With the help of the results derived in Part I of this investigation, a new representation is obtained for the field arising from diffraction of a monochromatic wave by an aperture in an opaque screen. It is shown that within the accuracy of the Kirchhoff diffraction theory, the diffracted field UK(P) may be expressed under very general conditions in the form Uk(P)=U(B)(P)+ΣiFi(P). (1) Here U(B) represents a disturbance originating at each point of the boundary of the aperture and ΣiFi(P) represents the total effect of disturbances propagated from certain special points Qi in the aperture. Expressions for U(B) and Fi(P) are given, in terms of the new vector potential which was introduced in the previous paper.
In the special case when the wave incident upon the aperture is plane or spherical, the last term in (1) is found to represent a wave disturbance U(G)(P) which obeys the laws of geometrical optics. The formula (1) then becomes equivalent to a classical result of Maggi and Rubinowicz, which may be regarded as a mathematical refinement of early ideas of Young about the nature of diffraction. It is shown further, that even when the incident wave is not plane or spherical, the last term in (1) is, at least approximately, equal to a “geometrical wave.”
The results suggest a new approach to the solution of certain types of diffraction problems and provide a new insight into the process of diffraction.
KENRO MIYAMOTO and EMIL WOLF, "Generalization of the Maggi-Rubinowicz Theory of the Boundary Diffraction Wave—Part II," J. Opt. Soc. Am. 52, 626-636 (1962)