The X-ray Transform and its Application in Nano Crystallography

Subject Areas : Journal of Optoelectronical Nanostructures

tajedin derikvand ¹ (nternational Campus, Faculty of Mathematic Sciences, Ferdowsi University of Mashhad)
Rajab Ali Kamyabi-Gol ² (Department of Pure Mathematics and Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad)
mohammad janfada ³ (Department of Pure Mathematics, Ferdowsi University of Mashhad)

Received: 2016-12-31 Accepted : 2017-01-17 Published : 2017-05-01

Keywords: X- ray transform, Nano crystallography, homogeneous spaces,

Abstract :

In this article a review on the definition of the X- ray transform and some of
its applications in Nano crystallography is presented. We shall show that the X- ray
transform is a special case of the Radon transform on homogeneous spaces when the
topological group E(n)- the Euclidean group - acts on ℝ² transitively. First some
properties of the Radon transform are investigated then the relationship to texture analysis
is briefly illustrated. Finally, some of its applications in material structure detection at the
Nano scale are studied.

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