Eur. Phys. J. E 5, 551-556 (2001)
Grayscale projection of finite size fractal clusters
O. VormoorInstitut für Röntgenphysik, Georg-August-Universität Göttingen, Geiststrasse 11, 37073 Göttingen, Germany ovormoo@gwdg.de
(Received 13 November 2000 and Received in final form 18 May 2001)
Abstract
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
