Abstract

Maggi and Rubinowicz formulated a boundary wave theory of diffraction at an aperture, which may be regarded as developments of early ideas of Young about the nature of diffraction. These investigations were based on the Kirchhoff diffraction theory. In the present paper it is shown that a theory of the boundary diffraction wave may also be formulated by taking as starting point the representation of the field in terms of the Rayleigh diffraction integrals, which are free from a mathematical inconsistency inherent in the Kirchhoff theory. It is shown that the Rayleigh integrals (with physically approximate but mathematically consistent boundary conditions of the Kirchhoff type) may be transformed into the sum of two terms. One term represents the effect of a disturbance which originates in each point of the boundary of the aperture (boundary wave); the other represents the combined effect of disturbances originating in certain special points situated within the aperture. In the special cases when the field incident upon the aperture is plane or spherical, the second term represents precisely the disturbances predicted by geometrical optics, in strict analogy with the classical results of Maggi and Rubinowicz. In these special cases the boundary wave of the present theory differs from the boundary wave of the earlier theories only in the form of an inclination factor.

© 1962 Optical Society of America

Generalization of the Maggi-Rubinowicz Theory of the Boundary Diffraction Wave—Part II†

Kenro Miyamoto and Emil Wolf
J. Opt. Soc. Am. 52(6) 626-636 (1962)

Generalization of the Maggi-Rubinowicz Theory of the Boundary Diffraction Wave—Part I†

Kenro Miyamoto and Emil Wolf
J. Opt. Soc. Am. 52(6) 615-625 (1962)

Comparison of the Kirchhoff and the Rayleigh–Sommerfeld Theories of Diffraction at an Aperture

E. Wolf and E. W. Marchand
J. Opt. Soc. Am. 54(5) 587-594 (1964)

Consistent Formulation of Kirchhoff’s Diffraction Theory*

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

Fictitious diffracted waves in the diffraction theory of Kirchhoff

Yusuf Z. Umul
J. Opt. Soc. Am. A 27(1) 109-115 (2010)