The X-ray Transform and its Application in Nano Crystallography
نویسندگان
1 nternational Campus, Faculty of Mathematic Sciences, Ferdowsi University of Mashhad
2 Department of Pure Mathematics and Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad
3 Department of Pure Mathematics, Ferdowsi University of Mashhad
doi
چکیده
In this article a review on the definition of the X- ray transform and some ofits applications in Nano crystallography is presented. We shall show that the X- raytransform is a special case of the Radon transform on homogeneous spaces when thetopological group E(n)- the Euclidean group - acts on ℝ2 transitively. First someproperties of the Radon transform are investigated then the relationship to texture analysisis briefly illustrated. Finally, some of its applications in material structure detection at theNano scale are studied.
