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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 2 — Feb. 1, 2001
  • pp: 352–359

In-depth resolution for a strip source in the Fresnel zone

Rocco Pierri, Angelo Liseno, Francesco Soldovieri, and Raffaele Solimene  »View Author Affiliations

JOSA A, Vol. 18, Issue 2, pp. 352-359 (2001)

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The problem of determining the achievable resolution limits in the reconstruction of a current distribution is considered. The analysis refers to the one-dimensional, scalar case of a rectilinear, bounded electric current distribution when data are collected by measurement of the radiated field over a finite rectilinear observation domain located in the Fresnel zone, orthogonal and centered with respect to the source. The investigation is carried out by means of analytical singular-value decomposition of the radiation operator connecting data and unknown, which is made possible by the introduction of suitable scalar products in both the unknown and data spaces. This strategy permits the use of the results concerning prolate spheroidal wave functions described by B. R. Frieden [Progress in Optics Vol. IX, WolfE., ed. (North-Holland, Amsterdam 1971), p. 311.] For values of the space–bandwidth product much larger than 1, the steplike behavior of the singular values reveals that the inverse problem is severely ill posed. This, in turn, makes it mandatory to use regularization to obtain a stable solution and suggests a regularization scheme based on a truncated singular-value decomposition. The task of determining the depth-resolving power is accomplished with resort to Rayleigh’s criterion, and the effect of the geometrical parameters of the measurement configuration is also discussed.

© 2001 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems
(290.3200) Scattering : Inverse scattering

Original Manuscript: March 6, 2000
Revised Manuscript: August 28, 2000
Manuscript Accepted: August 28, 2000
Published: February 1, 2001

Rocco Pierri, Angelo Liseno, Francesco Soldovieri, and Raffaele Solimene, "In-depth resolution for a strip source in the Fresnel zone," J. Opt. Soc. Am. A 18, 352-359 (2001)

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