Abstract

A new method for studying surface roughness is presented that uses a microdensitometer to analyze electron micrographs of shadowed surface replicas. First we give a preliminary description of the replication technique and the microdensitometer analysis. Then we proceed to show that the micrograph density (or transmittance) is approximately proportional to the slope of the surface elements, which enables us to determine the surface profile by integration of the microdensitometer data. Bidimensional and monodimensional median-filtering algorithms are used in the data reduction, and their validity is analyzed. With the help of a computer program that plots a perspective view of rough surfaces, we find that a close approach to the real profiles is obtained. This shows that our method may have other important applications in addition to the study of alterable metallic surfaces.

© 1981 Optical Society of America

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  1. H. Davies, "The reflection of electromagnetic waves from rough surfaces," Proc. IEEE 101, 209–214 (1954).
  2. E. A. Stern and R. A. Ferrel, "Surface plasma oscillations of a degenerate electron gas," Phys. Rev. 120, 130–139 (1960).
  3. H. E. Bennett and J. O. Porteus, "Relation between surface roughness and specular reflectance at normal incidence," J. Opt. Soc. Am. 51, 123–129 (1961).
  4. J. O. Porteus, "Relation between the height distribution of a rough surface and the reflectance at normal incidence," J. Opt. Soc. Am. 53, 1394–1402 (1963).
  5. H. E. Bennett, "Specular reflectance of aluminized ground glass and the height distribution of surface irregularities," J. Opt. Soc. Am. 53, 1389–1394 (1963).
  6. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).
  7. D. W. Berreman, "Anomalous reststrahl structure from slight surface roughness," Phys. Rev. 163, 855–864 (1967).
  8. J. Crowell and R. H. Ritchie, "Surface plasmon effect in the reflectance of a metal," J. Opt. Soc. Am. 60, 794–799 (1970).
  9. J. G. Endriz and W. Spicer, "Study of aluminum films. I. Optical studies of reflectance drops and surface oscillations on controlled roughness films," Phys. Rev. B 134, 4144–4158 (1971); "Study of aluminum films. II. Photoemission studies of surface plasmon oscillation on controlled roughness films," Phys. Rev. B 134, 4159–4184 (1971).
  10. T. F. Gesell, E. T. Arakawa, M. W. Williams, and R. N. Hamm, "Optical and photoelectric properties of Mg in the vacuum ultraviolet," Phys. Rev. B 7, 5141–5146 (1972).
  11. A. J. Braundmeier and D. G. Hall, "Some measurements of the angular distribution and polarization of surface plasmon radiation from Ag films," Surf. Sci. 49, 376–392 (1975).
  12. H. Raether, "Surface plasma oscillations and their applications," in Physics of Thin Films, Vol. 9, Georg Hass, ed. (Academic, New York, 1977), pp. 145–261.
  13. J. M. Elson and R. H. Ritchie, "Photon-surface plasmon coupling at a dielectric solid," Phys. Lett. 33A, 255–256 (1970); "Photon interactions at a rough metal surface," Phys. Rev. B 4, 4129–4138 (1971); "Diffuse scattering and surface-plasmon generation by photons at a rough dielectric surface," Phys. Status Solidi B 62, 461–468 (1974).
  14. P. Dobberstein, "Coupling between light and surface plasma-waves via non Gaussian surface roughness," Phys. Lett. 31A, 307–308 (1969).
  15. J. M. Bennett, "Measurement of the rms roughness, autocovariance function and other statistical properties of optical surfaces using a F.E.C.O. scanning interferometer," Appl. Opt. 15, 2705–2721 (1976).
