Fractal Methods for the Characterization of the Topography and Texture of a Surface

Surface Roughness Characterization of Poly(methylmethacrylate) Films with Immobilized Eu(III) β-Diketonates by Fractal Analysis

“…[18,22] Fractal analyses depend on the fractal analysis methods including the algorithm and specific calculation used, among others. [19,21,22,27,28] SURFACE ROUGHNESS CHARACTERIZATION OF PMMA FILM In our study, for these surfaces the best method of fractal analysis was morphological envelopes. [29] In this method, [30] the upper and lower envelopes are calculated by morphological opening and closing using a structuring element that is a horizontal line segment of length e. The graph of the calculated volume for surfaces (Ve) is drawn as a function of the scale (size of the structuring elements): ln(Ve)=ln(e).…”

“…[19,20] Fractal geometry allows a quantitative description of irregular micro and nano structures. [21][22][23] 406 Ş . Ţ A ALU ET AL.…”

“…[19,21] In comparison to statistical analyses, fractal analyses allow extracting different types of information from surface characteristics in accordance with their morphology, with low computational time and high precision. [19] Fractals are objects satisfying two criteria: being self-similar or self-affine and having a noninteger dimension.…”

“…Different methods of analyzing fractal surfaces have been proposed in the literature and can be related to functional models of interactions with surfaces. [21] Let's consider a fractal object recorded into a digital image. Let A be any nonempty bounded subset of R n (n-dimensional Euclidian space R n ).…”

“…It is strictly greater than its topological dimension. [21,22] The fractal dimension indicates for 3-D surfaces how much the fractal surface fills the 3-D volume. [18,19] Generally, the fractal dimension D f of a surface is a fractional value within the range 2 D f 3, where D f ¼ 2 (for ideally smooth surfaces) and D f ¼ 3 (for surfaces with a roughness that occupies all available volume).…”