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The Abel transform is a mathematical operation that transforms acylindrically symmetric three-dimensional (3D) object into its two-dimensional(2D) projection. The inverse Abel transform reconstructs the 3D object from the2D projection. Abel transforms have wide application across numerous fields ofscience, especially chemical physics, astronomy, and the study of laser-plasmaplumes. Consequently, many numerical methods for the Abel transform have beendeveloped, which makes it challenging to select the ideal method for a specificapplication. In this work eight transform methods have been incorporated into asingle, open-source Python software package (PyAbel) to provide a directcomparison of the capabilities, advantages, and relative computationalefficiency of each transform method. Most of the tested methods providesimilar, high-quality results. However, the computational efficiency variesacross several orders of magnitude. By optimizing the algorithms, we find thatsome transform methods are sufficiently fast to transform 1-megapixel images atmore than 100 frames per second on a desktop personal computer. In addition, wedemonstrate the transform of gigapixel images.

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