  16. J. M. Elson and J. M. Bennett, "Relation between the angular dependence of scattering and the statistical properties of optical surfaces," J. Opt. Soc. Am. 69, 31–47 (1979).
  17. R. J. Wagner, "Shadowing of randomly rough surfaces," J. Acoust. Soc. Am. 41, 138–147 (1966).
  18. J. C. Hardin, "Theoretical analysis of rough-surface shadowing from point-source radiation," J. Acoust. Soc. Am. 52, 227–233 (1971).
  19. M. Rasigni, G. Rasigni, C. T. Hua, and J. Pons, "Determination of the surface structure autocorrelation function for rough deposits of magnesium," Opt. Lett. 1, 126–127 (1977).
  20. M. Rasigni and G. Rasigni, "Surface structure autocorrelation functions and their Fourier transforms for rough deposits of magnesium," Phys. Rev. B 19, 1915–1919 (1978).
  21. M. Rasigni, J. P. Palmari, and G. Rasigni, "Addendum to: Surface structure autocorrelation functions and their Fourier transforms for rough deposits of magnesium," Phys. Rev B 22, 4092–4093 (1980).
  22. M. Rasigni, G. Rasigni, J. P. Palmari, and A. Llebaria, "Surface plasmon and autocorrelation function for rough surfaces of silver deposits," Phys. Rev. B 23, 527–531 (1981).
  23. M. Rasigni and G. Rasigni, "Experimental study of the optical absorption and structure of very thin lithium deposits," J. Opt. Soc. Am. 62, 1033–1036 (1972).
  24. G. Rasigni and M. Rasigni, "Plasma resonance in granular deposits and rough surfaces of magnesium," Phys. Rev. B 12, 1121–1131 (1975).
  25. A. Llebaria, "Digitized microdensitometer and processing data system" (unpublished).
  26. C. Magnan, Traité de Microscopie Électronique (Hermann, Paris, 1961).
  27. N. Digby, K. Firth, and R. J. Hercock, "The photographic effect of medium energy electrons," J. Photogr. Sci. 1, 194–208 (1953).
  28. J. F. Hamilton and J. C. Marchant, "Image recording in electron microscopy," J. Opt. Soc. Am. 57, 232–239 (1967).
  29. H. F. Premsela, J. M. Nievwenhuizen, and B. Schotanus, "Photographic techniques for electron microscopy. Basic principles and practice," Philips Industries, Scientific and Industrial Equipment Division, Electron Optics Group, Eindhoven, The Netherlands (not dated), p. 14.
  30. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965), pp. 437 and 503.
  31. T. S. Huang, G. J. Yang, and G. Y. Tang, "A fast two-dimensional median filtering algorithm," IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13–18 (1979).
  32. J. A. Bush, D. K. Cohen, K. D. Scherkoska, and S. O. Sari, "Measurement of roughness-induced wavelength correction to the surface-plasmon resonance in silver," J. Opt. Soc. Am. 70, 1020–1023 (1980).
  33. J. L. Stanford, "Determination of surface-film thickness from shift of optically excited surface plasma resonance," J. Opt. Soc. Am. 60, 49–53 (1970).
  34. L. J. Cunningham and A. J. Braundmeier, Jr., "Measurement of the correlation between the specular reflectance and surface roughness of Ag films," Phys. Rev. B 14, 479–483 (1976).
  35. E. Kretschmann, "Decay of non radiative surface plasmon into light on rough silver films. Comparison of experimental and theoretical results," Opt. Commun. 6, 185–187 (1972).
  36. D. L. Hornauer, "Light scattering experiments on silver films of different roughness using surface plasmon excitation," Opt. Commun. 16, 76–79 (1976).
  37. W. Pratt, Digital Image Processing (Wiley, New York, 1978), pp. 307–309.
  38. G. Rasigni, M. Rasigni, and J. P. Palmari, "Reflectance drops and surface plasmons on different roughness deposits of magnesium," Phys. Rev. B 14, 4235–4238 (1976).

