Optics and Spectroscopy

, Volume 124, Issue 2, pp 278–284 | Cite as

Tomography in Optically Axisymmetric Media

Geometrical and Applied Optics
First Online:
Received:
  • 2 Downloads

Abstract

A generalization of the Cormac algorithm for the inversion of the Radon transformation in an optical medium with an axisymmetric index of refraction has been proposed. The distribution of rays is such that only one ray passes through any two points in the circle. A “parallel scanning scheme” of tomography has been considered: a cylindrical object is illuminated by a parallel beam of light, the rays of which are deflected into the cylinder. There is no refraction on the surface of the cylinder. The algorithm assumes the possibility of attenuation on a ray, which also has an axisymmetric character. Such a type of ray deflection occurs in problematic issues of the tomography of GRADANs, light guides, and plasma.

This is a preview of subscription content, log in to check access

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    F. Monard, Inverse Probl. Imaging 10, 433 (2016).MathSciNetCrossRefGoogle Scholar
  2. 2.
    R. Illingworth, Opt. Commun. 23, 109 (1977).ADSCrossRefGoogle Scholar
  3. 3.
    D. D. Karov, Extended Abstract of Cand. Sci. Dissertation (St. Petersburg, 2012). http://fizmathim.com/read/369384/a?#?page=16.Google Scholar
  4. 4.
    L. Pagnotta and A. Poggialini, Soc. Exp. Mech. 43, 69 (2003).CrossRefGoogle Scholar
  5. 5.
    V. Sharafutdinov and J.-N. Wang, Inverse Probl. 28 (6) (2012). doi 10.1088/0266-5611/28/6/065017Google Scholar
  6. 6.
    M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1968).Google Scholar
  7. 7.
    A. M. Cormack, J. Appl. Phys. 34, 2722 (1963).ADSCrossRefGoogle Scholar
  8. 8.
    A. Puro and A. Garin, Inverse Probl. 29, 065004 (2013). doi 10.1088/0266-5611/29/6/065004ADSCrossRefGoogle Scholar
  9. 9.
    A. Puro, Inverse Probl. 14, 1315 (1998).ADSCrossRefGoogle Scholar
  10. 10.
    A. Puro, Opt. Spectrosc. 116, 122 (2014).CrossRefGoogle Scholar
  11. 11.
    F. Natterer, The Mathematics of Computerized Tomography (Teubner, Stuttgart, 1986). doi 10.1007/978-3-663- 01409-6MATHGoogle Scholar
  12. 12.
    G. Riguad and A. Lakhal, Inverse Probl. 31, 025007 (2015). doi 10.1088/0266-5611/31/2/025007ADSCrossRefGoogle Scholar
  13. 13.
    A. Puro, Opt. Spectrosc. 110, 947 (2011).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.EuroacademyTallinnEstonia

Personalised recommendations