Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 18, Issue 8, 2001, Pages 1832-1843

  Bucci, Ovidio M ^a   Cardace, Nicola ^a   Crocco, Lorenzo ^a   Isernia, Tommaso ^a  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; FREQUENCIES; INVERSE PROBLEMS; ITERATIVE METHODS; PERMITTIVITY;

INVERSE SCATTERING PROBLEMS;

LIGHT SCATTERING;

EID: 0001279746     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.18.001832     Document Type: Article

References (20)

1. J. B. Keller, “Accuracy and validity of the Born and Rytov approximations,” J. Opt. Soc. Am. 59, 1003-1004 (1969).
2. M. Slaney, A. Kak, and L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860-874 (1984).
3. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Theory, (Springer-Verlag, Berlin, 1992).
4. R. E. Kleinman and P. M. Van den Berg, “An extended modified gradient technique for profile inversion,” Radio Sci. 28, 877-884 (1993).
5. T. Isernia, V. Pascazio, and R. Pierri, “Anon-linear estimation method in tomographic imaging,” IEEE Trans. Geosci. Remote Sens. 35, 910-923 (1997).
6. R. Pierri and A. Brancaccio, “Imaging of a rotationally symmetric dielectric cylinder by a quadratic approach,” J. Opt. Soc. Am. A 14, 2777-2785 (1997).
7. W. C. Chew and Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imaging 9, 218-225 (1990).
8. T. M. Habashy, R. W. Groom, and B. P. Spies, “Beyond the Born and Rytov approximations: A non-linear approach to electromagnetic scattering,” J. Geophys. Res. 98 (B2), 1759-1776 (1993).
9. W. C. Chew, Waves and Fields in Inhomogenous Media, (IEEE Computer Society, Los Alamitos, Calif., 1995).
10. A. Kolmogorov and S. V. Fomine, Elementsdelatheorie des fonctions et de l’analyse fonctionelle (MIR Editions, Moscow, 1973).
11. R. E. Kleinman, G. F. Roach, and P. M. Van den Berg, “Convergent Born series for large refractive indices,” J. Opt. Soc. Am. A 7, 890-897 (1990).
12. O. M. Bucci and T. Isernia, “Electromagnetic inverse scattering: Retrievable information and measurement strategies,” Radio Sci. 32, 2123-2138 (1997).
13. A. Friedman, Partial Different Equations (Krieger, Malaba, Fla., 1976).
14. O. M. Bucci, L. Crocco, and T. Isernia, “Improving the reconstruction capabilities in inverse scattering problems by exploiting ’near proximity’ set-ups,” J. Opt. Soc. Am. A 16, 1788-1798 (1999).
15. W. C. Chew and J. H. Lin, “A frequency-hopping approach for microwave imaging of large inhomogeneous bodies,” IEEE Microwave Guided Wave Lett. 5, 439-441 (1995).
16. O. M. Bucci, L. Crocco, T. Isernia, and V. Pascazio, “Inverse scattering problems with multi-frequency data: Reconstruction capabilities and solution strategies,” IEEE Trans. Geosci. Remote Sens. 38, 1749-1756 (2000).
17. M. Bertero, “Linear inverse and ill-posed problems,” in Advances in Electronics and Electronic Physics (Academic, New York, 1989), pp. 1-120.
18. 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).
19. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, A. Jeffrey, ed. (Academic, London, 1997).
20. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).