Skip to main content

Rough or Structured Surfaces

  • Chapter
  • First Online:
Theory of Reflection

Part of the book series: Springer Series on Atomic, Optical, and Plasma Physics ((SSAOPP,volume 87))

  • 2469 Accesses

Abstract

We have seen in Chap. 1 that a planar surface, or arbitrary stratification, will give specular reflection of an incident plane wave. No real surface is perfectly planar, and thus in practice there is a diffuse or scattered component, as well as a specular component of the radiation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Agranovich VM, Mills DL (eds) (1982) Surface polaritons: electromagnetic waves at surfaces and interfaces, North-Holland

    Google Scholar 

  • Akkermans E, Wolf PE, Maynard R (1986) Coherent backscattering of light by disordered media: analysis of peak line shape. Phys Rev Lett 56:1471–1474

    Article  ADS  Google Scholar 

  • Andronov AA, Leontovich MA (1926) Zur Theorie der molekularen Lichtzerstreuung an Flüssigkeitsoberflächen. Z Physik 38:485–501

    Article  ADS  Google Scholar 

  • Ångström AK (1925) The albedo of various surfaces of ground. Geografiska Annaler 7:323

    Article  Google Scholar 

  • Baker BB, Copson ET (1950) The mathematical theory of Huygen’s principle. Clarendon Press, Oxford

    Google Scholar 

  • Bass FG, Fuks IM (1979) Wave scattering by statistically rough surfaces, Pergamon

    Google Scholar 

  • Beaglehole D (1980) Ellipsometric study of the surface of simple liquids. Physica 100B:163–174

    Google Scholar 

  • Beaglehole D (1982) Short-ranged roughness on the near-critical liquid interface. Physica 112B:320–330

    Google Scholar 

  • Beaglehole D (1983) Ellipsometry of liquid surfaces. J. de Physique C10:147–154

    Google Scholar 

  • Becker F, Ramanantsizehena P, Stoll M (1985) Angular variation of the bidirectional reflectance of bare solis in the thermal infrared band. Appl Opt 24:365–375

    Article  ADS  Google Scholar 

  • Beckmann P, Spizzichino A (1963) The scattering of electromagnetic waves from rough surfaces. Pergamon, New York

    MATH  Google Scholar 

  • Bedeaux D, Vlieger J (1973) A phenomenological theory of the dielectric properties of thin films. Physica 67:55–73

    Article  ADS  Google Scholar 

  • Bennett HE, Porteus JO (1961) Relation between surface roughness and specular reflectance at normal incidence. J Opt Soc Am 51:123–129

    Article  ADS  MathSciNet  Google Scholar 

  • Bohren CF (1983) Multiple scattering at the beach. Weatherwise, August 1983

    Google Scholar 

  • Bohren CF, Huffman DR (1983) Absorption and scattering of light by small particles. Wiley, New York

    Google Scholar 

  • Bouchiat MA, Langevin D (1978) Relation between molecular properties and the intensity scattered by a liquid interface. J Colloid Interface Sci 63:193–211

    Article  Google Scholar 

  • Chandley PJ, Welford WT (1975) A re-formulation of some results of P. Beckmann for scattering from rough surfaces. Opt Quant Electron 7:393–397

    Article  Google Scholar 

  • Cox C, Munk W (1954) Measurement of the roughness of the sea surface from photographs of the sun’s glitter. J Opt Soc Am 44:838–850

    Article  ADS  Google Scholar 

  • Egan WG, Hilgeman T (1976) Retroreflectance measurements of photometric standards and coatings. Appl Opt 15:1845–1849

    Article  ADS  Google Scholar 

  • Gans R (1926) Lichtzerstreuung infolge der molekularen Rauhigkeit der Trennungsfläche zweier durchsichtiger Medien. Ann Phys 79:204–226

    Article  MATH  Google Scholar 

  • Gehrels T, Coffeen T, Owings D (1964) Wavelength dependence of polarization. III The lunar surface. Astron J 69:826–852

    Article  ADS  Google Scholar 

  • Kretschmann E, Kroger E (1975) Reflection and transmission of light by a rough surface, including results for surface-plasmon effects. J Opt Soc Am 65:150–154

    Article  ADS  Google Scholar 

  • Lekner J, Dorf MC (1988) Why some things are darker when wet. Appl Opt 27:1278–1280

    Article  ADS  Google Scholar 

  • Longuet-Higgins MS (1960) Reflection and refraction at a random moving surface: I-pattern and paths of specular points; II-number of specular points in a Gaussian surface; III-frequency of twinkling in a Gaussian surface. J Opt Soc Am 50:838–856

    Article  ADS  MathSciNet  Google Scholar 

  • Lynch DK (1985) Reflections on closed loops. Nature 316:216–217

    Article  ADS  Google Scholar 

  • Mandelstam L (1913) Uber die Rauhigkeit freier Flussigkeitsoberflächen. Ann Phys 41:609–624

