Dimension of similarity as a characteristic of the solid-surface relief

Abstract

It is proposed that the dimension of similarity of the relief profile be used as an integral characteristic of solid-surface roughness. This parameter coincides with the fractal dimension of the line only in the case of the same length scales in the surface plane and in the direction that is normal to it. The interrelation between the dimension of similarity and the usually used fractal dimension of the relief profile is obtained and analyzed. The optical surface of single-crystal Ge is used as an example in order to reveal the correlation between the dimension of similarity of the relief surface and the transmission coefficient in the infrared range.