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Soft Matter and Biological Physics

Eur. Phys. J. E 5, 551-556 (2001)

Grayscale projection of finite size fractal clusters

O. Vormoor

Institut für Röntgenphysik, Georg-August-Universität Göttingen, Geiststrasse 11, 37073 Göttingen, Germany


(Received 13 November 2000 and Received in final form 18 May 2001)

Microscopy techniques are suitable to obtain structural information of colloidal clusters with high resolution, but yield only a two dimensional projection of the objects. When imaging finite size objects with fractal properties, such as clusters of colloidal particles, this projection process has to be taken into account for the calculation of the fractal dimension. In this paper we present a technique to calculate the fractal dimension of finite size clusters with fractal properties using grayscale projections such as images obtained by X-ray microscopy. The grayscales are interpreted as different occupation counts within a projection. It is shown, that the radial distribution of these occupation counts varies with the fractal dimension d of the cluster. Using the radius of maximum occupation probability the fractal dimension up to 2.2 of finite size clusters can be calculated. The theoretical predictions are verified by test calculations employing numerically generated clusters.

61.43.Hv - Fractals: macroscopic aggregates.
82.70.Dd - Colloids.

© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001