**1. Introduction**

100 Numerical Simulation – From Theory to Industry

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Strozzi, D., Shoucri, M., Bers, A., Williams, E.A. & Langdon, A.B. (2006). Vlasov Simulations of Trapping and Inhomogeneity in Raman Scattering. *J. Plasma Phys.*, Vol. 72, pp. 1299-

Waltz, R.E., Candy, J., Rosenbluth, M.N. & Hinton, F.L. (1999). Progress on a Full Radius Electromagnetic Gyrokinetic Code. *Proceedings of EPS 1999 26th Conference on Contr. Fusion and Plasma Phys.*, ECA Vol. 23J, pp. 1233-1236, Maastricht, Holland,

Yanenko, N.N. (1971). *The Method of Fractional Steps*, Springer-Verlag, New York.

Progress in nuclear physics acquired during World War II has naturally led many scientists to devote their research activities to the field of tomographic imaging techniques using ionizing radiation. This was, in the post-war booming economy, particularly of great importance for medical diagnostic as well as for industrial non destructive evaluation (NDE). As the objective is to extract information on the inner part of objects of interest, penetrating radiation was the most appropriate agent for this purpose. With the availability of high quality X-ray and gamma-ray sources (either directly originated from nuclear transitions or from pair annihilation) and the emergence of sensitive detectors, three types of imaging have been introduced and developed throughout half a century. Nowadays they have emerged as mature standard investigation methods for several domains of application.

These are: a) the X-ray transmission Computed Tomography (CT), which exploits the physical law of radiation attenuation in matter, b) the Single Photon Emission Tomography (SPECT), which uses the possibility of implanting radiation sources inside objects, c) the Positron Emission Tomography (PET), which uses the possibility of implanting positron sources in objects and exploits the properties of electron-positron pair annihilation. Milestones of their sensational evolution throughout decades are vividly recalled in recent reviews, see *e.g.* [35, 47].

It is observed that all three cited imaging methods deal exclusively with primary (or non-deviated) radiation. The physical quantity, which is non-uniformly distributed over an object and responsible for the imaging process, is respectively: the linear attenuation coefficient for CT, the *γ*-ray radio-activity density inside the object for SPECT, and the *β*+-ray (or positron) radio-activity density for PET.

However right at the start, scientists were also attracted by the idea of using scattered radiation by Compton effect (the scattering of X- or gamma photons by an electron) to image the inner parts of an object by reconstructing its electron density map. While this last imaging technology has not yet reached the same level of maturity as the three quoted above, it has

©2012 Truong and Nguyen, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

gone through revolutionary conceptual steps which have led to what is nowadays known as Compton scatter tomography (CST). Yet it has stirred continuous interest in numerous applications, see *e.g.* [2], [4], [11], [18], [5], [22], [29], [1], [23]. The aim of this chapter is to recount the past episodes of research, to give a comprehensive account of what has been accomplished in CST and to describe some new ideas which have arisen recently, see [42, 54]. The emphasis of the discussion shall be placed at the theoretical level. Negative effects on imaging such as beam attenuation and multiple scattering, which complicate enormously the analytic treatment, shall be dealt with conventional retrieval or compensation methods. The crux of the matter is to see how fertile ideas evolve in time and generate new fruitful concepts.
