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The orientation of fibers with elliptical cross-sections cannot be estimated using standard optical microscopy analysis methods in which the ratio of the minor-axis to the major-axis and orientation of the major-axis are directly used to determine the fiber spherical coordinates, θ and ϕ . A new method for estimating the orientation of fibers with elliptical cross-sections is presented and validated using both simulations and experiments. Fibers with elliptical cross-sections rather than circular possess a roll degree of freedom, which significantly affects the dimensions of projected cross-sections in viewing planes. The equations of the projected ellipse of an elliptic cylinder onto a viewing plane are determined in terms of typical spherical coordinate system angles, θ and ϕ , the roll angle, α , and the fiber semi-major and semi-minor diameters. Fiber angles are determined by numerical fitting of the developed equations to measured ellipses. An ambiguity in the determined angles is identified, and, in the special case of fiber bundles, a scheme is presented by which the ambiguity can be resolved. Validation experiments showed that the method is quite effective at estimating fiber orientation from micrographs when fiber cross-section dimensions are measured beforehand, and the additional ambiguity is resolved easily in the case of fiber bundles.

Measuring Fiber Orientation of Elliptical Fibers from Optical Microscopy