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Fractal and Lacunarity Analyses: Quantitative Characterization of Hierarchical Surface Topographies

Published online by Cambridge University Press:  13 January 2016

Edwin J. Y. Ling ,
Phillip Servio  and
Anne-Marie Kietzig
Edwin J. Y. Ling
Affiliation:
Department of Chemical Engineering, McGill University, 3610 University Street, Montréal, Québec, Canada, H3A 0C5
Phillip Servio
Affiliation:
Department of Chemical Engineering, McGill University, 3610 University Street, Montréal, Québec, Canada, H3A 0C5
Anne-Marie Kietzig*
Affiliation:
Department of Chemical Engineering, McGill University, 3610 University Street, Montréal, Québec, Canada, H3A 0C5
*
*Corresponding author. anne.kietzig@mcgill.ca
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Abstract

Biomimetic hierarchical surface structures that exhibit features having multiple length scales have been used in many technological and engineering applications. Their surface topographies are most commonly analyzed using scanning electron microscopy (SEM), which only allows for qualitative visual assessments. Here we introduce fractal and lacunarity analyses as a method of characterizing the SEM images of hierarchical surface structures in a quantitative manner. Taking femtosecond laser-irradiated metals as an example, our results illustrate that, while the fractal dimension is a poor descriptor of surface complexity, lacunarity analysis can successfully quantify the spatial texture of an SEM image; this, in turn, provides a convenient means of reporting changes in surface topography with respect to changes in processing parameters. Furthermore, lacunarity plots are shown to be sensitive to the different length scales present within a hierarchical structure due to the reversal of lacunarity trends at specific magnifications where new features become resolvable. Finally, we have established a consistent method of detecting pattern sizes in an image from the oscillation of lacunarity plots. Therefore, we promote the adoption of lacunarity analysis as a powerful tool for quantitative characterization of, but not limited to, multi-scale hierarchical surface topographies.

Keywords

fractal dimensionlacunaritytexture analysislaser-induced hierarchical surface topographiesscanning electron microscopy
Type
Materials Applications
Information
Microscopy and Microanalysis , Volume 22 , Issue 1 , February 2016 , pp. 168 - 177
Copyright
© Microscopy Society of America 2016 

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