Measurement and evaluation of three-dimensional particle shape under constant particle orientation with a tri-axial viewer

A tri-axial viewer was developed to measure the three-dimensional(3D) shape of a particle from three orthogonal directions, t, u and v, simultaneously. The angle of a particle's orientation δ was determined by the analysis of the principal moment of inertia for the vertical image of the particle under a stable position. The angle δ was set at zero by rotating the stage of the viewer (the S/C method). The particle images through the tri-axial viewer were magnified 10 times and the shapes were measured by an image analyzer. Shape measurements under random orientation were also carried out (the S/R method). Canonical discriminant analysis proved that the differences in 3D shapes among particles were detected effectively by the S/C method rather than the S/R method. The largest correct discrimination ratio, D, was obtained by the combination of 3D shape indices, ψ1 (tuv) and ψ2 (tuv) . Therefore, both indices were found to be useful for evaluating the particle's 3D shape.