## Information content of Born scattered fields: results in the circular cylindrical case

JOSA A, Vol. 15, Issue 7, pp. 1909-1917 (1998)

http://dx.doi.org/10.1364/JOSAA.15.001909

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### Abstract

In this analysis some limitations of the linear Born approximation in the diffraction tomography problem from far-zone data are pointed out. The analysis is performed by means of singular-value decomposition of the scattering operator in the scalar two-dimensional case of a circular dielectric cylinder illuminated by a TM-polarized plane wave. It is shown that the validity of the Born approximation entails the important condition that the scattering object not present too-fast spatial variations of the permittivity profile. For the rotationally symmetric cylinder, evidence is presented that the imaginary part of the normalized scattered far field has no information content for real permittivity objects. Moreover, for angularly varying cylinders the information content of the scattered far field for a single view is approximately the same as in the multiview case. Examples of singular-value and singular-function behavior and of profile reconstruction are depicted for the considered geometries.

© 1998 Optical Society of America

**OCIS Codes**

(100.3010) Image processing : Image reconstruction techniques

(100.3190) Image processing : Inverse problems

(290.3200) Scattering : Inverse scattering

**Citation**

Adriana Brancaccio, Giovanni Leone, and Rocco Pierri, "Information content of Born scattered fields: results in the circular cylindrical case," J. Opt. Soc. Am. A **15**, 1909-1917 (1998)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-7-1909

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### References

- D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlag, Berlin, 1992).
- A. J. Devaney, “Diffraction tomographic reconstruction from intensity data,” IEEE Trans. Image Process. 1, 221–228 (1992).
- M. H. Maleki, A. J. Devaney, and A. Shatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 9, 1356–1363 (1992).
- M. H. Maleki and A. J. Devaney, “Noniterative reconstruction of complex-valued objects from two intensity measurements,” Opt. Eng. 33, 3243–3253 (1994).
- T. C. Wedberg and W. C. Wedberg, “Tomographic reconstruction of the cross sectional refractive index distribution in semi-transparent, birefringent fibres,” J. Microsccopy 177, 53–67 (1995).
- T. C. Wedberg and J. J. Stamnes, “Experimental examination of the quantitative imaging properties of optical diffraction tomography,” J. Opt. Soc. Am. A 12, 493–500 (1995).
- W. Tabbara, B. Duchene, C. Pichot, D. Lesselier, L. Chommeloux, and N. Joachimovicz, “Diffraction tomography: contribution to the analysis of some applications in microwaves and ultrasonics,” Inverse Probl. 4, 305–331 (1988).
- L. Monch, “A Newton method for solving the inverse scattering problem for a sound-hard obstacle,” Inverse Probl. 12, 309–323 (1996).
- C. Lu, J. Lin, W. Chew, and G. Otto, “Image reconstruction with acoustic measurement using distorted Born iteration method,” Ultrason. Imaging 18, 140–156 (1996).
- I. Akduman, “An inverse scattering problem related to buried cylindrical bodies illuminated by gaussian beams,” Inverse Probl. 10, 213–226 (1994).
- S. Gutman and M. Klibanov, “Iterative method for multi-dimensional inverse scattering problems at fixed frequencies,” Inverse Probl. 10, 573–599 (1994).
- N. Joachimowitz, C. Pichot, and J. P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 39, 1742–1752 (1991).
- M. Moghaddam and W. C. Chew, “Study of some practical issues in inversion with the Born iterative method using time-domain data,” IEEE Trans. Antennas Propag. 41, 177–184 (1993).
- N. G. Gencer, M. Kuzouglu, and Y. Z. Ider, “Electrical impedance tomography using induced currents,” IEEE Trans. Med. Imaging 13, 338–350 (1994).
- C. Torres-Verdin and T. M. Habashy, “A two-step linear inversion of two-dimensional electrical conductivity,” IEEE Trans. Antennas Propag. 43, 405–415 (1995).
- A. Brancaccio, V. Pascazio, and R. Pierri, “A quadratic model for inverse profiling: the one dimensional case,” J. Electromagn. Waves Appl. 9, 673–696 (1995).
- R. Pierri and G. Leone, “Inverse scattering of dielectric cylinders by second order Born approximation,” IEEE Trans. Geosci. Remote Sens. (to be published).
- R. Pierri and A. Brancaccio, “Imaging of a rotationally symmetric cylinder by a quadratic approach,” J. Opt. Soc. Am. A 14, 2777–2785 (1997).
- T. Isernia, V. Pascazio, and R. Pierri, “A nonlinear estimation method in tomographic imaging,” IEEE Trans. Geosci. Remote Sens. 35, 910–923 (1997).
- M. Slaney, A. C. Kak, and L. E. Larsen, “Limitations of imaging with first order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
- J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross section shape,” IEEE Trans. Antennas Propag. AP-13, 334–341 (1965).
- M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).
- R. P. Porter and A. J. Devaney, “Generalized holography and computational solutions to inverse source problems,” J. Opt. Soc. Am. 72, 1707–1713 (1982).
- D. Slepian, “On bandwidth,” Proc. IEEE 64, 292–300 (1976).
- H. Harada, D. J. N. Wall, T. Takenaka, and M. Tanaka, “Conjugate gradient method applied to inverse scattering problem,” IEEE Trans. Antennas Propag. 43, 784–792 (1995).
- M. Azimi and K. C. Kak, “Distortion in diffraction tomography caused by multiple scattering,” IEEE Trans. Med. Imaging MI-2, 176–195 (1983).
- R. Pierri and A. Tamburino, “On the local minima problem in conductivity imaging via a quadratic approach,” Inverse Probl. 13, 1547–1568 (1997).
- R. Pierri and F. Soldovieri, “On the information content of the radiated fields in near zone over bounded domains,” Inverse Probl. 14, 321–337 (1998).

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