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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 5 — Mar. 10, 2014
  • pp: 5216–5227

Tomographic reconstruction of the refractive index with hard X-rays: an efficient method based on the gradient vector-field approach

Sergei Gasilov, Alberto Mittone, Emmanuel Brun, Alberto Bravin, Susanne Grandl, Alessandro Mirone, and Paola Coan  »View Author Affiliations

Optics Express, Vol. 22, Issue 5, pp. 5216-5227 (2014)

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The refractive-index gradient vector field approach establishes a connection between a tomographic data set of differential phase contrast images and the distribution of the partial spatial derivatives of the refractive index in an object. The reconstruction of the refractive index in a plane requires the integration of its gradient field. This work shows how this integration can be efficiently performed by converting the problem to the Poisson equation, which can be accurately solved even in the case of noisy and large datasets. The performance of the suggested method is discussed and demonstrated experimentally by computing the refractive index distribution in both a simple plastic phantom and a complex biological sample. The quality of the reconstruction is evaluated through the direct comparison with other commonly used methods. To this end, the refractive index is retrieved from the same data set using also (1) the filtered backprojection algorithm for gradient projections, and (2) the regularized phase-retrieval procedure. Results show that the gradient vector field approach combined with the developed integration technique provides a very accurate depiction of the sample internal structure. Contrary to the two other techniques, the considered method does not require a preliminary phase-retrieval and can be implemented with any advanced computer tomography algorithm. In this work, analyzer-based phase contrast images are used for demonstration. Results, however, are generally valid and can be applied for processing differential phase-contrast tomographic data sets obtained with other phase-contrast imaging techniques.

© 2014 Optical Society of America

OCIS Codes
(110.7440) Imaging systems : X-ray imaging
(120.5710) Instrumentation, measurement, and metrology : Refraction
(110.6955) Imaging systems : Tomographic imaging
(110.3010) Imaging systems : Image reconstruction techniques

ToC Category:
X-ray Optics

Original Manuscript: November 28, 2013
Revised Manuscript: January 9, 2014
Manuscript Accepted: January 11, 2014
Published: February 27, 2014

Virtual Issues
Vol. 9, Iss. 5 Virtual Journal for Biomedical Optics

Sergei Gasilov, Alberto Mittone, Emmanuel Brun, Alberto Bravin, Susanne Grandl, Alessandro Mirone, and Paola Coan, "Tomographic reconstruction of the refractive index with hard X-rays: an efficient method based on the gradient vector-field approach," Opt. Express 22, 5216-5227 (2014)

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