Abstract

We demonstrate a solution to the problem pertaining to the reconstruction of the profile of an interface separating two media of different refractive index, using near-field scattered intensity measurements. This is achieved by integration of the intensities of the scattered near fields over several angles of incidence, hence producing an effective incoherent source on the surface.

© 1995 Optical Society of America

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References

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  1. D. Gabor, Proc. R. Soc. London Ser. A 197, 454 (1949).
    [CrossRef]
  2. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 8, p. 198.
  3. E. Wolf, Opt. Commun. 1, 153 (1969); R. P. Porter, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27, pp. 315–397.
    [CrossRef]
  4. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991), Chap. 9, p. 322.
  5. R. P. Millane, J. Opt. Soc. Am. A 7, 394 (1990).
    [CrossRef]
  6. J. R. Fienup, in International Trends in Optics, J. W. Goodman, ed. (Academic, New York, 1991), pp. 407–422.
  7. N. Garcia, M. Nieto-Vesperinas, Opt. Lett. 18, 2090 (1993)l
    [CrossRef] [PubMed]
  8. N. Garcia, M. Nieto-Vesperinas, Phys. Rev. Lett. 71, 3645 (1993).
    [CrossRef] [PubMed]
  9. N. Garcia, N. Cabrera, Phys. Rev. B 18, 576 (1978).
    [CrossRef]
  10. D. Marcuse, Light Transmission Optics, 2nd ed. (Van Nostrand Reinhold, New York, 1982), Chap. 6, p. 296.
  11. J. A. de Santo, G. S. Brown, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1986), Vol. 23, pp. 2–62; M. Nieto-Vesperinas, J. C. Dainty, eds., Scattering in Volumes and Surfaces (North-Holland, Amsterdam, 1990); J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, London, 1991); R. J. Wombell, J. A. de Santo, J. Opt. Soc. Am. A 8, 1892 (1991).
    [CrossRef]
  12. D. W. Pohl, W. Denk, M. Lanz, Appl. Phys. Lett. 44, 651 (1984); D. W. Pohl, in Advances in Optical and Electron Microscopy, C. J. R. Sheppard, T. Mulvey, eds. (Academic, New York, 1990), pp. 243–312; D. W. Pohl, D. Courjon, Near Field Optics, Vol. 242 of NATO ASI Series (Kluwer, Dordrecht, The Netherlands, 1992).
    [CrossRef]
  13. E. Betzig, A. Harootunian, A. Lewis, M. Isaacson, Appl. Opt. 25, 1890 (1986); E. Betzig, J. K. Trautman, Science 257, 189 (1992).
    [CrossRef] [PubMed]
  14. E. Wolf, M. Nieto-Vesperinas, J. Opt. Soc. Am. A 2, 886 (1985).
    [CrossRef]
  15. R. F. Millar, Proc. Cambridge Philos. Soc. 65, 773 (1969).
    [CrossRef]

1993 (2)

N. Garcia, M. Nieto-Vesperinas, Opt. Lett. 18, 2090 (1993)l
[CrossRef] [PubMed]

N. Garcia, M. Nieto-Vesperinas, Phys. Rev. Lett. 71, 3645 (1993).
[CrossRef] [PubMed]

1990 (1)

1986 (1)

1985 (1)

1984 (1)

D. W. Pohl, W. Denk, M. Lanz, Appl. Phys. Lett. 44, 651 (1984); D. W. Pohl, in Advances in Optical and Electron Microscopy, C. J. R. Sheppard, T. Mulvey, eds. (Academic, New York, 1990), pp. 243–312; D. W. Pohl, D. Courjon, Near Field Optics, Vol. 242 of NATO ASI Series (Kluwer, Dordrecht, The Netherlands, 1992).
[CrossRef]

1978 (1)

N. Garcia, N. Cabrera, Phys. Rev. B 18, 576 (1978).
[CrossRef]

1969 (2)

E. Wolf, Opt. Commun. 1, 153 (1969); R. P. Porter, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27, pp. 315–397.
[CrossRef]

R. F. Millar, Proc. Cambridge Philos. Soc. 65, 773 (1969).
[CrossRef]

1949 (1)

D. Gabor, Proc. R. Soc. London Ser. A 197, 454 (1949).
[CrossRef]

Betzig, E.

