Abstract

We present an analytical proof of the equivalence of scanning near-field optical images of small objects obtained by two alternative operating modes: (1) scanning at a constant distance from the mean plane of the surface and recording the detected intensity (constant-height images) and (2) keeping the detected intensity constant and recording the vertical motion of the tip (constant-intensity images). Numerical simulations with homogeneous and inhomogeneous samples illustrate this result.

© 1996 Optical Society of America

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  1. H. Heinzelmann, D. Pohl, Appl. Phys. A 59, 89 (1994).
    [CrossRef]
  2. D. Courjon, K. Sarayeddine, M. Spajer, Opt. Commun. 71, 23 (1989); F. de Fornel, J.-P. Goudonnet, L. Salomon, E. Lesniewska, Proc. SPIE 1139, 77 (1989).
    [CrossRef]
  3. T. Ferrell, S. Sharp, R. Warmack, Ultramicroscopy 42–44, 408 (1992).
    [CrossRef] [PubMed]
  4. E. Betzig, M. Isaacson, A. Lewis, Appl. Phys. Lett. 51, 2088 (1987).
    [CrossRef]
  5. N. F. Van Hulst, M. H. P. Moers, B. Bolger, J. Microsc. 171, 95 (1993); F. Baida, C. Mered, D. Courjon, Microsc. Microanal. Microstruct. 5, 19 (1994 ); S. Kawata, Y. Inouye, T. Sugiura, Jpn. J. Appl. Phys. 33, L1725 (1994);R. Bachelot, P. Gleyzes, A. C. Boccara, Opt. Lett. 20, 1924 (1995).
    [CrossRef] [PubMed]
  6. R. Carminati, J.-J. Greffet, N. Garcia, M. Nieto-Vesperinas, Opt. Lett. 21, 501 (1996).
    [CrossRef] [PubMed]
  7. C. Girard, Scanning 16, 333 (1994).
    [CrossRef]
  8. D. Van Labeke, D. Barchiesi, J. Opt. Soc. Am. A 10, 2193 (1993).
    [CrossRef]
  9. R. Carminati, J.-J. Greffet, Opt. Commun. 116, 316 (1995).
    [CrossRef]
  10. J. Cites, M. F. M. Sanghadasa, C. S. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrell, J. Appl. Phys. 71, 7 (1992).
    [CrossRef]
  11. R. Carminati, J.-J. Greffet, J. Opt. Soc. Am. A 12, 2716 (1995).
    [CrossRef]
  12. J.-J. Greffet, A. Sentenac, R. Carminati, Opt. Commun. 116, 20 (1995).
    [CrossRef]
  13. J.-J. Greffet, R. Carminati, in Optics at the Nanometer Scale, M. Nieto-Vesperinas, N. Garcia, eds. (Kluwer, Dordrecht, The Netherlands, 1996), pp. 1–26.
  14. F. Pincemin, A. Sentenac, J.-J. Greffet, J.Opt. Soc. Am. A 11, 1117 (1994).
    [CrossRef]
  15. S. Bozhevolnyi, S. Bernsten, E. Bozhelvolnaya, J. Opt. Soc. Am. A 11, 609 (1994).
    [CrossRef]
  16. N. Garcia, M. Nieto-Vesperinas, Opt. Lett. 18, 2090 (1993); Opt. Lett. 20, 949 (1995).
    [CrossRef] [PubMed]

1996

1995

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]

1994

C. Girard, Scanning 16, 333 (1994).
[CrossRef]

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

F. Pincemin, A. Sentenac, J.-J. Greffet, J.Opt. Soc. Am. A 11, 1117 (1994).
[CrossRef]

S. Bozhevolnyi, S. Bernsten, E. Bozhelvolnaya, J. Opt. Soc. Am. A 11, 609 (1994).
[CrossRef]

1993

D. Van Labeke, D. Barchiesi, J. Opt. Soc. Am. A 10, 2193 (1993).
[CrossRef]

N. Garcia, M. Nieto-Vesperinas, Opt. Lett. 18, 2090 (1993); Opt. Lett. 20, 949 (1995).
[CrossRef] [PubMed]

N. F. Van Hulst, M. H. P. Moers, B. Bolger, J. Microsc. 171, 95 (1993); F. Baida, C. Mered, D. Courjon, Microsc. Microanal. Microstruct. 5, 19 (1994 ); S. Kawata, Y. Inouye, T. Sugiura, Jpn. J. Appl. Phys. 33, L1725 (1994);R. Bachelot, P. Gleyzes, A. C. Boccara, Opt. Lett. 20, 1924 (1995).
[CrossRef] [PubMed]

1992

J. Cites, M. F. M. Sanghadasa, C. S. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrell, J. Appl. Phys. 71, 7 (1992).
[CrossRef]

T. Ferrell, S. Sharp, R. Warmack, Ultramicroscopy 42–44, 408 (1992).
[CrossRef] [PubMed]

1989

D. Courjon, K. Sarayeddine, M. Spajer, Opt. Commun. 71, 23 (1989); F. de Fornel, J.-P. Goudonnet, L. Salomon, E. Lesniewska, Proc. SPIE 1139, 77 (1989).
[CrossRef]

1987

E. Betzig, M. Isaacson, A. Lewis, Appl. Phys. Lett. 51, 2088 (1987).
[CrossRef]

Barchiesi, D.

