CHARACTERIZATION OF BIVARIATE SIZE-ORIENTATION DISTRIBUTION OF CIRCULAR PLATE PARTICLES

Abstract

The paper is devoted to the stereological unfolding problem of bivariate size-orientation distribution of platelike particles in metallography. Gokhale (1996) derived an integral equation which relates this bivariate distribution in three-dimensional (3D) space to the corresponding size-orientation distribution of planar sections of the specimen. The present paper yields a numerical algorithm which enables to transform a bivariate histogram of observed quantities to the histogram of 3D characteristics. The use of the method is demonstrated in examples with simulated data, where an easy analytical solution is available and can be compared with the results of estimation. The spectrum of unfolding problems solved numerically (cf. Ohser and Muecklich, 2000) is thus extended.

Keywords

• circular plate particles
• EM algorithm
• unfolding VUR sampling