Abstract
One of the main motivations for studying rough surface scattering problems consists in the desire to obtain information about the surface. The information obtained can be of a varied nature. One may be interested, for instance, on the surface profile function, on the optical properties of the surface, or, for random surfaces, on some statistical parameter of the height fluctuations. These are all inverse scattering problems. This chapter contains a review of some aspects of this broad field.
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References
J.A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Institute of Physics Publishing, Bristol, UK, 1991).
M. Saillard and A. Sentenac, “Rigorous solutions for electromagnetic scattering from rough surfaces,” Waves Random Media 11, R103–R137 (2001).
A.A. Maradudin and E.R. Méndez, “Scattering by surfaces and phase screens,” in Scattering: Scattering and Inverse Scattering in Pure and Applied Science. Roy Pike and Pierre Sabatier, ed., (Academic Press, San Diego, 2002), pp. 864–894.
T.M. Elfouhaily and C.-A. Guérin, “A critical survey of approximate scattering wave tehories from random rough surfaces,” Waves Random Media 14, R1–R40 (2004).
A.V. Shchegrov, A.A. Maradudin, and E.R. Méndez, “Multiple Scattering of Light from Randomly Rough Surfaces,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2004), pp. 117–241.
J.C. Dainty (ed.), Laser Speckle and Related Phenomena, 2nd edn (Springer-Verlag, Berlin, 1984).
W.T. Welford, “Optical estimation of statistics of surface roughness from light scattering measurements,” Opt. Quantum Electron. 9, 269–387 (1977).
W.T. Welford, “Laser speckle and surface roughness,” Contemp. Phys. 21, 401–412 (1980).
J.A. Ratcliffe, “Some aspects of diffraction theory and their application to the ionosphere,” Rep. Prog. Phys. 19, 188–267 (1956).
P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon Press, London, 1963).
J.W. Goodman, Statistical Optics (Wiley New York, 1985).
M.V. Berry, “Diffractals,” J. Phys. A: Math. Gen. 12, 781–797 (1979).
E. Jakeman, “Scattering by a corrugated random surface with fractal slope,” J. Phys. A: Math. Gen. 15, L55–L59 (1982)
E. Jakeman, “Fraunhofer scattering by a sub-fractal diffuser,” Opt. Acta 30, 1207–1212 (1983).
A. Mendoza-Suárez and E.R. Méndez, “Light scattering by reentrant fractal surfaces,” Appl. Opt. 36, 3521–3531 (1997).
C. A. Guérin, M. Holschneider, and M. Saillard, “Electromagnetic scattering from multi-scale rough surfaces,” Waves Random Media 7, 331–349 (1997).
J.A. Sánchez-Gil, J.V. García-Ramos, and E.R. Méndez, “Influence of nanoscale cutoff in random self-affine fractal silver surfaces on the excitation of localized optical modes,” Opt. Lett. 26, 1286–1288 (2001).
P. Beckmann, “Scattering by non-Gaussian surfaces,” IEEE Trans. Antennas Propag. AP-21, 169–175 (1973).
M.J. Kim, E.R. Méndez, and K.A. O’Donnell, “Scattering from gamma-distributed surfaces,” J. Mod. Opt. 34, 1107–1119 (1987).
V.I. Tatarskii, “Characteristic functional for one class of non-Gaussian random functions,” Waves Random Media 5, 243–252 (1995).
V.V. Tatarskii and V.l. Tatarskii, “Non-Gaussian statistical model of the ocean surface for wave-scattering theories,” Waves Random Media 6, 419–435 (1996).
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).
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.C. Stover, S.A. Serati, and C.H. Guillespie, “Calculation of surface statistics from light scatter,” Opt.Eng. 23, 406–412 (1984).
J.W. Goodman, “Statistical properties of speckle patterns,” in Laser Speckle and Related Phenomena, 2nd edn (Springer-Verlag, Berlin, 1984). Pp. 9–75.
D. Léger, E. Mathieu, and J.C. Perrin, “Optical surface roughness determination using speckle correlation techniques,” Appl. Opt. 14, 872–877 (1975).
D. Léger and J.C. Perrin, “Real-time measurement of surface roughness by correlation of speckle patterns,” J. Opt. Soc. Am. 66, 1210–1217 (1976).
J. Shen and A.A. Maradudin, “Multiple scattering of waves from random rough surfaces,” Phys. Rev. B 22, 4234–4240 (1980).
J.A. Sánchez-Gil, A.A. Maradudin, and E.R. Méndez, “Limits of validity of three perturbation theories of the coherent scattering of light from a one-dimensional randomly rough dielectric surface,” J. Opt. Soc. Am. A 12, 1547–1558 (1995).
E.I. Chaikina, A.G. Navarrete, E.R. Méndez, A. Martinez, and A.A. Maradudin, “Coherent scattering by one-dimensional randomly rough metallic surfaces,” Appl. Opt. 37, 1110–1121(1998).
