Functionalintegral representation of rough surfaces
Abstract
A functionalintegral approach to representing the statistics of rough surfaces is developed. The assumption of locality is discussed from both the mathematical and physical points of view, and it is noted that the assumption produces a probability distribution for the shape of the surface that has the form of an exponential of a power series in surface height, slope, curvature, and higher surface derivatives, while each term in the series has a straightforward interpretation with respect to the surface statistics. The surfacecorrelation function, to the lowest nontrivial order of approximation and within the assumption of locality, is predicted to be a K(0) Bessel function away from the origin and to be finite and equal to the meansquared surfaceheight variation at the origin. The power spectrum corresponding to this result for the correlation function is shown to be in good agreement with measured power spectra. It is also observed that the fractal behavior of rough surfaces occurs naturally in this formalism.
 Publication:

Journal of the Optical Society of America A
 Pub Date:
 January 1991
 DOI:
 10.1364/JOSAA.8.000097
 Bibcode:
 1991JOSAA...8...97G
 Keywords:

 Bessel Functions;
 Electromagnetic Scattering;
 LandauGinzburg Equations;
 Power Spectra;
 Probability Distribution Functions;
 Surface Roughness;
 Correlation Detection;
 Fractals;
 Phase Transformations;
 Vertical Distribution;
 Physics (General);
 SURFACES;
 SCATTERING;
 ROUGHNESS