1981 (1)

M. Rasigni, G. Rasigni, J. P. Palmari, and A. Llebaria, "Surface plasmon and autocorrelation function for rough surfaces of silver deposits," Phys. Rev. B 23, 527–531 (1981).

1980 (2)

M. Rasigni, J. P. Palmari, and G. Rasigni, "Addendum to: Surface structure autocorrelation functions and their Fourier transforms for rough deposits of magnesium," Phys. Rev B 22, 4092–4093 (1980).

J. A. Bush, D. K. Cohen, K. D. Scherkoska, and S. O. Sari, "Measurement of roughness-induced wavelength correction to the surface-plasmon resonance in silver," J. Opt. Soc. Am. 70, 1020–1023 (1980).

1979 (2)

J. M. Elson and J. M. Bennett, "Relation between the angular dependence of scattering and the statistical properties of optical surfaces," J. Opt. Soc. Am. 69, 31–47 (1979).

T. S. Huang, G. J. Yang, and G. Y. Tang, "A fast two-dimensional median filtering algorithm," IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13–18 (1979).

1978 (1)

M. Rasigni and G. Rasigni, "Surface structure autocorrelation functions and their Fourier transforms for rough deposits of magnesium," Phys. Rev. B 19, 1915–1919 (1978).

1977 (1)

1976 (4)

J. M. Bennett, "Measurement of the rms roughness, autocovariance function and other statistical properties of optical surfaces using a F.E.C.O. scanning interferometer," Appl. Opt. 15, 2705–2721 (1976).

L. J. Cunningham and A. J. Braundmeier, Jr., "Measurement of the correlation between the specular reflectance and surface roughness of Ag films," Phys. Rev. B 14, 479–483 (1976).

D. L. Hornauer, "Light scattering experiments on silver films of different roughness using surface plasmon excitation," Opt. Commun. 16, 76–79 (1976).

G. Rasigni, M. Rasigni, and J. P. Palmari, "Reflectance drops and surface plasmons on different roughness deposits of magnesium," Phys. Rev. B 14, 4235–4238 (1976).

1975 (2)

G. Rasigni and M. Rasigni, "Plasma resonance in granular deposits and rough surfaces of magnesium," Phys. Rev. B 12, 1121–1131 (1975).

A. J. Braundmeier and D. G. Hall, "Some measurements of the angular distribution and polarization of surface plasmon radiation from Ag films," Surf. Sci. 49, 376–392 (1975).

1972 (3)

T. F. Gesell, E. T. Arakawa, M. W. Williams, and R. N. Hamm, "Optical and photoelectric properties of Mg in the vacuum ultraviolet," Phys. Rev. B 7, 5141–5146 (1972).

E. Kretschmann, "Decay of non radiative surface plasmon into light on rough silver films. Comparison of experimental and theoretical results," Opt. Commun. 6, 185–187 (1972).

M. Rasigni and G. Rasigni, "Experimental study of the optical absorption and structure of very thin lithium deposits," J. Opt. Soc. Am. 62, 1033–1036 (1972).

1971 (2)

J. C. Hardin, "Theoretical analysis of rough-surface shadowing from point-source radiation," J. Acoust. Soc. Am. 52, 227–233 (1971).

J. G. Endriz and W. Spicer, "Study of aluminum films. I. Optical studies of reflectance drops and surface oscillations on controlled roughness films," Phys. Rev. B 134, 4144–4158 (1971); "Study of aluminum films. II. Photoemission studies of surface plasmon oscillation on controlled roughness films," Phys. Rev. B 134, 4159–4184 (1971).

1970 (3)

J. M. Elson and R. H. Ritchie, "Photon-surface plasmon coupling at a dielectric solid," Phys. Lett. 33A, 255–256 (1970); "Photon interactions at a rough metal surface," Phys. Rev. B 4, 4129–4138 (1971); "Diffuse scattering and surface-plasmon generation by photons at a rough dielectric surface," Phys. Status Solidi B 62, 461–468 (1974).

J. L. Stanford, "Determination of surface-film thickness from shift of optically excited surface plasma resonance," J. Opt. Soc. Am. 60, 49–53 (1970).

J. Crowell and R. H. Ritchie, "Surface plasmon effect in the reflectance of a metal," J. Opt. Soc. Am. 60, 794–799 (1970).

1969 (1)

P. Dobberstein, "Coupling between light and surface plasma-waves via non Gaussian surface roughness," Phys. Lett. 31A, 307–308 (1969).

1967 (2)

D. W. Berreman, "Anomalous reststrahl structure from slight surface roughness," Phys. Rev. 163, 855–864 (1967).

J. F. Hamilton and J. C. Marchant, "Image recording in electron microscopy," J. Opt. Soc. Am. 57, 232–239 (1967).

1966 (1)

R. J. Wagner, "Shadowing of randomly rough surfaces," J. Acoust. Soc. Am. 41, 138–147 (1966).

1963 (2)

1961 (1)

1960 (1)

E. A. Stern and R. A. Ferrel, "Surface plasma oscillations of a degenerate electron gas," Phys. Rev. 120, 130–139 (1960).

