Morphological Dilation as Fractal Scaling in Roughness Measurement

Abstract

In this work we propose, that the morphological dilation acts as fractal filters rebuilding white noise roughness surfaces into fractal 1/fm noise surfaces. The fractality indicates that the dilation does not have characteristic length scale, and the structuring element follows power-law distribution. Yashchuk's binary pseudo-random grating standard has been dilated with spherical and free form tips between 50 nm and 2000 nm and two scaling regions are referred to the tip diameter versus scaling exponent diagram. The first one in the smaller tip diameter region has a fast slope and the second one in the intermediate and larger tip diameter has a gradual slope. The results show that the dilated surfaces arise from the activity of at least two dynamical systems.