Higher order integral solutions

Hopcraft, K. I.; Smith, P. R.

doi:10.1007/978-94-015-8014-4_4

K. I. Hopcraft⁴ &
P. R. Smith⁵

Part of the book series: Developments in Electromagnetic Theory and Applications ((DETA,volume 7))

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Abstract

In §3.2 a detailed discussion of the inverse Born solution was presented for the reduced wave equation (2.5.5) which we again quote for convenience:

$$ \frac{{{d^2}\psi }}{{d{x^2}}} + {k^2}\left[ {{\varepsilon _1}{{\cos }^2}\theta + \Delta \varepsilon (x)} \right]\psi = 0$$

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Bibliography

D.S. Jones, ‘Acoustic and Electromagnetic Waves’, Clarendon Press, Oxford, (1986).
Google Scholar
V.H. Weston, ‘On the convergence of the Rytov approximation for the reduced wave equation’, J. Math. Phys. 26, 1979–1985, (1985).
Article MathSciNet ADS MATH Google Scholar
H.E. Moses, ‘Calculation of the scattering potential from reflection coefficients’, Physical Review 102, 559–567, (1956).
Article MathSciNet ADS MATH Google Scholar
R.T. Prosser, ‘Formal solution of inverse scattering problems III’, J. Math. Phys. 21, 2648–2653, (1980).
Article MathSciNet ADS MATH Google Scholar
R.E Kleinman, G.F. Roach and P.M. van den Berg, ‘Convergent Born series for large refractive indices’, J. Op. Soc. Am. 7, 890–897, (1990).
Article ADS Google Scholar
J.R. Taylor, ‘Scattering Theory’, Wiley, New York, (1972).
Google Scholar
A.J. Devaney, ‘Inversion procedure for inverse scattering within the distorted-wave Born approximation’, Phys. Rev. Lett. 51, 237–240, (1983).
Article ADS Google Scholar
W.C. Chew and Y.M. Wang, ‘Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method’, IEEE Trans. Medical Imaging 9, 218–225, (1990).
Article Google Scholar
M.A. Fiddy, A. Alavi, F.C. Lin and R. McGahan, ‘Inversion of 10GHz scattered field data using distorted-wave Born approximations’, Proc. SPIE 1351, 200–211, (1990).
Article ADS Google Scholar
H. Jeffries, ‘On certain approximate solutions of linear differential equations of the second order’, Proc. Lond. Math. Soc 23, 428–436, (1923).
Article Google Scholar
L. Brillouin, ‘Remarques sur la mechanique ondulatoire’, J. Phys. Radium 7, 353–368, (1926).
Article Google Scholar
H.A. Kramers, “Wellenmechanik und halbzahlige Quantisierung’, Zeit. Phys. 39, 828–840, (1926).
Article ADS MATH Google Scholar
G. Wentzel, ‘Ene Verallemeinerung der Quantenbedingung dur die Zweke de Wellenmechanik, Zeit. Phys. 38, 518–529, (1926).
Article ADS MATH Google Scholar
Lord Rayleigh, ‘On the Propagation of Waves through a Stratified Medium, with Special Reference to the Question of Reflection’, Proc. Roy. Soc. Lond. A 86, 207–226, (1912).
Article MATH Google Scholar
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).
Article ADS Google Scholar

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Authors and Affiliations

Department of Theoretical Mechanics, University of Nottingham, Nottingham, UK
K. I. Hopcraft
Department of Electronic and Electrical Engineering, University of Technology, Loughborough, UK
P. R. Smith

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K. I. Hopcraft
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Hopcraft, K.I., Smith, P.R. (1992). Higher order integral solutions. In: An Introduction to Electromagnetic Inverse Scattering. Developments in Electromagnetic Theory and Applications, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8014-4_4

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DOI: https://doi.org/10.1007/978-94-015-8014-4_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4070-1
Online ISBN: 978-94-015-8014-4
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