1953 (1)

N. Digby, K. Firth, and R. J. Hercock, "The photographic effect of medium energy electrons," J. Photogr. Sci. 1, 194–208 (1953).

Arakawa, E. T.

T. F. Gesell, E. T. Arakawa, M. W. Williams, and R. N. Hamm, "Optical and photoelectric properties of Mg in the vacuum ultraviolet," Phys. Rev. B 7, 5141–5146 (1972).

Beckmann, P.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Bennett, H. E.

Bennett, J. M.

Berreman, D. W.

D. W. Berreman, "Anomalous reststrahl structure from slight surface roughness," Phys. Rev. 163, 855–864 (1967).

Braundmeier, A. J.

A. J. Braundmeier and D. G. Hall, "Some measurements of the angular distribution and polarization of surface plasmon radiation from Ag films," Surf. Sci. 49, 376–392 (1975).

Braundmeier, Jr., A. J.

L. J. Cunningham and A. J. Braundmeier, Jr., "Measurement of the correlation between the specular reflectance and surface roughness of Ag films," Phys. Rev. B 14, 479–483 (1976).

Bush, J. A.

Cohen, D. K.

Crowell, J.

Cunningham, L. J.

L. J. Cunningham and A. J. Braundmeier, Jr., "Measurement of the correlation between the specular reflectance and surface roughness of Ag films," Phys. Rev. B 14, 479–483 (1976).

Davies, H.

H. Davies, "The reflection of electromagnetic waves from rough surfaces," Proc. IEEE 101, 209–214 (1954).

Digby, N.

N. Digby, K. Firth, and R. J. Hercock, "The photographic effect of medium energy electrons," J. Photogr. Sci. 1, 194–208 (1953).

Dobberstein, P.

P. Dobberstein, "Coupling between light and surface plasma-waves via non Gaussian surface roughness," Phys. Lett. 31A, 307–308 (1969).

Elson, J. M.

J. M. Elson and J. M. Bennett, "Relation between the angular dependence of scattering and the statistical properties of optical surfaces," J. Opt. Soc. Am. 69, 31–47 (1979).

J. M. Elson and R. H. Ritchie, "Photon-surface plasmon coupling at a dielectric solid," Phys. Lett. 33A, 255–256 (1970); "Photon interactions at a rough metal surface," Phys. Rev. B 4, 4129–4138 (1971); "Diffuse scattering and surface-plasmon generation by photons at a rough dielectric surface," Phys. Status Solidi B 62, 461–468 (1974).

Endriz, J. G.

J. G. Endriz and W. Spicer, "Study of aluminum films. I. Optical studies of reflectance drops and surface oscillations on controlled roughness films," Phys. Rev. B 134, 4144–4158 (1971); "Study of aluminum films. II. Photoemission studies of surface plasmon oscillation on controlled roughness films," Phys. Rev. B 134, 4159–4184 (1971).

Ferrel, R. A.

E. A. Stern and R. A. Ferrel, "Surface plasma oscillations of a degenerate electron gas," Phys. Rev. 120, 130–139 (1960).

Firth, K.

N. Digby, K. Firth, and R. J. Hercock, "The photographic effect of medium energy electrons," J. Photogr. Sci. 1, 194–208 (1953).

Gesell, T. F.

T. F. Gesell, E. T. Arakawa, M. W. Williams, and R. N. Hamm, "Optical and photoelectric properties of Mg in the vacuum ultraviolet," Phys. Rev. B 7, 5141–5146 (1972).

Hall, D. G.

A. J. Braundmeier and D. G. Hall, "Some measurements of the angular distribution and polarization of surface plasmon radiation from Ag films," Surf. Sci. 49, 376–392 (1975).

Hamilton, J. F.

Hamm, R. N.

T. F. Gesell, E. T. Arakawa, M. W. Williams, and R. N. Hamm, "Optical and photoelectric properties of Mg in the vacuum ultraviolet," Phys. Rev. B 7, 5141–5146 (1972).

Hardin, J. C.

J. C. Hardin, "Theoretical analysis of rough-surface shadowing from point-source radiation," J. Acoust. Soc. Am. 52, 227–233 (1971).

Hercock, R. J.

