PATH-LINKING INTERPRETATION OF KIRCHHOFF DIFFRACTION

The Kirchhoff-diffraction integral is often used to describe the (scal ar) wave field from a monochromatic point source in the presence of 'o paque' screens. Despite criticisms that can be made of its 'derivation ', the Kirchhoff field is an exact solution of the wave equation, and exactly obeys definite, though unusual, boundary conditions (Kottler 1 923, 1965). Here, the path-integral picture of wave fields is used to interpret the Kirchhoff-diffraction field in terms of all conceivable propagation paths, whether or not they pass through the opaque screens . Specifically, it is noted that the Kirchhoff field equals Sigma(1 - m)psi(m), where the sum is over all integers m, and psi(m) is the wave field due to all paths from the source to the field point for which t he number of outward screen crossings minus the number of backwards sc reen crossings is m. Expressed more topologically, m is the total link ing number of a path, when closed by any unobstructed path, with the s creen edge lines. Other models of diffraction by screens are compared with Kirchhoff diffraction in the path interpretation.