A comparative study of correlation methods for determination of fractal parameters in surface characterization

• Published in: Applied surface science Vol. 293; pp. 196 - 201
• Main Authors: Kulesza, Slawomir, Bramowicz, Miroslaw
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 28.02.2014; Elsevier
• Subjects: Condensed matter: electronic structure, electrical, magnetic, and optical properties; Condensed matter: structure, mechanical and thermal properties; Cross-disciplinary physics: materials science; rheology; Exact sciences and technology; Fractal analysis; Physics; Polycrystalline films; Surface topography; Polycrystalline films; Fractal analysis; Surface topography; Fractals; Correlation methods
• ISSN: 0169-4332
• DOI: 10.1016/j.apsusc.2013.12.132

•Determination of fractal dimension by the autocorrelation method, structure function method, roughness method, and cube count method.•Comparison of the numerical accuracy of the methods.•Time-evolution of fractal parameters and anisotropy measures.•Recommendations for using each method. An analysis of several methods of extraction of fractal parameters from the simulated, artificial surfaces and AFM images of the real, polycrystalline diamond films is presented in the paper. The methods involve the cube count method, the roughness method, the autocorrelation function method, and the structure function method. By comparing the four methods, the roughness method is found to be superior for its high numerical accuracy, whereas the cube count method appears to be inferior in that aspect. The changes in the fractal dimension and the anisotropy ratio values observed over deposition time are also shown and discussed in the paper.