## Improving the reconstruction capabilities in inverse scattering problems by exploitation of close-proximity setups

JOSA A, Vol. 16, Issue 7, pp. 1788-1798 (1999)

http://dx.doi.org/10.1364/JOSAA.16.001788

Enhanced HTML Acrobat PDF (553 KB)

### Abstract

It has recently been shown that the measurement setups usually adopted in inverse scattering problems, in which the primary sources and the receiving antennas are placed at some wavelength apart from the object under test, suffer from intrinsic limitations in the reconstruction capabilities because of the essentially finite-dimensional nature of the space of data (the scattered fields). To investigate whether it is possible to overcome these limitations, two (novel to our knowledge) measurement configurations for inverse scattering experiments at a fixed frequency are analyzed and discussed. By means of an analysis of the properties of the radiation operator, it is shown that positioning the measurement probes (and possibly the primary sources) in the close proximity of the object under test allows an improvement of the reconstruction capabilities of inversion algorithms with respect to conventional setups. However, such an improvement can be achieved only in a region close to the border of the region under test. Quantitative rules for the achievable improvement are given and are exemplified through numerical examples.

© 1999 Optical Society of America

**OCIS Codes**

(100.3190) Image processing : Inverse problems

(100.6640) Image processing : Superresolution

(100.6950) Image processing : Tomographic image processing

(290.3200) Scattering : Inverse scattering

**History**

Original Manuscript: December 1, 1998

Manuscript Accepted: January 25, 1999

Published: July 1, 1999

**Citation**

O. M. Bucci, L. Crocco, and T. Isernia, "Improving the reconstruction capabilities in inverse scattering problems by exploitation of close-proximity setups," J. Opt. Soc. Am. A **16**, 1788-1798 (1999)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-7-1788

Sort: Year | Journal | Reset

### References

- J. C. Bolomey, “Recent European developments in active microwave imaging for industrial, scientific, and medical applications,” IEEE Trans. Microwave Theory Tech. 37, 2109–2117 (1991). [CrossRef]
- P. M. Meaney, K. D. Paulsen, J. T. Chang, “Near-field microwave imaging of biologically-based materials using a monopole transceiver system,” IEEE Trans. Microwave Theory Tech. 46, 31–45 (1998). [CrossRef]
- D. J. Daniels, “Surface penetrating radar,” Electron. Commun. Eng. J. 8, 165–182 (1996). [CrossRef]
- M. Bertero, “Linear inverse and ill-posed problems,” Adv. Electron. Electron Phys. 75, 1–120 (1989). [CrossRef]
- T. Isernia, V. Pascazio, R. Pierri, “A nonlinear estimation method in tomographic imaging,” IEEE Trans. Geosci. Remote Sens. 35, 910–923 (1997). [CrossRef]
- R. Pierri, A. Brancaccio, “Imaging of a rotationally symmetric dielectric cylinder by a quadratic approach,” J. Opt. Soc. Am. A 14, 2777–2785 (1997). [CrossRef]
- W. C. Chew, Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imaging 9, 218–225 (1990). [CrossRef] [PubMed]
- T. M. Habashy, R. W. Groom, B. P. Spies, “Beyond the Born and Rytov approximations: a nonlinear approach to electromagnetic scattering,” J. Geophys. Res. 98, 1759–1775 (1993). [CrossRef]
- O. M. Bucci, T. Isernia, “Electromagnetic inverse scattering: retrievable information and measurement strategies,” Radio Sci. 32, 2123–2138 (1997). [CrossRef]
- W. Liang, “A probe for making near-field measurement with minimal disturbance: the optically modulated scatterer,” IEEE Trans. Antennas Propag. 45, 772–779 (1997). [CrossRef]
- G. Breglio, O. M. Bucci, A. Cutolo, R. Massa, G. Panariello, “Electro-optical sensing of GHz electromagnetic fields,” in Proceedings of International Conference on Electromagnetics in Advanced Applications 1997 (Politecnico di Torino, Torino, Italy, 1997), pp. 499–502.
- F. N. Kong, T. L. By, “Performance of a GPR system which uses step frequency signals,” J. Appl. Geophys. 33, 15–26 (1995). [CrossRef]
- R. P. Porter, A. J. Devaney, “Generalized holography and computational solutions to inverse source problems,” J. Opt. Soc. Am. 72, 1707–1713 (1982). [CrossRef]
- O. M. Bucci, G. Franceschetti, “On the degrees of freedom of scattered fields,” IEEE Trans. Antennas Propag. 37, 918–926 (1989). [CrossRef]
- T. Isernia, G. Leone, R. Pierri, F. Soldovieri, “On the local minima problem in phase reconstruction algorithms,” Radio Sci. 31, 1887–1899 (1996). [CrossRef]
- M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).
- I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products, A. Jeffrey, ed. (Academic, London, 1997).
- W. C. Chew, Y. M. Wang, G. Otto, D. Lesselier, J. Ch. Bolomey, “On the inverse source method of solving inverse scattering problems,” Inverse Probl. 10, 547–553 (1994). [CrossRef]
- This is equivalent to assuming that the actual field in a given point depends mainly on the incident field in that point, or, alternatively, that the value of the incident field in a given point affects only values of E in the points nearby.
- W. C. Chew, J. H. Lin, “A frequency-hopping approach for microwave imaging of large inhomogeneous bodies,” IEEE Microwave Guid. Wave Lett. 5, 439–441 (1995). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.