| Issue |
EPL
Volume 143, Number 2, July 2023
|
|
|---|---|---|
| Article Number | 22002 | |
| Number of page(s) | 6 | |
| Section | Mathematical and interdisciplinary physics | |
| DOI | https://doi.org/10.1209/0295-5075/ace4ee | |
| Published online | 24 July 2023 | |
Inverse projection of axisymmetric orientation distributions
Department of Materials Science & Metallurgy, University of Cambridge - 27 Charles Babbage Road, Cambridge, UK
(a) E-mail: pak37@cam.ac.uk
(b) E-mail: jae1001@cam.ac.uk (corresponding author)
Received: 10 November 2022
Accepted: 6 July 2023
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 rod-like 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.
© 2023 The author(s)
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