Abstract

With a view to elucidating the effect of a well-known mathematical inconsistency in Kirchhoff’s diffraction theory, a comparison is made of the predictions relating to the field diffracted at an aperture, based on Kirchhoff’s theory (U_K) and on formulas due to Rayleigh and Sommerfeld (U_R). It is shown that, when the incident wave is plane or spherical, the difference δ = U_K−U_R represents a boundary wave, i.e., a wave which may be thought of as originating at each point of the edge of the aperture. It is shown further that, when the linear dimensions of the aperture are large compared with the wavelength, the boundary values of δ in the plane of the aperture change very rapidly and almost periodically from point to point, with the mean period close to the wavelength of the incident radiation. This result is shown to imply that if the linear dimensions of the aperture are large compared with the wavelength, the two theories predict essentially the same behavior for the diffracted field in the far zone, at moderate angles of diffraction.

© 1964 Optical Society of America

Boundary Diffraction Wave in the Domain of the Rayleigh–Kirchhoff Diffraction Theory*

E. W. Marchand and E. Wolf
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Scalar Rayleigh–Sommerfeld and Kirchhoff diffraction integrals: A comparison of exact evaluations for axial points*

John C. Heurtley
J. Opt. Soc. Am. 63(8) 1003-1008 (1973)

Consistent Formulation of Kirchhoff’s Diffraction Theory*

E. W. Marchand and E. Wolf
J. Opt. Soc. Am. 56(12) 1712-1721 (1966)

Validity of the scalar Kirchhoff and Rayleigh–Sommerfeld diffraction theories in the near field of small phase objects

M. Totzeck
J. Opt. Soc. Am. A 8(1) 27-32 (1991)

Young-Kirchhoff-Rubinowicz theory of diffraction in the light of Sommerfeld's solution

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