This paper extends the parabolic integral equation method, which is very effective for forward scattering from one-dimensional rough surfaces, to include backscatter. This is done by applying left-right splitting to a modied two-way governing integral operator, to express the solution as a series of Volterra operators; this series describes successively higher-order surface interactions between forward and backward going components, and allows highly efficient numerical evaluation. This and equivalent methods such as ordered multiple interactions have been developed for the full Helmholtz integral equations, but not previously applied to the parabolic Green's function. Equations are derived for both Dirichlet and Neumann boundary conditions (TE and TM).
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