N. Digby, K. Firth, and R. J. Hercock, "The photographic effect of medium energy electrons," J. Photogr. Sci. 1, 194–208 (1953).

Hornauer, D. L.

D. L. Hornauer, "Light scattering experiments on silver films of different roughness using surface plasmon excitation," Opt. Commun. 16, 76–79 (1976).

Hua, C. T.

Huang, T. S.

T. S. Huang, G. J. Yang, and G. Y. Tang, "A fast two-dimensional median filtering algorithm," IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13–18 (1979).

Kretschmann, E.

E. Kretschmann, "Decay of non radiative surface plasmon into light on rough silver films. Comparison of experimental and theoretical results," Opt. Commun. 6, 185–187 (1972).

Llebaria, A.

M. Rasigni, G. Rasigni, J. P. Palmari, and A. Llebaria, "Surface plasmon and autocorrelation function for rough surfaces of silver deposits," Phys. Rev. B 23, 527–531 (1981).

A. Llebaria, "Digitized microdensitometer and processing data system" (unpublished).

Magnan, C.

C. Magnan, Traité de Microscopie Électronique (Hermann, Paris, 1961).

Marchant, J. C.

Nievwenhuizen, J. M.

H. F. Premsela, J. M. Nievwenhuizen, and B. Schotanus, "Photographic techniques for electron microscopy. Basic principles and practice," Philips Industries, Scientific and Industrial Equipment Division, Electron Optics Group, Eindhoven, The Netherlands (not dated), p. 14.

Palmari, J. P.

M. Rasigni, G. Rasigni, J. P. Palmari, and A. Llebaria, "Surface plasmon and autocorrelation function for rough surfaces of silver deposits," Phys. Rev. B 23, 527–531 (1981).

M. Rasigni, J. P. Palmari, and G. Rasigni, "Addendum to: Surface structure autocorrelation functions and their Fourier transforms for rough deposits of magnesium," Phys. Rev B 22, 4092–4093 (1980).

G. Rasigni, M. Rasigni, and J. P. Palmari, "Reflectance drops and surface plasmons on different roughness deposits of magnesium," Phys. Rev. B 14, 4235–4238 (1976).

Papoulis, A.

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965), pp. 437 and 503.

Pons, J.

Porteus, J. O.

Pratt, W.

W. Pratt, Digital Image Processing (Wiley, New York, 1978), pp. 307–309.

Premsela, H. F.

H. F. Premsela, J. M. Nievwenhuizen, and B. Schotanus, "Photographic techniques for electron microscopy. Basic principles and practice," Philips Industries, Scientific and Industrial Equipment Division, Electron Optics Group, Eindhoven, The Netherlands (not dated), p. 14.

Raether, H.

H. Raether, "Surface plasma oscillations and their applications," in Physics of Thin Films, Vol. 9, Georg Hass, ed. (Academic, New York, 1977), pp. 145–261.

Rasigni, G.

M. Rasigni, G. Rasigni, J. P. Palmari, and A. Llebaria, "Surface plasmon and autocorrelation function for rough surfaces of silver deposits," Phys. Rev. B 23, 527–531 (1981).

M. Rasigni, J. P. Palmari, and G. Rasigni, "Addendum to: Surface structure autocorrelation functions and their Fourier transforms for rough deposits of magnesium," Phys. Rev B 22, 4092–4093 (1980).

M. Rasigni and G. Rasigni, "Surface structure autocorrelation functions and their Fourier transforms for rough deposits of magnesium," Phys. Rev. B 19, 1915–1919 (1978).

M. Rasigni, G. Rasigni, C. T. Hua, and J. Pons, "Determination of the surface structure autocorrelation function for rough deposits of magnesium," Opt. Lett. 1, 126–127 (1977).

G. Rasigni, M. Rasigni, and J. P. Palmari, "Reflectance drops and surface plasmons on different roughness deposits of magnesium," Phys. Rev. B 14, 4235–4238 (1976).

G. Rasigni and M. Rasigni, "Plasma resonance in granular deposits and rough surfaces of magnesium," Phys. Rev. B 12, 1121–1131 (1975).

M. Rasigni and G. Rasigni, "Experimental study of the optical absorption and structure of very thin lithium deposits," J. Opt. Soc. Am. 62, 1033–1036 (1972).

