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Article Dans Une Revue Journal of Physics A: Mathematical and General (1975 - 2006) Année : 2003

Correlation dimension of self-similar surfaces and application to Kirchhoff integrals

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For surfaces generated by a class of asymptotically self-similar processes we define a probability measure, supported by the surface. We show that the correlation dimension of that surface measure is linked to the self-similarity exponent almost surely. This result is applied to the Kirchhoff integral well known in scattering from rough surfaces. We show that a certain average of the scattered intensity exhibits almost surely a scaling that allows us to recover the self-similarity index of the surface in an experiment involving only one sample of the surface.
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hal-00083207 , version 1 (10-07-2016)

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Charles-Antoine Guérin, Matthias Holschneider. Correlation dimension of self-similar surfaces and application to Kirchhoff integrals. Journal of Physics A: Mathematical and General (1975 - 2006), 2003, 36 (34), pp.9067-9079. ⟨10.1088/0305-4470/36/34/309⟩. ⟨hal-00083207⟩
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