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In view of the importance of clinical applications of ruthenium-106 beta-ray sources for the treatment of choroidal melanoma, experimental, and theoretical approaches are presented for the dosimetry of such sources. The absolute dose and percentage depth dose of ruthenium applicators have been measured with an extrapolation ionization chamber. For a special flat applicator the absolute dose could be measured with an accuracy of +/- 5%, which is determined by the collection efficiency of the extrapolation chamber. The percentage depth dose of concave applicators, employed in the clinical situation, could only be measured at a distance larger than 5 mm due to their geometry and the outer dimensions of the extrapolation chamber. A computer simulation was therefore developed for the absorption and scattering of electrons, taking into account the geometry and materials of the applicator, to predict the percentage depth dose at distances smaller than 5 mm. The calculated and experimentally determined depth doses are in good agreement. With the aid of the computer simulation a depth dose determination for concave applicators can be made for clinically relevant distances less than 10 mm from the source surface with an absolute accuracy of +/- 10%.