Abstract
We present a study of rough surface inverse scattering problems using evolutionary strategies. The input data consists of far-field angle-resolved scattered intensity data, and the objective is to reconstruct the surface profile function that produced the data. To simplify the problem, the random surface is assumed to be one-dimensional and perfectly conducting. The optimum of the fitness function is searched using the evolutionary strategies (μ, λ) and (μ + λ). On the assumption that some knowledge about the statistical properties of the unknown surface profile is given or can be obtained, the search space is restricted to surfaces that belong to that particular class. In our case, as the original surface, the trial surfaces constitute realizations of a stationary zeromean Gaussian random process with a Gaussian correlation function. We find that, for the conditions and parameters employed, the surface profile can be retrieved with high degree of confidence. Some aspects of the convergence and the lack of uniqueness of the solution are also discussed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces, (Pergamon Press, London, 1963), p. 29.
J. A. Oglivy, Theory of wave scattering from random rough surfaces, (Institute of Physics Publishing, Bristol, 1991), p. 277.
Rice, S. O.: Reflection of electromagnetic waves from slightly rough surfaces, Commun. Pure Appl. Math. 4, 351, 1951.
Thorsos, E. I.: The validity of the Kirchho. approximation for rough surface scattering using a Gaussian roughness spectrum, J. Acoust. Soc. Amer. 83, 78 (1988).
Maradudin, A. A., Michel, T., McGurn, A. R., Méndez, E. R.: Enhanced backscattering of light from a random grating, Ann. Phys. (N. Y.) 203, 255 (1990).
McGurn, A. R., Maradudin, A. A., Celli, V.: Localization effects in the scattering of light from a randomly rough grating, Phys. Rev. B31, 4866, 1985.
Méndez, E. R., O’Donnell, K. A.: Observation of depolarization and backscattering enhancement in light scattering from Gaussian random surfaces, Opt. Commun. 61, 91, 1987.
Chandley, P. J.: Determination of the autocorrelation function of height on a rough surface from coherent light scattering, Opt. Quant. Electron. 8, 329, 1976.
Welford, W. T.: Optical estimation of statistics of surface roughness from light scattering measurements, Opt. Quant. Electron. 9, 269, 1977.
Chandley, P. J.: Determination of the probability density function of height on a rough surface from far-field coherent light scattering, Opt. Quant. Electron. 11, 413, 1979.
Elson, J. M., Bennett, J. M.: Relation between the angular dependence of scattering and the statistical properties of optical surfaces, J. Opt. Soc. Am. 69, 31, 1979.
Stover, J. C., Serati, S. A.: Calculation of surface statistics from light scatter, Opt. Eng. 23, 406, 1984.
Wombel, R. J., De Santo, J. A.: Reconstruction of rough-surface profiles with the Kirchho. approximation, J. Opt. Soc. Am. A 8, 1892, (1991).
Wombel, R. J., De Santo, J. A.: The reconstruction of shallow rough-surfaces profiles from scattered field data, Inverse Problems 7, L7, (1991).
Quartel, J. C., Sheppard, C. J. R.: Surface reconstruction using an algorithm based on confocal imaging, J. Modern Optics 43, 496, (1996).
Quartel, J. C., Sheppard, C. J. R.: A surface reconstruction algorithm based on confocal interferometric profiling, J. Modern Optics 43, 591, (1996).
Macías, D., Méndez, E. R., Ruiz-Cortés, V.: Numerical study of an inverse scattering algorithm for perfectly conducting one-dimensional surfaces, in Scattering and Surfaces Roughness, A. A. Maradudin and Z. H. Gu, eds., Proc. SPIE 4100, 57–64 (2000).
Walther, A.: The question of phase retrieval in optics, Opt. Acta 10, 41,(1963).
O’Neill, E., Walther, A.: The question of phase in image formation, Opt. Acta 10, 33,(1963).
Nelder, J., Mead, R.: A simplex method for function optimization Computer Journal, 7, 308,(1965).
Press, W. H. (editor) Numerical Recipes in Fortran, (Cambridge University Press, Cambridge, 1992) p. 402.
H. P. Schwefel, Evolution and Optimum Seeking, (John Wiley & Sons Inc., NY, 1995), p. 444.
Macías, D., Méndez, E. R.: Unpublished work (2001).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Macías, D., Olague, G., Méndez, E.R. (2002). Surface Profile Reconstruction from Scattered Intensity Data Using Evolutionary Strategies. In: Cagnoni, S., Gottlieb, J., Hart, E., Middendorf, M., Raidl, G.R. (eds) Applications of Evolutionary Computing. EvoWorkshops 2002. Lecture Notes in Computer Science, vol 2279. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46004-7_24
Download citation
DOI: https://doi.org/10.1007/3-540-46004-7_24
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43432-0
Online ISBN: 978-3-540-46004-6
eBook Packages: Springer Book Archive