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.
E. W. MARCHAND and E. WOLF, "Boundary Diffraction Wave in the Domain of the Rayleigh-Kirchhoff Diffraction Theory," J. Opt. Soc. Am. 52, 761-763 (1962)