Consistent Formulation of Kirchhoff’s Diffraction Theory*

Kirchhoff's diffraction theory, which is often criticized because of an apparent internal inconsistency, is shown to be a rigorous solution to a certain boundary-value problem that has a clear physical meaning. This new interpretation of Kirchhoff's theory is a direct consequence of the Rubinowicz theory of the boundary diffraction wave.We argue that these true boundary conditions of Kirchhoff's theory are physically reasonable for diffraction at an aperture in a black screen whose linear dimensions are large compared with the wavelength. The boundary values which Kirchhoff's solution takes in the plane of the aperture and in the near zone on the axis for the case of a normally incident plane wave diffracted at a circular aperture are compared with previously published results of experiments with microwaves, and reasonable agreement is found. (Strict agreement cannot be expected since the screens used in the microwave experiments were not black.) Moreover, Kirchhoff's solution is found to be in closer agreement with the experimental results than the "manifestly consistent" Rayleigh–Sommerfeld theory.We also suggest an extension of the Kirchhoff theory, which might provide a physically reasonable approximation to the solution of the problems of diffraction at an aperture in a black screen whose linear dimensions are of the order of magnitude of or smaller than the wavelength of the light.