Brown, G. S.

J. A. de Santo, G. S. Brown, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1986), Vol. 23, pp. 2–62; M. Nieto-Vesperinas, J. C. Dainty, eds., Scattering in Volumes and Surfaces (North-Holland, Amsterdam, 1990); J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, London, 1991); R. J. Wombell, J. A. de Santo, J. Opt. Soc. Am. A 8, 1892 (1991).
[CrossRef]

Cabrera, N.

N. Garcia, N. Cabrera, Phys. Rev. B 18, 576 (1978).
[CrossRef]

de Santo, J. A.

J. A. de Santo, G. S. Brown, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1986), Vol. 23, pp. 2–62; M. Nieto-Vesperinas, J. C. Dainty, eds., Scattering in Volumes and Surfaces (North-Holland, Amsterdam, 1990); J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, London, 1991); R. J. Wombell, J. A. de Santo, J. Opt. Soc. Am. A 8, 1892 (1991).
[CrossRef]

Denk, W.

D. W. Pohl, W. Denk, M. Lanz, Appl. Phys. Lett. 44, 651 (1984); D. W. Pohl, in Advances in Optical and Electron Microscopy, C. J. R. Sheppard, T. Mulvey, eds. (Academic, New York, 1990), pp. 243–312; D. W. Pohl, D. Courjon, Near Field Optics, Vol. 242 of NATO ASI Series (Kluwer, Dordrecht, The Netherlands, 1992).
[CrossRef]

Fienup, J. R.

J. R. Fienup, in International Trends in Optics, J. W. Goodman, ed. (Academic, New York, 1991), pp. 407–422.

Gabor, D.

D. Gabor, Proc. R. Soc. London Ser. A 197, 454 (1949).
[CrossRef]

Garcia, N.

N. Garcia, M. Nieto-Vesperinas, Phys. Rev. Lett. 71, 3645 (1993).
[CrossRef] [PubMed]

N. Garcia, M. Nieto-Vesperinas, Opt. Lett. 18, 2090 (1993)l
[CrossRef] [PubMed]

N. Garcia, N. Cabrera, Phys. Rev. B 18, 576 (1978).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 8, p. 198.

Harootunian, A.

Isaacson, M.

Lanz, M.

D. W. Pohl, W. Denk, M. Lanz, Appl. Phys. Lett. 44, 651 (1984); D. W. Pohl, in Advances in Optical and Electron Microscopy, C. J. R. Sheppard, T. Mulvey, eds. (Academic, New York, 1990), pp. 243–312; D. W. Pohl, D. Courjon, Near Field Optics, Vol. 242 of NATO ASI Series (Kluwer, Dordrecht, The Netherlands, 1992).
[CrossRef]

Lewis, A.

Marcuse, D.

D. Marcuse, Light Transmission Optics, 2nd ed. (Van Nostrand Reinhold, New York, 1982), Chap. 6, p. 296.

Millane, R. P.

Millar, R. F.

R. F. Millar, Proc. Cambridge Philos. Soc. 65, 773 (1969).
[CrossRef]

Nieto-Vesperinas, M.

N. Garcia, M. Nieto-Vesperinas, Phys. Rev. Lett. 71, 3645 (1993).
[CrossRef] [PubMed]

N. Garcia, M. Nieto-Vesperinas, Opt. Lett. 18, 2090 (1993)l
[CrossRef] [PubMed]

E. Wolf, M. Nieto-Vesperinas, J. Opt. Soc. Am. A 2, 886 (1985).
[CrossRef]

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991), Chap. 9, p. 322.

Pohl, D. W.

D. W. Pohl, W. Denk, M. Lanz, Appl. Phys. Lett. 44, 651 (1984); D. W. Pohl, in Advances in Optical and Electron Microscopy, C. J. R. Sheppard, T. Mulvey, eds. (Academic, New York, 1990), pp. 243–312; D. W. Pohl, D. Courjon, Near Field Optics, Vol. 242 of NATO ASI Series (Kluwer, Dordrecht, The Netherlands, 1992).
[CrossRef]

Wolf, E.

