## Detection and localization of a slab by a linearlike *δ* approach

JOSA A, Vol. 24, Issue 9, pp. 2661-2672 (2007)

http://dx.doi.org/10.1364/JOSAA.24.002661

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### Abstract

The problem of the detection and localization of a dielectric slab under a multifrequency plane-wave illumination is addressed. A linear inversion scheme, based on *δ*-functions, whose support represents the positions of the two slab interfaces, and on the truncated singular-value decomposition is exploited. The closed-form derivation of the amplitude of the reconstruction at the slab interface positions when the inversion scheme acts on exact model data allows us to analyze by means of analytical results the role played by the parameters of the slab, the frequency bandwidth, and the noise on the achievable probability of detection.

© 2007 Optical Society of America

**OCIS Codes**

(100.3010) Image processing : Image reconstruction techniques

(100.3190) Image processing : Inverse problems

(290.3200) Scattering : Inverse scattering

**ToC Category:**

Scattering

**History**

Original Manuscript: June 19, 2006

Revised Manuscript: March 7, 2007

Manuscript Accepted: April 12, 2007

Published: July 30, 2007

**Citation**

Raffaele Solimene and Rocco Pierri, "Detection and localization of a slab by a linearlike δ approach," J. Opt. Soc. Am. A **24**, 2661-2672 (2007)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-9-2661

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### References

- D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlag, 1992).
- M. Idemen and I. Akduman, "One-dimensional profile inversion of a half-space over two-part impedance ground," IEEE Trans. Antennas Propag. 44, 933-942 (1996). [CrossRef]
- D. B. Ge, A. K. Jordan, and J. A. Kong, "Numerical inverse scattering theory for the design of planar waveguides," J. Opt. Soc. Am. A 11, 2809-2815 (1994). [CrossRef]
- R. Persico and F. Soldovieri, "One-dimensional inverse scattering with a Born model in a three-layered medium," J. Opt. Soc. Am. A 21, 35-45 (2004). [CrossRef]
- K. P. Bube and R. Burridge, "The one-dimensional inverse problem of reflection seismology," SIAM Rev. 45, 497-559 (1983). [CrossRef]
- D. L. Jaggard, Y. Kim, K. I. Schultz, and P. V. Fragos, "Experimental confirmation of nonlinear inverse scattering algorithms," J. Opt. Soc. Am. A 4, 1228-1232 (1987). [CrossRef]
- C. Song and S. Lee, "Permittivity profile inversion of a one-dimensional medium using the fractional linear transformation and the phase compensation constant," Microwave Opt. Technol. Lett. 31, 10-13 (2001). [CrossRef]
- T. Uno and S. Adachi, "Inverse scattering method for one-dimensional inhomogeneous layered media," IEEE Trans. Antennas Propag. 35, 1456-1466 (1987). [CrossRef]
- G. Leone, A. Brancaccio, and R. Pierri, "Quadratic distorted approximation for the inverse scattering of dielectric cylinders," J. Opt. Soc. Am. A 18, 600-609 (2001). [CrossRef]
- H. D. Ladouceur and A. K. Jordan, "Renormalization of an inverse-scattering theory for inhomogeneous dielectrics," J. Opt. Soc. Am. A 2, 1916-1921 (1985). [CrossRef]
- T. J. Cui and C. H. Liang, "Direct profile inversion for a half-space weakly lossy medium," J. Opt. Soc. Am. A 10, 1950-1952 (1993). [CrossRef]
- A. Gretzula and W. H. Carter, "Structural measurement by inverse scattering in the Rytov approximation," J. Opt. Soc. Am. A 2, 1958-1960 (1985). [CrossRef]
- F. C. Lin and M. A. Fiddy, "Born-Rytov controversy II. Applications to nonlinear and stochastic scattering problems in one-dimensional half-space media," J. Opt. Soc. Am. A 10, 1971-1983 (1993). [CrossRef]
- M. A. Trantanella, D. G. Dudley, and A. Nabulsi, "Beyond the Born and Rytov approximations in one-dimensional profile reconstruction," J. Opt. Soc. Am. A 12, 1469-1478 (1995). [CrossRef]
- M. A. Hooshyar, "Variational principles and the one-dimensional profile reconstruction," J. Opt. Soc. Am. A 15, 1867-1876 (1998). [CrossRef]
- R. S. Marger and N. Bleistein, "An examination of the limited aperture problem of physical optics inverse scattering," IEEE Trans. Antennas Propag. 26, 695-699 (1978). [CrossRef]
- R. Solimene and R. Pierri, "Localization of a planar perfect-electric-conducting interface embedded in a half-space," J. Opt. A, Pure Appl. Opt. 8, 10-16 (2006). [CrossRef]
- A. Liseno and R. Pierri, "Imaging perfectly conducting objects as support of induced currents: Kirchhoff approximation and frequency diversity," J. Opt. Soc. Am. A 19, 1308-1318 (2002). [CrossRef]
- M. Bertero, "Linear inverse and ill-posed problems," Adv. Electron. Electron Phys. 75, 1-120 (1989).
- P. Z. Peebles, Radar Principles (Wiley, 1998).
- W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE, 1995).
- D. M. Pozar, Microwave Engineering (Wiley, 1998).
- K. I. Hopcraft and P. R. Smith, "Geometrical properties of backscattered radiation and their relation to inverse scattering," J. Opt. Soc. Am. A 6, 508-516 (1989). [CrossRef]
- I. Stakgols, Boundary Value Problems of Mathematical Physics (SIAM, 2000).
- D. Slepian and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis and uncertainty--I," Bell Syst. Tech. J. 40, 43-64 (1961).
- B. R. Frieden, "Evaluation design and extrapolation methods for optical signals, based on use of the prolate functions," in Progress in Optics, E.Wolf, ed. (North-Holland, 1971), Vol. IX, pp. 311-407. [CrossRef]
- J. G. Proakis, Digital Communications (McGraw-Hill, 1995).
- I. S. Gradshteyn and I. M. Ryzhih, Table of Integrals, Series, and Products (Academic, 1994).

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