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Hickstein DD, Gibson ST, Yurchak R, et al. A direct comparison of high-speed methods for the numerical Abel transform. Rev Sci Instrum. 2019;90(6):065115doi: 10.1063/1.5092635.
Hickstein, D. D., Gibson, S. T., Yurchak, R., Das, D. D., & Ryazanov, M. (2019). A direct comparison of high-speed methods for the numerical Abel transform. The Review of scientific instruments, 90(6), 065115. https://doi.org/10.1063/1.5092635
Hickstein, Daniel D, et al. "A direct comparison of high-speed methods for the numerical Abel transform." The Review of scientific instruments vol. 90,6 (2019): 065115. doi: https://doi.org/10.1063/1.5092635
Hickstein DD, Gibson ST, Yurchak R, Das DD, Ryazanov M. A direct comparison of high-speed methods for the numerical Abel transform. Rev Sci Instrum. 2019 Jun;90(6):065115. doi: 10.1063/1.5092635. PMID: 31255037.
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Rev Sci Instrum. 2019 Jun;90(6):065115. doi: 10.1063/1.5092635.

A direct comparison of high-speed methods for the numerical Abel transform.

The Review of scientific instruments

Daniel D Hickstein, Stephen T Gibson, Roman Yurchak, Dhrubajyoti D Das, Mikhail Ryazanov

Affiliations

  1. Kapteyn-Murnane Laboratories, Inc., Boulder, Colorado 80301, USA.
  2. Research School of Physics and Engineering, The Australian National University, Canberra ACT 2601, Australia.
  3. Symerio, 91120 Palaiseau, France.
  4. Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06511, USA.
  5. JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309, USA.

PMID: 31255037 DOI: 10.1063/1.5092635

Abstract

The Abel transform is a mathematical operation that transforms a cylindrically symmetric three-dimensional (3D) object into its two-dimensional (2D) projection. The inverse Abel transform reconstructs the 3D object from the 2D projection. Abel transforms have wide application across numerous fields of science, especially chemical physics, astronomy, and the study of laser-plasma plumes. Consequently, many numerical methods for the Abel transform have been developed, which makes it challenging to select the ideal method for a specific application. In this work, eight published transform methods have been incorporated into a single, open-source Python software package (PyAbel) to provide a direct comparison of the capabilities, advantages, and relative computational efficiency of each transform method. Most of the tested methods provide similar, high-quality results. However, the computational efficiency varies across several orders of magnitude. By optimizing the algorithms, we find that some transform methods are sufficiently fast to transform 1-megapixel images at more than 100 frames per second on a desktop personal computer. In addition, we demonstrate the transform of gigapixel images.

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