Salomon, J. P. Goudonnet, Opt. Commun. 107, 347 (1994).
[CrossRef]

Sentenac, A.

Van-Labeke, D.

Wolf, E.

E. Wolf, J. Opt. Soc. Am. 68, 6 (1978).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. X.

Appl. Phys. A (1)

H. Heinzelmann, D. W. Pohl, Appl. Phys. A 59, 89 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (4)

J.-J. Greffet, A. Sentenac, R. Carminati, Opt. Commun. 116, 20 (1995).
[CrossRef]

R. Carminati, J.-J. Greffet, Opt. Commun. 116, 316 (1995).
[CrossRef]

G. Chabrier, F. de Fornel, E. Bourillot, L. Salomon, J. P. Goudonnet, Opt. Commun. 107, 347 (1994).
[CrossRef]

J.-J. Greffet, Opt. Commun. 72, 274 (1989).
[CrossRef]

Opt. Lett. (2)

Other (1)

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. X.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Surface profile used in the numerical simulation. h = λ/40, w = λ/4, l = λ/10, z0 = 0.0625λ.

Fig. 2
Fig. 2

(a) |E|2 along the line z0 = 0.0625λ for illumination with one angle of incidence, θi = 45°. (b) |E|2 along the line z0 = 0.0625λ averaged over 43 angles of incidence between −84° and 84°. Solid curves, s polarization; dashed curves, p polarization.

Fig. 3
Fig. 3

IRF’s normalized by their peak values. z0 = λ/20. (a) One direction of incidence θi = 45°. (b) Integration over all directions of incidence. Solid curves, s polarization; dashed curves, p polarization.

Fig. 4
Fig. 4

Numerical inversion of the integrated image in Fig. 2(b).

Equations (5)

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

I ˜ ( 1 ) ( k | | , k i | | , z 0 ) = H ˜ c ( k | | , k i | | , z 0 ) S ˜ ( k | | ) ,
I ( 1 ) ( r | | , k i | | , z 0 ) = H c ( r | | - r | | , k i | | , z 0 ) S ( r | | ) d r | | .
I ( 1 ) ( r | | , z 0 ) = H in ( r | | - r | | , z 0 ) S ( r | | ) d r | | ,
E inc ( r | | , z 0 ) = e inc ( k i | | ) exp [ i k i | | · r | | + i γ ( k i | | ) z 0 ] d k i | | ,
e inc ( k i | | ) · e inc * ( k i | | ) = e inc 2 δ ( k i | | - k i | | ) .

Metrics