Abstract
In this tutorial paper we discuss the concept of resolution in problems of inverse diffraction. These problems have direct applications in areas such as acoustic holography and can also be considered as intermediate steps of more general problems of inverse scattering. We justify the generally accepted principle that the resolution achievable is of the order of the wavelength of the radiation used in the experiment. Moreover we indicate two cases where super-resolution, i.e. resolution beyond the limit of the wavelength, can be achieved. The first is the case of near-field data where super-resolution is possible thanks to the information conveyed by evanescent waves. The second is the case of subwavelength sources, where super-resolution is possible thanks to out-of-band extrapolation of far-field data. Simple algorithms for obtaining this result are also described.
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References
Bertero M. and Pike E. R. (1982): Resolution in diffraction-limited imaging, a singular value analysis-I: The case of coherent illumination Opt. Acta 29 727–746.
Born M. and Wolf E. (1980): Principles of Optics (Pergamon Press, Oxford).
De Santis P. and Gori F. (1975): On an iterative method for super-resolution Opt. Acta 22 691–695.
Gerchberg R. W. (1974): Super-resolution through error energy reduction Opt. Acta 21 709–720.
Groetsch C. W. (1977): Generalized Inverses of Linear Operators (Dekker, New York).
Habashy T. and Wolf E. (1994): Reconstruction of scattering potentials from incomplete data J. Modern Opt. 41 1679–1685.
Levi B. R. and Keller G. B. (1959): Diffraction by a smooth object Comm. Pure Appl. Math. 12 159–209.
Miller K. (1970): Least squares method for ill-posed problems with a prescribed bound SIAM J. Math. Anal. 1 52–74.
Piana M. and Bertero M. (1996): Projected Landweber method and preconditioning Inverse Problems (in press).
Pohl D. W. and Courjon D. eds. (1993): Near-Field Optics (Kluwer, Dordrecht).
Shewell J. R. and Wolf E. (1968): Inverse diffraction and a new reciprocity theorem J. Opt. Soc. Am. 58 1596–1603.
Slepian D. (1964): Prolate spheroidal wave functions, Fourier analysis and uncertainty — IV: Extensions to many dimensions, generalized prolate spheroidal functions Bell. Syst. Tech. J. 43 3009–3057.
Sommerfeld A. (1896): Mathematische theorie der diffraction Math. Ann. 47 317–336.
Sondhi M. M. (1969): Reconstruction of objects from their sound-diffraction patterns J. Acoust. Soc. Am. 4b 1158–1164.
Williams E. G. and Maynard J. D. (1980): Holographic imaging without the wavelength resolution limit Phys. Rev. Lett. 45 554–557.
Wolf E. (1970): Determination of the amplitude and the phase of scattered fields by holography J. Opt. Soc. Am. 60 18–20.
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© 1997 Springer-Verlag
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Bertero, M., Boccacci, P., Piana, M. (1997). Resolution and super-resolution in inverse diffraction. In: Chavent, G., Sabatier, P.C. (eds) Inverse Problems of Wave Propagation and Diffraction. Lecture Notes in Physics, vol 486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105756
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DOI: https://doi.org/10.1007/BFb0105756
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