Several Maggi-Rubinowicz representations of the electric field

The Maggi-Rubinowicz technique for scalar and vector fields can be interpreted as a transformation of an integral over an open surface to a line integral around the rim and geometrical optics terms. Using this transformation, Maggi-Rubinowicz analogues are obtained for several integral representations of the electric field. In the case of diffraction from a circular aperture, numerical comparisons between a physical optics and the corresponding Maggi-Rubinowicz formulation show the methods to be in good agreement. To circumvent certain convergence difficulties in the Maggi-Rubinowicz solution that occur as the observer approaches the shadow boundary, a variable mesh integration is used. For the examples considered, where the ratio of the aperture diameter to wavelength is about ten, the Maggi-Rubinowicz formulation yields a significant decrease in computation time relative to the physical optics formulation.