Higher-order boundary-diffraction-wave formulation

We consider propagation of radiation through N apertures in series modelled using the Huygens-Kirchhoff Green's function method. We present a method to evaluate the final radiation field using at most N-fold integrals over aperture perimeters instead of the 2N-fold integration over the aperture areas that one might anticipate. This generalizes the boundary-diffraction-wave formulation to higher orders. After deriving a formula for the boundary-diffraction wave at all orders of diffraction, we provide sufficient detail to realize its implementation at first, second and third order. We provide a sample calculation of first-, second- and third-order boundary diffraction waves, discuss ramifications of geometrical blocking effects that complicate boundary-diffraction-wave formulations in general, and indicate three key potential applications of the present work in radiometry.