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 particleʹs 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 particleʹs 3D shape.