Skip to main content

Part of the book series: Springer Series on Wave Phenomena ((SSWAV,volume 15))

  • 239 Accesses

Abstract

Inserting an opaque screen to obscure the passage of rays gives rise to penumbra caustics. In this case the standard integrals are incomplete Airy functions and their extensions. A close type of caustics is formed by the diffracted rays in the region of a diffraction penumbra. Both types of caustic, treated first by Yu.I. Orlov, correspond to the so-called edge catastrophes.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Yu.I. Orlov: Radiotekh. Elektron. 20, 242 (1975) [English transl.: Radio Eng. Electron. Phys. 145 (1975)

    Google Scholar 

  2. L. Levey, L.B. Felsen: Radio Sci. 4, 959 (1969)

    Article  MathSciNet  ADS  Google Scholar 

  3. L. Levey, L.B. Felsen: J. Instt. Math. Appl. 3, 76 (1976)

    Article  Google Scholar 

  4. M.M. Agrest, M.Z. Maksimov: Teoriya Nepolnykh Tsilindrichekikh Funktsii i ikh Prilozheniya (theory of incomplete cylindrical functions and their applications) ( Atomizdat, Moscow 1965 )

    Google Scholar 

  5. D.S. Ahluwalia, R.M. Lewis, J. Boersma: SIAM J. Appl. Math. 16, 783 (1968)

    Article  MathSciNet  Google Scholar 

  6. R.M. Lewis, J. Boersma: J. Appl. Math. 10, 2291 (1969)

    Google Scholar 

  7. D.S. Ahluwalia: SIAM J. Appl. Math. 18, 287 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  8. R.S. Hansen: Geometrical Theory of Diffraction ( IEEE Press, New York 1981 )

    Google Scholar 

  9. Yu.I. Orlov, S.A. Vlasov: Izv. VUZ Radiofiz. 21, 422 (1978) [English transl.: Radiophys. Quantum Electron. 21, 290 (1978)

    ADS  Google Scholar 

  10. Yu.I. Orlov: Radiotekh. Electron. 21, 730 (1976) [English transl.: Radio Eng. Electron. Phys. 21, no. 4, 50 (1976)]

    Google Scholar 

  11. Yu.A. Kravtsov, Yu.I. Orlov: GeometricI Optics of Inhomogeneous Media, Springer Ser. Wave Phenom., Vol. 6 ( Springer, Berlin, Heidelberg 1990 )

    Google Scholar 

  12. Yu.I. Orlov: Radiotekh. Elektron. 21, 62 (1976) [English transl.: Radio Eng. Electron. Phys. 21, no. 1, 50 (1976)

    Google Scholar 

  13. Yu.I. Orlov, S.A. Vlasov: Radiotekh. Elektron. 23, 17 (1978) [English transl.: Radio Eng. Electron. Phys. 23, no. 1, 14 (1978)

    Google Scholar 

  14. V.I. Arnold: Usp. Mat. Nauk 34, 91, 206 (1978)

    Google Scholar 

  15. V.I. Arnold, A.N. Varchenko, S.M. Gussein-Zade: Singularities of Differential Mappings (Brikhauser, Boston, MA 1985, 1988 ) Vols. 1, 2

    Google Scholar 

  16. E.B. Ipatov, A.S. Kryukovskii, D.S. Lukin, E.A. Palkin: Dokl. Akad. Nauk USSR 291, 823 (1986) [English transl.: Sov. Phys. - Doklady 31, 962 (1986)]

    Google Scholar 

  17. A.S. Kryukoskii, D.S. Lukin, E.A. Palkin: Sov. J. Numer. Anal. Math. Model 2, 279 (1987)

    Google Scholar 

  18. A.S. Kryukovskii, D.S. Lukin, E.A. Palkin: Kraevye i Uglovye Katastrophy v Zadachakh Difraktsii i Rasprostranenia Voln (edge and corner catastrophes in problems of wave diffraction and propagation) ( Kazanskii Aviatsionnyi Institut, Kazan 1988 )

    Google Scholar 

  19. A.S. Kryukovskii, D.S. Lukin, E.A. Palkin: In Difraktsia i Rasprostranenie Voln (wave diffraction and propagation) ( MFTI, Moscow, 1985 ) p. 4

    Google Scholar 

  20. A.S. Kryukovskii, D.S. Lukin, E.A. Palkin, E. Yu. Chelenger: In Papers of Technical Meeting on Electrical Engineering Theory–OFSET’90 (The Institute of Electrical Engineers of Japan, Fukuoha, Japan, 1990 ) p. 109

    Google Scholar 

  21. A.S. Kryukovskii, D.S. Lukin, E.A. Palkin: In Trudy X Shkoly-Seminara po Difraktsii i Rasprostraneniyu Voln (proceedings of X school-seminar on waves diffraction and propagation), Moscow, Feb. 2–15, 1993 ( MFTI, Moscow 1993 ) p. 3

    Google Scholar 

  22. E.B. Ipatov, A.S. Kryukovskii, D.S. Lukin, E.A. Palkin: In Rasprostranenie i Difraktsia Voln (waves propagation and diffraction) ( MFTI, Moscow 1988 ) p. 144

    Google Scholar 

  23. A.S. Kryukovskii, D.V. Rastyagaev: In Proceedings of the 1992 International Symposium on Antennas and Propagation (Sapporo, Japan 1992 ) vol. 2, p. 581

    Google Scholar 

  24. A.S. Kryukovskii, D.V. Rastyagaev: In Problemy Rasprostranenia i Difraktsii Elektromagnetic Voln (problems of electromagnetic waves propagation and diffraction) ( MFTI, Moscow 1995 ) p. 54

    Google Scholar 

  25. A.S. Kryukovskii, D.V. Rastyagaev. In Voprosy Difraktsii i Rasprostranenia Voln ( problems of waves diffraction and propagation) (MFTI, Moscow 1991 ) p. 51

    Google Scholar 

  26. A.S. Kryukovskii, D.V. Rastyagaev: Funktsionalnyi analiz i ego prilozhenia (functional analysis and applications) 26, 77 (1992)

    MathSciNet  Google Scholar 

  27. A.S. Kryukovskii, D.S. Lukin, E.A. Palkin: Doklady RAN 341, 456 (1995)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Kravtsov, Y.A., Orlov, Y.I. (1999). Penumbra Caustics. In: Caustics, Catastrophes and Wave Fields. Springer Series on Wave Phenomena, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59887-6_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-59887-6_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64167-1

  • Online ISBN: 978-3-642-59887-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics