Functional-integral representation of rough surfaces
Abstract
A functional-integral 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 surface-correlation 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 mean-squared surface-height 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;
- Landau-Ginzburg Equations;
- Power Spectra;
- Probability Distribution Functions;
- Surface Roughness;
- Correlation Detection;
- Fractals;
- Phase Transformations;
- Vertical Distribution;
- Physics (General)