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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 68, Iss. 4 — Apr. 1, 1978
  • pp: 485–489

Wave propagation in optical systems with large apertures

Frank D. Feiock  »View Author Affiliations


JOSA, Vol. 68, Issue 4, pp. 485-489 (1978)
http://dx.doi.org/10.1364/JOSA.68.000485


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Abstract

The Kirchhoff-Huygens equation is used to investigate wave propagation in optical systems, with large propagation Fresnel numbers NF and aperture-to-length ratios (a /L) which are not small. The limit of applicability of the Fresnel approximation is analytically established for a thin rectangular aperture. It is shown that the error introduced by the Fresnel approximation to the Kirchhoff integral is comparable to the effects of diffraction, computed by the approximation, times the dimensionless parameter πNF (a /2L)2.

© 1978 Optical Society of America

Citation
Frank D. Feiock, "Wave propagation in optical systems with large apertures," J. Opt. Soc. Am. 68, 485-489 (1978)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-68-4-485


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References

  1. N. G. VanKampen, "An Asymptotic Treatment of Diffraction Problems," Physica XIV, 575–589 (1949).
  2. Paul Horwitz, "Asymptotic theory of unstable resonator modes," J. Opt. Soc. Am. 63, 1528–1543 (1973).
  3. Joseph W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 59.
  4. J. Boersma, "Computation of Fresnel Integrals," Math of Computation 14, 380 (1960).
  5. A. Erdelyi, Asymptotic Expansions (Dover, New York, 1956).
  6. F. D. Feiock, "Finite-size effects in Rayleigh scattering," Phys. Rev. 169, 165–171 (1968).

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