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arXiv · 2305.06433

Inverse projection of axisymmetric orientation distributions

Philipp A. Kloza·James A. Elliott
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Abstract

We show that the projection of an axisymmetric three-dimensional orientation distribution to two dimensions can be cast into an Abel transform. Based on this correspondence, we derive an exact integral inverse, which allows for the quantification of three-dimensional uniaxial alignment of rodlike units from two-dimensional sliced images, thus providing an alternative to X-ray or tomographic analysis. A matrix representation of the projection and its inverse is derived, providing a direct relationship between two- and three-dimensional order parameters for both polar and non-polar systems.

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Philipp A. Kloza, James A. Elliott. 2023-05-10. Inverse projection of axisymmetric orientation distributions. https://doi.org/10.1209/0295-5075%2Face4ee

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