    Article  MATH  Google Scholar 

  • Maradudin AA (1982) Interaction of surface polaritons and plasmons with surface roughness. Chapter 10 in the volume edited by Agranovich and Mills

    Google Scholar 

  • Maystre D (1982) General study of grating anomalies from electromagnetic surface modes. In: Boardman AD (ed) Chapter 17 in Electromagnetic surface modes, Wiley, New York

    Google Scholar 

  • Millar RF (1971) On the Rayleigh assumption in scattering by a periodic surface, 2. Proc Camb Phil Soc 69:217–225

    Article  ADS  MathSciNet  Google Scholar 

  • Millar RF (1973) The Rayleigh hypothesis and a related least-squares solution to scattering problems for periodic surfaces and other scatterers. Radio Sci 8:785–796

    Article  ADS  MathSciNet  Google Scholar 

  • Nieto-Vesperinas M, Garcia N (1981) A detailed study of the scattering of scalar waves from random rough surfaces. Optica Acta 289:1651–1672

    Article  ADS  MathSciNet  Google Scholar 

  • Nieto-Vesperinas M (2006) Chapter 7 of scattering and diffraction in physical optics, 2nd edn. World Scientific, Singapore

    Book  Google Scholar 

  • Nordam T, Letnes PA, Simonsen I, Maradudin AA (2014) Numerical solutions of the Rayleigh equations for the scattering of light from a two-dimesional randomly rough perfectly conducting surface. J Opt Soc Am A 31:1126–1134

    Article  ADS  Google Scholar 

  • Nussenzveig HM (2002) Does the glory have a simple explanation? Opt Lett 27:1379–1381

    Article  ADS  Google Scholar 

  • O’Donnell KA, Mendez ER (1987) Experimental study of scattering from characterized random surfaces. J Opt Soc Am A 4:1194–1205

    Google Scholar 

  • Oetking P (1966) Photometric studies of diffusely reflecting surfaces with applications to the brightness of the moon. J. Geophys Res 71:2505–2513

    Article  ADS  Google Scholar 

  • Ogilvy JA (1991) Theory of wave scattering from random rough surfaces. Adam Hilger, Bristol

    MATH  Google Scholar 

  • Petit R, Cadilhac M (1966) Sur la diffraction d’une onde plane par un réseau infiniment conducteur. C R Acad Sci Paris B 263:468–471

    Google Scholar 

  • Raether H (1982) Surface plasmons and roughness. Chapter 9 in the volume edited by Agranovich and Mills

    Google Scholar 

  • Rayleigh JWS (1879) On the accuracy required in optical surfaces. Section 5 of Article 62, Scientific papers, vol I (Cambridge 1899, Dover 1964)

    Google Scholar 

  • Rayleigh JWS (1896) Theory of sound, section 272a (Dover 1954)

    Google Scholar 

  • Rayleigh JWS (1901) Polish. Article 268 in scientific papers, vol IV

    Google Scholar 

  • Rayleigh JWS (1907a) On the dynamical theory of gratings. Article 322 in scientific papers, vol V

    Google Scholar 

  • Rayleigh JWS (1907b) Note on the remarkable case of diffraction spectra described by Prof. Wood. Article 323 in scientific papers, vol V

    Google Scholar 

  • Rice SO (1951) Reflection of electromagnetic waves from slightly rough surfaces. Commun Pure Appl Math 4:351–378

    Article  MATH  Google Scholar 

  • Shmelev AB (1972) Wave scattering by statistically uneven surfaces. Sov Phys Uspekhi 15:173–183

    Article  ADS  Google Scholar 

  • Simonsen I, Maradudin AA, Leskova TA (2010a) Scattering of electromagnetic waves from two-dimesional randomly rough perfectly conducting surfaces: the full angular intensity distribution. Phys Rev A 81:013806 (13 pp)

    Google Scholar 

  • Simonsen I, Maradudin AA, Leskova TA (2010b) Scattering of electromagnetic waves from two-dimesional randomly rough penetrable surfaces. Phys Rev Lett 104:233904 (4 pp)

    Google Scholar 

  • Simonsen I, Kryvi JB, Maradudin AA, Leskova TA (2011) Light scattering from anisotropic, randomly rough, perfectly conducting surfaces. Comput Phys Commun 182:1904–1908

    Article  ADS  MATH  Google Scholar 

  • Triezenberg DG (1973) Capillary surface waves in a diffuse liquid-gas interface. Ph.D. Thesis, University of Maryland

    Google Scholar 

  • Twomey SA, Bohren CF, Mergenthaler JL (1986) Reflectance and albedo differences between wet and dry surfaces. Appl Opt 25:431

