DIFFRACTION OF CYLINDRICAL AND PLANE-WAVES BY AN ARRAY OF ABSORBING HALF-SCREENS

Multiple forward diffraction past an array of many absorbing half-screens whose separation is large compared to wavelength is examined. Starting with the physical optics approximation for half-planes that are equally spaced and of equal height, the field incident on successive edges is represented by a multidimensional Fresnel integral, which is then expanded into a series of functions studied by Boersma. When the angle of incidence with respect to the plane containing the edges is small, as is of interest here, each edge is in the transition region of the previous edge, which precludes the use of the geometrical theory of diffraction and related asymptotic theories. The solution obtained here applies for incidence either from above or below the plane containing the edges, and is especially suited to the case of near-grazing incidence. This method of solution allows for numerical evaluation of a large number of half-screens and shows how the multiply diffracted fields are influenced by the physical parameters. Both incident plane waves and incident cylindrical waves can be treated, and it is found that the numerical results for the cylindrical wave case can be related to those of the plane wave via the settling concept.