Rasigni, M.

M. Rasigni, G. Rasigni, J. P. Palmari, and A. Llebaria, "Surface plasmon and autocorrelation function for rough surfaces of silver deposits," Phys. Rev. B 23, 527–531 (1981).

M. Rasigni, J. P. Palmari, and G. Rasigni, "Addendum to: Surface structure autocorrelation functions and their Fourier transforms for rough deposits of magnesium," Phys. Rev B 22, 4092–4093 (1980).

M. Rasigni and G. Rasigni, "Surface structure autocorrelation functions and their Fourier transforms for rough deposits of magnesium," Phys. Rev. B 19, 1915–1919 (1978).

M. Rasigni, G. Rasigni, C. T. Hua, and J. Pons, "Determination of the surface structure autocorrelation function for rough deposits of magnesium," Opt. Lett. 1, 126–127 (1977).

G. Rasigni, M. Rasigni, and J. P. Palmari, "Reflectance drops and surface plasmons on different roughness deposits of magnesium," Phys. Rev. B 14, 4235–4238 (1976).

G. Rasigni and M. Rasigni, "Plasma resonance in granular deposits and rough surfaces of magnesium," Phys. Rev. B 12, 1121–1131 (1975).

M. Rasigni and G. Rasigni, "Experimental study of the optical absorption and structure of very thin lithium deposits," J. Opt. Soc. Am. 62, 1033–1036 (1972).

Ritchie, R. H.

J. M. Elson and R. H. Ritchie, "Photon-surface plasmon coupling at a dielectric solid," Phys. Lett. 33A, 255–256 (1970); "Photon interactions at a rough metal surface," Phys. Rev. B 4, 4129–4138 (1971); "Diffuse scattering and surface-plasmon generation by photons at a rough dielectric surface," Phys. Status Solidi B 62, 461–468 (1974).

J. Crowell and R. H. Ritchie, "Surface plasmon effect in the reflectance of a metal," J. Opt. Soc. Am. 60, 794–799 (1970).

Sari, S. O.

Scherkoska, K. D.

Schotanus, B.

H. F. Premsela, J. M. Nievwenhuizen, and B. Schotanus, "Photographic techniques for electron microscopy. Basic principles and practice," Philips Industries, Scientific and Industrial Equipment Division, Electron Optics Group, Eindhoven, The Netherlands (not dated), p. 14.

Spicer, W.

J. G. Endriz and W. Spicer, "Study of aluminum films. I. Optical studies of reflectance drops and surface oscillations on controlled roughness films," Phys. Rev. B 134, 4144–4158 (1971); "Study of aluminum films. II. Photoemission studies of surface plasmon oscillation on controlled roughness films," Phys. Rev. B 134, 4159–4184 (1971).

Spizzichino, A.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Stanford, J. L.

Stern, E. A.

E. A. Stern and R. A. Ferrel, "Surface plasma oscillations of a degenerate electron gas," Phys. Rev. 120, 130–139 (1960).

Tang, G. Y.

T. S. Huang, G. J. Yang, and G. Y. Tang, "A fast two-dimensional median filtering algorithm," IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13–18 (1979).

Wagner, R. J.

R. J. Wagner, "Shadowing of randomly rough surfaces," J. Acoust. Soc. Am. 41, 138–147 (1966).

Williams, M. W.

T. F. Gesell, E. T. Arakawa, M. W. Williams, and R. N. Hamm, "Optical and photoelectric properties of Mg in the vacuum ultraviolet," Phys. Rev. B 7, 5141–5146 (1972).

Yang, G. J.

T. S. Huang, G. J. Yang, and G. Y. Tang, "A fast two-dimensional median filtering algorithm," IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13–18 (1979).

Appl. Opt. (1)

IEEE Trans. Acoust. Speech Signal Process. (1)

T. S. Huang, G. J. Yang, and G. Y. Tang, "A fast two-dimensional median filtering algorithm," IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13–18 (1979).

J. Acoust. Soc. Am. (2)

R. J. Wagner, "Shadowing of randomly rough surfaces," J. Acoust. Soc. Am. 41, 138–147 (1966).

J. C. Hardin, "Theoretical analysis of rough-surface shadowing from point-source radiation," J. Acoust. Soc. Am. 52, 227–233 (1971).

