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Eikonal Functions: Old and New

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Abstract

Eikonal functions are among the oldest and most useful tools in optics. They form the foundations of geometrical optics and optical aberrations theory. We survey here the basic theory of eikonal functions and recent applications of them to imaging, to diffraction theory, and to optical design.

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References

  • Alonso, M.A. and G.W. Forbes (1997). “Semigeometrical estimation of Green’s functions and wave propagation in optics,”J. Opt. Soc. Amer. A 14, 1076–1086.

    Google Scholar 

  • Born, M. and E. Wolf (1980).Principles of Optics, Pergamon Press. Bruns, H. (1895). “Das eikonal,”Leipzig. Abh. Sachs. Ges. Wiss. Math. Phys.21, 321–436.

    Google Scholar 

  • Forbes, G.W. and J.K. Wallace (1995). “Can the bounds to system performance in geometrical optics be attained?”J. Opt. Soc. Amer. A12, 2064–2071.

    Google Scholar 

  • Hamilton W.R. (1828). “Systems of rays”Trans. Roy. Irish Acad.15, 69–178.

    Google Scholar 

  • Hertzberger, M. (1931).Strahlenoptik,Springer.

    Google Scholar 

  • Keller, J.B. and H.B. Keller (1950). “Determination of reflected and transmitted fields by geometrical optics”,J. Opt. Soc. Amer.40, 4852.

    Google Scholar 

  • Keller, J.B. (1958). “Corrected Born-Sommerfeld quantum conditions for nonseparable systems” Ann.Phys.4, 180–188.

    Article MATH  Google Scholar 

  • Keller, J.B. and R.M. Lewis (1993). “Asymptotic methods for partial differential equations: The reduced wave equation and Maxwell’s equations”,in Surveys in Applied Mathematics,Vol1, J.B. Keller et al. Eds., Plenum Press, 1–82.

    Google Scholar 

  • Kneisly, J.A. (1964). “Local curvature of a wavefront in an optical system,”J. Opt. Soc. Amer.5, 229–235.

    MathSciNet  Google Scholar 

  • Luneburg, R.K. (1964).The Mathematical Theory of Optics, UCLA Press (based on Luneburg’s Brown University Lecture Notes from 1944 ).

    Google Scholar 

  • Luneburg, R.K. (1948).The Propagation of Electromagnetic Waves,NYU Lecture Notes.

    Google Scholar 

  • Maslov, V.P. (1972).Theorie de perturbations, Dunod, Paris. Rubinstein, J. and G. Wolansky (to appear). “Differential relations for the imaging coefficients of asymmetric optical systems”.

    Google Scholar 

  • Rubinstein, J. and G. Wolansky (draft), “The virtual eikonal method in lens design”.

    Google Scholar 

  • Rubinstein, J. and G. Wolansky (in preparation), AMathematical Theory of Optics.

    Google Scholar 

  • Sommerfeld A. and J. Runge (1911). “Anwendung der Vektorrechnung auf die Grundlagen der Geometrischen Optik,” Ann.Phys.35, 277298.

    Google Scholar 

  • Wolansky, G. and J. Rubinstein (2002). “A class of elliptic equations related to optical design,”Math. Research Letters9, 537–548.

    MathSciNet MATH  Google Scholar 

  • Wolansky, G. and J. Rubinstein (preprint). “On diffraction integrals”.

    Google Scholar 

  • Walther, A. (1995).The Ray and Wave Theory of Lenses. Cambridge University Press.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Mathematics Department, Indiana University and the Technion, USA

    Jacob Rubinstein

  2. Department of Mathematics, Technion, USA

    Gershon Wolansky

Authors
  1. Jacob Rubinstein
  2. Gershon Wolansky

Editor information

Editors and Affiliations

  1. Department of Aerospace Engineering, Technion — Israel Institute of Technology, Haifa, Israel

    Dan Givoli

  2. Department of Mathematics, University of Basel, Basel, Switzerland

    Marcus J. Grote

  3. Department of Mathematics, Stanford University, Stanford, California, USA

    George C. Papanicolaou

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© 2004 Springer Science+Business Media Dordrecht

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Rubinstein, J., Wolansky, G. (2004). Eikonal Functions: Old and New. In: Givoli, D., Grote, M.J., Papanicolaou, G.C. (eds) A Celebration of Mathematical Modeling. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0427-4_10

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eBook
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Softcover Book
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Price includes VAT (Japan)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
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