The X-ray Transform and its Application in Nano Crystallography
الموضوعات : فصلنامه نانوساختارهای اپتوالکترونیکیtajedin derikvand 1 , Rajab Ali Kamyabi-Gol 2 , mohammad janfada 3
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
الکلمات المفتاحية: X- ray transform, Nano crystallography, homogeneous spaces,
ملخص المقالة :
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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