Abstract

The Kirchhoff-Huygens equation is used to investigate wave propagation in optical systems, with large propagation Fresnel numbers <i>N</i><sub><i>F</i></sub> and aperture-to-length ratios (<i>a</i> /<i>L</i>) 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 π<i>N</i><sub><i>F</i></sub> (<i>a</i> /2<i>L</i>)<sup>2</sup>.

© 1978 Optical Society of America

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  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).

1973 (1)

1968 (1)

F. D. Feiock, "Finite-size effects in Rayleigh scattering," Phys. Rev. 169, 165–171 (1968).

1960 (1)

J. Boersma, "Computation of Fresnel Integrals," Math of Computation 14, 380 (1960).

1949 (1)

N. G. VanKampen, "An Asymptotic Treatment of Diffraction Problems," Physica XIV, 575–589 (1949).

Boersma, J.

J. Boersma, "Computation of Fresnel Integrals," Math of Computation 14, 380 (1960).

Erdelyi, A.

A. Erdelyi, Asymptotic Expansions (Dover, New York, 1956).

Feiock, F. D.

F. D. Feiock, "Finite-size effects in Rayleigh scattering," Phys. Rev. 169, 165–171 (1968).

Goodman, Joseph W.

Joseph W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 59.

Horwitz, Paul

VanKampen, N. G.

N. G. VanKampen, "An Asymptotic Treatment of Diffraction Problems," Physica XIV, 575–589 (1949).

J. Opt. Soc. Am. (1)

Math of Computation (1)

J. Boersma, "Computation of Fresnel Integrals," Math of Computation 14, 380 (1960).

Phys. Rev. (1)

F. D. Feiock, "Finite-size effects in Rayleigh scattering," Phys. Rev. 169, 165–171 (1968).

Physica (1)

N. G. VanKampen, "An Asymptotic Treatment of Diffraction Problems," Physica XIV, 575–589 (1949).

Other (2)

A. Erdelyi, Asymptotic Expansions (Dover, New York, 1956).

Joseph W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 59.

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