Bernsten, S.

Betzig, E.

E. Betzig, M. Isaacson, A. Lewis, Appl. Phys. Lett. 51, 2088 (1987).
[CrossRef]

Bolger, B.

N. F. Van Hulst, M. H. P. Moers, B. Bolger, J. Microsc. 171, 95 (1993); F. Baida, C. Mered, D. Courjon, Microsc. Microanal. Microstruct. 5, 19 (1994 ); S. Kawata, Y. Inouye, T. Sugiura, Jpn. J. Appl. Phys. 33, L1725 (1994);R. Bachelot, P. Gleyzes, A. C. Boccara, Opt. Lett. 20, 1924 (1995).
[CrossRef] [PubMed]

Bozhelvolnaya, E.

Bozhevolnyi, S.

Carminati, R.

R. Carminati, J.-J. Greffet, N. Garcia, M. Nieto-Vesperinas, Opt. Lett. 21, 501 (1996).
[CrossRef] [PubMed]

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, R. Carminati, in Optics at the Nanometer Scale, M. Nieto-Vesperinas, N. Garcia, eds. (Kluwer, Dordrecht, The Netherlands, 1996), pp. 1–26.

Cites, J.

J. Cites, M. F. M. Sanghadasa, C. S. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrell, J. Appl. Phys. 71, 7 (1992).
[CrossRef]

Courjon, D.

D. Courjon, K. Sarayeddine, M. Spajer, Opt. Commun. 71, 23 (1989); F. de Fornel, J.-P. Goudonnet, L. Salomon, E. Lesniewska, Proc. SPIE 1139, 77 (1989).
[CrossRef]

Ferrell, T.

T. Ferrell, S. Sharp, R. Warmack, Ultramicroscopy 42–44, 408 (1992).
[CrossRef] [PubMed]

Ferrell, T. L.

J. Cites, M. F. M. Sanghadasa, C. S. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrell, J. Appl. Phys. 71, 7 (1992).
[CrossRef]

Garcia, N.

Girard, C.

C. Girard, Scanning 16, 333 (1994).
[CrossRef]

Greffet, J.-J.

R. Carminati, J.-J. Greffet, N. Garcia, M. Nieto-Vesperinas, Opt. Lett. 21, 501 (1996).
[CrossRef] [PubMed]

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]

F. Pincemin, A. Sentenac, J.-J. Greffet, J.Opt. Soc. Am. A 11, 1117 (1994).
[CrossRef]

J.-J. Greffet, R. Carminati, in Optics at the Nanometer Scale, M. Nieto-Vesperinas, N. Garcia, eds. (Kluwer, Dordrecht, The Netherlands, 1996), pp. 1–26.

Heinzelmann, H.

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

Isaacson, M.

E. Betzig, M. Isaacson, A. Lewis, Appl. Phys. Lett. 51, 2088 (1987).
[CrossRef]

Lewis, A.

E. Betzig, M. Isaacson, A. Lewis, Appl. Phys. Lett. 51, 2088 (1987).
[CrossRef]

Moers, M. H. P.

N. F. Van Hulst, M. H. P. Moers, B. Bolger, J. Microsc. 171, 95 (1993); F. Baida, C. Mered, D. Courjon, Microsc. Microanal. Microstruct. 5, 19 (1994 ); S. Kawata, Y. Inouye, T. Sugiura, Jpn. J. Appl. Phys. 33, L1725 (1994);R. Bachelot, P. Gleyzes, A. C. Boccara, Opt. Lett. 20, 1924 (1995).
[CrossRef] [PubMed]

Nieto-Vesperinas, M.

Pincemin, F.

F. Pincemin, A. Sentenac, J.-J. Greffet, J.Opt. Soc. Am. A 11, 1117 (1994).
[CrossRef]

Pohl, D.

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

Reddick, R. C.

J. Cites, M. F. M. Sanghadasa, C. S. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrell, J. Appl. Phys. 71, 7 (1992).
[CrossRef]

Sanghadasa, M. F. M.

J. Cites, M. F. M. Sanghadasa, C. S. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrell, J. Appl. Phys. 71, 7 (1992).
[CrossRef]

Sarayeddine, K.

D. Courjon, K. Sarayeddine, M. Spajer, Opt. Commun. 71, 23 (1989); F. de Fornel, J.-P. Goudonnet, L. Salomon, E. Lesniewska, Proc. SPIE 1139, 77 (1989).
[CrossRef]

Sentenac, A.

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

F. Pincemin, A. Sentenac, J.-J. Greffet, J.Opt. Soc. Am. A 11, 1117 (1994).
[CrossRef]

Sharp, S.

T. Ferrell, S. Sharp, R. Warmack, Ultramicroscopy 42–44, 408 (1992).
[CrossRef] [PubMed]

Spajer, M.