A.G. Navarrete, E.I. Chaikina, E.R. Méndez, and T.A. Leskova, “Experimental study of the reflectance of two-dimensional metal surfaces with a random roughness distribution,” J. Opt. Technol. 69, 71–76 (2002).
J.C. Stover, Optical Scattering: Measurement and Analysis, 2nd edn (SPIE Optical Engineering Press, Bellingham, Washington, D.C., 1995).
J.M. Bennett and L. Mattsson, Introduction to Surface Roughness and Scattering, 2nd edn (Optical Society of America, Washington, D.C., 1999).
J.J. Greffet, “Scattering of electromagnetic waves by rough dielectric surfaces,” Phys. Rev. B 37, 6436–6441 (1988).
M.U. González, J.A. Sánchez-Gil, Y. González, L. González, and E.R. Méndez, “Polarized laser light scattering applied to surface morphology characterization of epitaxial III–V semiconductor layers,” J. Vac. Sci. Technol. B 18, 1980–1990 (2000).
C.S. West and K.A. O’Donnell, “Observations of backscattering enhancement from polaritons on a rough metal surface,” J. Opt. Soc. Am. A 12, 390–397 (1995).
V. Malyshkin, S. Simeonov, A.R. McGurn, and A.A. Maradudin, “Determination of surface profile statistics from electromagnetic scattering data,” Opt. Lett. 22, 58–60 (1997).
A.A. Maradudin and E.R. Méndez, “Enhanced backscattering of light from a weakly rough, random metal surface,” Appl. Opt. 32, 3335–3343 (1993).
C.S. West and K.A. O’Donnell, “Angular correlation functions of light scattered from weakly rough metal surfaces,” Phys. Rev. B 59, 2393–2406 (1999).
R.J. Wombell and J.A. DeSanto, “Reconstruction of rough-surface profiles with the Kirchhoff approximation,” J. Opt. Soc. Am. A 8, 1892–1897 (1991).
R. J. Wombell and J.A. DeSanto, “The reconstruction of shallow rough-surfaces profiles from scattered field data,” Inverse Problems 7, L7–L12 (1991).
J.C. Quartel and C.J.R. Sheppard, “Surface reconstruction using an algorithm based on confocal imaging,” J. Mod. Opt. 43, 469–486 (1996).
J.C. Quartel and C.J.R. Sheppard, “A surface reconstruction algorithm based on confocal interferometric profiling,” J. Mod. Opt. 43, 591–605 (1996).
C.J.R. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta, 24, 1051–1073 (1977).
T. Wilson and C.J.R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic Press, New York, 1984).
D. Macías, E.R. Méndez, and V. Ruiz-Cortés, “Inverse scattering with a wave-front-matching algorithm,” J. Opt. Soc. Am. A 19, 2064–2073 (2002).
E. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999), p. 485.
D.K. Hamilton and C.J.R. Sheppard, “A confocal interference microscope,” Opt. Acta 29, 1573–1577 (1982).
A.A. Maradudin, T. Michel, A.R. McGurn, and E.R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (N.Y.) 203, 255–307 (1990).
J.F. Aguilar, M. Lera, and C.J.R. Sheppard, “Imaging of spheres and surface profiling by confocal microscopy,” Appl. Opt. 39, 4621–4628 (2000).
Macías, D., Estudios numéricos de esparcimiento inverso de ondas electromagnéticas, PhD Thesis (Centro de Investigación Científica y de Educación Superior de Ensenada, México, 2003).
D. Macías, G. Olague, and E.R. Méndez, “Surface profile reconstruction from scattered intensity data using evolutionary strategies,” S. Cagnoni et al., eds. (EvoWorkshops: Springer LNCS 2279 Berlin, 2002), pp. 233–244.
D. Macías, G. Olague and E.R. Méndez, “Hybrid evolution strategy-downhill simplex algorithm for inverse light scattering problems” S. Cagnoni et al., eds. (EvoWorkshops: Springer LNCS 2611, Berlin, 2003), pp. 339–409.
T.G. Kold, R.M. Lewis, and V. Torczon, “Optimization by direct search: new perspectives on some classical and modern methods,” SIAM Rev. 45, 385–482 (2003).
J.H. Holland, Adaption in Natural and Artificial Systems (MIT Press/Bradford Books, Cambridge, Massachusetts, 1992).
H.P. Schwefel, Evolution and Optimum Seeking (Wiley, New York, 1995).
J.R. Koza, “Genetic programming,” in Encyclopedia of Computer Science and Technology, J.G. Williams and A. Kent, eds. (Marcel-Dekker, US, 1998), pp. 29–43.
L.J. Fogel, “Autonomous automata,” Ind. Res. 4, 14–19 (1962).
J. Neider and R. Mead, “A simplex method for function optimization,” Comput. J. 7, 308–313 (1965).
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Méndez, E.R., Macías, D. (2007). Inverse Problems in Optical Scattering. In: Maradudin, A.A. (eds) Light Scattering and Nanoscale Surface Roughness. Nanostructure Science and Technology. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35659-4_16
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DOI: https://doi.org/10.1007/978-0-387-35659-4_16
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