    Article  ADS  Google Scholar 

  • Watson GN (1944) Theory of Bessel functions. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Wood RW (1902) On a remarkable case of uneven distribution of light in a diffraction grating spectrum. Phil Mag 4:396–402

    Article  Google Scholar 

  • Wood RW (1934) Physical optics. Macmillan, New York

    Google Scholar 

  • Yasuura K (1971) A view of numerical methods in diffraction problems. Progress in radio science 1966–1969, 3:257–270, (International Union of Radio Science, Brussels)

    Google Scholar 

  • Zielinska BJA, Bedeaux D, Vlieger J (1981, 1983) Electric and magnetic susceptibilities for a fluid-fluid interface: I the ellipsometric coefficient. Physica 107A:81–108; II critical behaviour. Physica 117A:28–46

    Google Scholar 

Further Readings

  • Additional references on gratings

    Google Scholar 

  • Hutley MC (1982) Diffraction gratings. Academic Press, New York

    Google Scholar 

  • Petit R (ed) (2013) Electromagnetic theory of gratings. Springer, Berlin

    Google Scholar 

  • Stroke GW (1967) Diffraction gratings. Handbuch der Physik 29:426–754, Springer

    Google Scholar 

  • Metallic rough surfaces and surface plasmons

    Google Scholar 

  • Beaglehole D, Hunderi O (1970) Study of the interaction of light with rough metal surfaces. I-experiment, II-theory. Phys Rev B 2(309–321):321–329

    ADS  Google Scholar 

  • Celli V, Marvin A, Toigo F (1975) Light scattering from rough surfaces. Phys. Rev. B 11:1779–1786

    Article  ADS  Google Scholar 

  • Elson JM, Ritchie RH (1971) Photon interactions at a rough metal surface. Phys Rev B 4:4129–4138

    Article  ADS  Google Scholar 

  • Hornauer DL, Raether H (1981) Determination of roughness of LiF films using guided light modes. Opt Commun 40:105–110

    Article  ADS  Google Scholar 

  • Hunderi O (1980) Optics of rough surfaces, discontinuous films and heterogeneous materials. Surf Sci 96:1–31

    Article  ADS  Google Scholar 

  • Keller JM, Fuchs R, Kliever KL (1975) p-polarized optical properties of a metal with a diffusely scattering surface. Phys Rev B 12:2012–2029

    Article  ADS  Google Scholar 

  • Kroger E, Kretschmann E (1970) Scattering of light by slightly rough surfaces on thin films including plasmon resonance emission. Z Physik 237:1–15

    Article  ADS  Google Scholar 

  • Marvin A, Toigo F, Celli V (1975) Light scattering from rough surfaces: general incidence angle and polarization. Phys. Rev. B 11:2777–2782

    Article  ADS  Google Scholar 

  • Scattering from liquid surfaces

    Google Scholar 

  • Vrij A, Joosten JGH, Fijnaut HM (1981) Light scattering from thin liquid films. Adv Chem Phys 48:329–396

    Google Scholar 

  • Peternelj J (1981) Scattering of light due to the density fluctuations in the interface region of a liquid-vapour system. Can J Phys 59:1009–1019

    Article  ADS  Google Scholar 

  • Meunier J, Langevin D (1982) Optical reflectivity of a diffuse interface. J de Physique Lett 43:185–191

    Article  Google Scholar 

  • Experimental studies of surface roughness

    Google Scholar 

  • Elson JM, Bennett HE, Bennett JM (1979) Scattering from optical surfaces. Chapter 7 of vol 7, applied optics and optical engineering, Academic Press

    Google Scholar 

  • Rufenach CL, Alpers WR (1981) Imaging ocean waves by synthetic aperture radars with long integration times. IEEE Trans AP-29:422–428

    Google Scholar 

  • Wang Y, Wolfe WL (1983) Scattering from microrough surfaces: comparison of theory and experiment. J Opt Soc Am 73:1596–1602

    Article  ADS  Google Scholar 

  • Bennett JM (1985) Comparison of techniques for measuring the roughness of optical surfaces. Opt Eng 24:380–387

    Article  ADS  Google Scholar 

  • Laser speckle and surface roughness

    Google Scholar 

  • Rabal HJ, Braga RA (eds) (2009) Dynamic laser speckle and applications. CRC Press, New York

    Google Scholar 

  • Dainty JC (ed) (1975) Laser speckle and related phenomena. Springer, New York

    Google Scholar 

  • Welford WT (1980) Laser speckle and surface roughness. Contemp. Phys. 21:401–412

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to John Lekner .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Lekner, J. (2016). Rough or Structured Surfaces. In: Theory of Reflection. Springer Series on Atomic, Optical, and Plasma Physics, vol 87. Springer, Cham. https://doi.org/10.1007/978-3-319-23627-8_14

Download citation

Publish with us

Policies and ethics