# Onion Peeling (Bordas)¶

## Introduction¶

The onion peeling method, also known as “back projection” has been ported to Python from the original Matlab implementation, created by Chris Rallis and Eric Wells of Augustana University, and described in [1]. The algorithm actually originates from Bordas ~et al. [2].

See the discussion in issue #56.

## How it works¶

This algorithm calculates the contributions of particles, at a given kinetic energy, to the signal in a given pixel (in a row). This signal is then subtracted from the projected (experimental) pixel and also added to the back-projected image pixel. The procedure is repeated until the center of the image is reached. The whole procedure is done for each pixel row of the image.

## When to use it¶

This is a historical implementation of the onion-peeling method.

## How to use it¶

To complete the inverse transform of a full image with the onion_bordas method, simply use the abel.Transform: class

abel.Transform(myImage, method='onion_bordas').transform


If you would like to access the onion-peeling algorithm directly (to transform a right-side half-image), you can use abel.onion_bordas.onion_bordas_transform().

Source code

## Citation¶

 [1] C. E. Rallis, T. G. Burwitz, P. R. Andrews, M. Zohrabi, R. Averin, S. De, B. Bergues, B. Jochim, A. V. Voznyuk, N. Gregerson, B. Gaire, I. Znakovskaya, J. McKenna, K. D. Carnes, M. F. Kling, I. Ben-Itzhak, E. Wells, “Incorporating real time velocity map image reconstruction into closed-loop coherent control”, Rev. Sci. Instrum. 85, 113105 (2014).
 [2] C. Bordas, F. Paulig, “Photoelectron imaging spectrometry: Principle and inversion method”, Rev. Sci. Instrum. 67, 2257–2268 (1996).