Abstract
Tomography — the reconstruction of a two-dimensional image from a series of its one-dimensional projections — is now a very broad topic with a wealth of algorithms for the reconstructions of both qualitative and quantitative images. One of the simplest algorithms has been modified to take into account the nonlinearity of large-amplitude synchrotron motion in a particle accelerator. This permits the accurate reconstruction of longitudinal phase space density from one-dimensional bunch profile data. The algorithm was developed in Mathematica™ in order to exploit the extensive built-in functions and graphics. Subsequently, it has been recoded in Fortran 90 with the aim of reducing the execution time by at least a factor of one hundred. The choice of Fortran 90 was governed by the desire ultimately to exploit parallel architectures, but sequential compilation and execution have already largely yielded the required gain in speed. The use of the method to produce longitudinal phase space plots, animated sequences of the evolution of phase space density and to estimate accelerator parameters is presented. More generally, the new algorithm constitutes an extension of computerized tomography which carers for nonrigid bodies whose projections cannot be measured simultaneously.
Highlights
The underlying principle of tomography is to combine the information in a sufficiently large number of profiles to be able to reconstruct unambiguously the fuller picture with the extra dimension reinstated
For example, many one-dimensional profiles of x-ray transparency taken from different angles can give doctors an image of a two-dimensional slice through a patient
The application of tomography to longitudinal phase space becomes obvious once it is realised that a bunch performing synchrotron motion is analogous to a patient rotating in a stationary body scanner
Summary
The underlying principle of tomography is to combine the information in a sufficiently large number of profiles to be able to reconstruct unambiguously the fuller picture with the extra dimension reinstated. Back projection is a key process by which the contents of the bins of a one-dimensional histogram are redistributed over the two-dimensional array of cells which comprise the reconstructed image. The back projection of all bins of all profiles yields a first approximation to the original distribution.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
