Determination of the distribution of the number of specular points of a random cylindrical homogeneous Gaussian surface

Abstract

Statistical characteristics of light reflected by the rough random cylindrical homogeneous Gaussian surface are being investigated by using the method of specular points. The inverse problem, in the form of a Fredholm integral equation of the first kind for determining the distribution of the number of specular points from the known reflected radiance distribution, is formulated. The kernel of this equation is determined by the characteristic function of the distribution of radii of curvature in specular points, derived by Gardashov. The validity of the obtained original formulas is controlled by numerical simulations.

Keywords:

• Specular points
• Radius of curvature
• Gardashov's distribution
• Gaussian surface
• Inverse problem
• Integral equation