E. Wolf, M. Nieto-Vesperinas, J. Opt. Soc. Am. A 2, 886 (1985).
[CrossRef]

E. Wolf, Opt. Commun. 1, 153 (1969); R. P. Porter, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27, pp. 315–397.
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

D. W. Pohl, W. Denk, M. Lanz, Appl. Phys. Lett. 44, 651 (1984); D. W. Pohl, in Advances in Optical and Electron Microscopy, C. J. R. Sheppard, T. Mulvey, eds. (Academic, New York, 1990), pp. 243–312; D. W. Pohl, D. Courjon, Near Field Optics, Vol. 242 of NATO ASI Series (Kluwer, Dordrecht, The Netherlands, 1992).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

E. Wolf, Opt. Commun. 1, 153 (1969); R. P. Porter, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27, pp. 315–397.
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (1)

N. Garcia, N. Cabrera, Phys. Rev. B 18, 576 (1978).
[CrossRef]

Phys. Rev. Lett. (1)

N. Garcia, M. Nieto-Vesperinas, Phys. Rev. Lett. 71, 3645 (1993).
[CrossRef] [PubMed]

Proc. Cambridge Philos. Soc. (1)

R. F. Millar, Proc. Cambridge Philos. Soc. 65, 773 (1969).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

D. Gabor, Proc. R. Soc. London Ser. A 197, 454 (1949).
[CrossRef]

Other (5)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 8, p. 198.

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991), Chap. 9, p. 322.

J. R. Fienup, in International Trends in Optics, J. W. Goodman, ed. (Academic, New York, 1991), pp. 407–422.

D. Marcuse, Light Transmission Optics, 2nd ed. (Van Nostrand Reinhold, New York, 1982), Chap. 6, p. 296.

J. A. de Santo, G. S. Brown, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1986), Vol. 23, pp. 2–62; M. Nieto-Vesperinas, J. C. Dainty, eds., Scattering in Volumes and Surfaces (North-Holland, Amsterdam, 1990); J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, London, 1991); R. J. Wombell, J. A. de Santo, J. Opt. Soc. Am. A 8, 1892 (1991).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Scattering geometry. V(r) = −k2[(r) − 1].

Fig. 2
Fig. 2

Crosses show the near-field scattered intensities averaged over 35 angles of incidence at four distances z0 given by z0 = [1.25 + 2(n − 1)]h, n = 1, 2, 3, 4, with the incident wave impinging from the vacuum side and = 1.5. The open squares show the test profile D(x) = h[sin(2πx/a) + cos(6πx/a)]; a = 3.18λ, h = 0.095λ. (b) Same as (a) for nine incident plane waves. (c) Same as (a) for one single incident plane wave at 40°, at five distances given by z0 = [1.25 + 2(n − 1)]h, n = 1, 2, 3, 4, 5.

Fig. 3
Fig. 3

Asterisks show the near-field scattered intensities averaged over 35 angles of incidence at distance z0 = 1.25h with the incident wave impinging from the medium side and = 1.5. The open squares show the test profile D(x) = h[sin(2πx/a) + cos(6πx/a)]; a = 3.18λ, h = 0.095λ. The crosses show the same as the asterisks for nine incident plane waves.

Equations (5)

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U ( R , z ; K i ) = - A ( K , K i ) exp [ i ( K · R + k z z ] d K ,
A ( K , K i ) A n = ( 1 / k n z ) - a / 2 a / 2 F ( R ; K i ) × exp { - i [ K n · R + k n z D ( R ) ] } d R .
I T ( R , z ) = - k k I ( R , z ; K i ) d K i = - k k k i z k - - exp [ i ( K · R + k z z ) ] × exp [ - i ( K · R + k z * z ) ] × A ( K , K i ) A * ( K , K i ) d K i d K d K .
Scattered intensity P Scattered amplitude T Profile ,
Scattered Intensity S Integrated NFO Scattered Intensity T = 1 Profile ,

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