J. Opt. Soc. Am. (9)

J. Photogr. Sci. (1)

N. Digby, K. Firth, and R. J. Hercock, "The photographic effect of medium energy electrons," J. Photogr. Sci. 1, 194–208 (1953).

Opt. Commun. (2)

E. Kretschmann, "Decay of non radiative surface plasmon into light on rough silver films. Comparison of experimental and theoretical results," Opt. Commun. 6, 185–187 (1972).

D. L. Hornauer, "Light scattering experiments on silver films of different roughness using surface plasmon excitation," Opt. Commun. 16, 76–79 (1976).

Opt. Lett. (1)

Phys. Lett. (2)

J. M. Elson and R. H. Ritchie, "Photon-surface plasmon coupling at a dielectric solid," Phys. Lett. 33A, 255–256 (1970); "Photon interactions at a rough metal surface," Phys. Rev. B 4, 4129–4138 (1971); "Diffuse scattering and surface-plasmon generation by photons at a rough dielectric surface," Phys. Status Solidi B 62, 461–468 (1974).

P. Dobberstein, "Coupling between light and surface plasma-waves via non Gaussian surface roughness," Phys. Lett. 31A, 307–308 (1969).

Phys. Rev B (1)

M. Rasigni, J. P. Palmari, and G. Rasigni, "Addendum to: Surface structure autocorrelation functions and their Fourier transforms for rough deposits of magnesium," Phys. Rev B 22, 4092–4093 (1980).

Phys. Rev. (2)

E. A. Stern and R. A. Ferrel, "Surface plasma oscillations of a degenerate electron gas," Phys. Rev. 120, 130–139 (1960).

D. W. Berreman, "Anomalous reststrahl structure from slight surface roughness," Phys. Rev. 163, 855–864 (1967).

Phys. Rev. B (7)

G. Rasigni, M. Rasigni, and J. P. Palmari, "Reflectance drops and surface plasmons on different roughness deposits of magnesium," Phys. Rev. B 14, 4235–4238 (1976).

L. J. Cunningham and A. J. Braundmeier, Jr., "Measurement of the correlation between the specular reflectance and surface roughness of Ag films," Phys. Rev. B 14, 479–483 (1976).

J. G. Endriz and W. Spicer, "Study of aluminum films. I. Optical studies of reflectance drops and surface oscillations on controlled roughness films," Phys. Rev. B 134, 4144–4158 (1971); "Study of aluminum films. II. Photoemission studies of surface plasmon oscillation on controlled roughness films," Phys. Rev. B 134, 4159–4184 (1971).

T. F. Gesell, E. T. Arakawa, M. W. Williams, and R. N. Hamm, "Optical and photoelectric properties of Mg in the vacuum ultraviolet," Phys. Rev. B 7, 5141–5146 (1972).

M. Rasigni, G. Rasigni, J. P. Palmari, and A. Llebaria, "Surface plasmon and autocorrelation function for rough surfaces of silver deposits," Phys. Rev. B 23, 527–531 (1981).

G. Rasigni and M. Rasigni, "Plasma resonance in granular deposits and rough surfaces of magnesium," Phys. Rev. B 12, 1121–1131 (1975).

M. Rasigni and G. Rasigni, "Surface structure autocorrelation functions and their Fourier transforms for rough deposits of magnesium," Phys. Rev. B 19, 1915–1919 (1978).

Surf. Sci. (1)

A. J. Braundmeier and D. G. Hall, "Some measurements of the angular distribution and polarization of surface plasmon radiation from Ag films," Surf. Sci. 49, 376–392 (1975).

Other (8)

H. Raether, "Surface plasma oscillations and their applications," in Physics of Thin Films, Vol. 9, Georg Hass, ed. (Academic, New York, 1977), pp. 145–261.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

H. Davies, "The reflection of electromagnetic waves from rough surfaces," Proc. IEEE 101, 209–214 (1954).

H. F. Premsela, J. M. Nievwenhuizen, and B. Schotanus, "Photographic techniques for electron microscopy. Basic principles and practice," Philips Industries, Scientific and Industrial Equipment Division, Electron Optics Group, Eindhoven, The Netherlands (not dated), p. 14.

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