D. Courjon, K. Sarayeddine, M. Spajer, Opt. Commun. 71, 23 (1989); F. de Fornel, J.-P. Goudonnet, L. Salomon, E. Lesniewska, Proc. SPIE 1139, 77 (1989).
[CrossRef]

Sung, C. S.

J. Cites, M. F. M. Sanghadasa, C. S. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrell, J. Appl. Phys. 71, 7 (1992).
[CrossRef]

Van Hulst, N. F.

N. F. Van Hulst, M. H. P. Moers, B. Bolger, J. Microsc. 171, 95 (1993); F. Baida, C. Mered, D. Courjon, Microsc. Microanal. Microstruct. 5, 19 (1994 ); S. Kawata, Y. Inouye, T. Sugiura, Jpn. J. Appl. Phys. 33, L1725 (1994);R. Bachelot, P. Gleyzes, A. C. Boccara, Opt. Lett. 20, 1924 (1995).
[CrossRef] [PubMed]

Van Labeke, D.

Warmack, R.

T. Ferrell, S. Sharp, R. Warmack, Ultramicroscopy 42–44, 408 (1992).
[CrossRef] [PubMed]

Warmack, R. J.

J. Cites, M. F. M. Sanghadasa, C. S. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrell, J. Appl. Phys. 71, 7 (1992).
[CrossRef]

Appl. Phys. A

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

Appl. Phys. Lett.

E. Betzig, M. Isaacson, A. Lewis, Appl. Phys. Lett. 51, 2088 (1987).
[CrossRef]

J. Appl. Phys.

J. Cites, M. F. M. Sanghadasa, C. S. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrell, J. Appl. Phys. 71, 7 (1992).
[CrossRef]

J. Microsc.

N. F. Van Hulst, M. H. P. Moers, B. Bolger, J. Microsc. 171, 95 (1993); F. Baida, C. Mered, D. Courjon, Microsc. Microanal. Microstruct. 5, 19 (1994 ); S. Kawata, Y. Inouye, T. Sugiura, Jpn. J. Appl. Phys. 33, L1725 (1994);R. Bachelot, P. Gleyzes, A. C. Boccara, Opt. Lett. 20, 1924 (1995).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

J.Opt. Soc. Am. A

F. Pincemin, A. Sentenac, J.-J. Greffet, J.Opt. Soc. Am. A 11, 1117 (1994).
[CrossRef]

Opt. Commun.

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

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

D. Courjon, K. Sarayeddine, M. Spajer, Opt. Commun. 71, 23 (1989); F. de Fornel, J.-P. Goudonnet, L. Salomon, E. Lesniewska, Proc. SPIE 1139, 77 (1989).
[CrossRef]

Opt. Lett.

Scanning

C. Girard, Scanning 16, 333 (1994).
[CrossRef]

Ultramicroscopy

T. Ferrell, S. Sharp, R. Warmack, Ultramicroscopy 42–44, 408 (1992).
[CrossRef] [PubMed]

Other

J.-J. Greffet, R. Carminati, in Optics at the Nanometer Scale, M. Nieto-Vesperinas, N. Garcia, eds. (Kluwer, Dordrecht, The Netherlands, 1996), pp. 1–26.

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Figures (3)

Fig. 1
Fig. 1

Geometry of the problem, z = S(x, y) is the surface profile, and z = f(x, y) is a constant-intensity surface.

Fig. 2
Fig. 2

Samples used in the numerical simulations: (a) Two gold particles of width w = λ/10 and height h = λ/40, embedded in a glass substrate and separated by l = λ/8. The sample is illuminated in transmission with one plane wave (λ = 633 nm; θi =45°). (b) Glass substrate with two ridges of rectangular cross section. The ridges are of height h = λ/40 and width w = λ/4 and are separated by l = λ/10. The sample is illuminated in transmission with monochromatic spatially incoherent light (λ = 633 nm).

Fig. 3
Fig. 3

(a) Constant-intensity curves (dashed curves, right-hand ordinate axis) and constant-height curves (solid curves, left-hand ordinate axis) with z0 = 0.03λ (curve 1) and z0 = 0.09λ (curve 2) and with p polarization. The sample and the illuminating field are described in Fig. 2(a). (b) Same as (a) with z0 = 0.07λ (curve 1) and z0 = 0.12λ (curve 2). The sample and the illuminating field are described in Fig. 2(b).

Equations (4)

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I ( x , y , z ) = I ( 0 ) ( z ) + I ( 1 ) ( x , y , z ) ,
I ( 0 ) [ f ( x , y ) ] + I ( 1 ) [ x , y , f ( x , y ) ] = I ( 0 ) ( z 0 ) .
d I ( 0 ) ( z 0 ) d z δ f ( x , y ) + I ( 1 ) ( x , y , z 0 ) + I ( 1 ) z ( x , y , z 0 ) δ f ( x , y ) = 0 .
f ( x , y ) = I ( 1 ) ( x , y , z 0 ) d I ( 0 ) d z ( z 0 ) + z 0 ,

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