A Study of High Order Born Approximations for Low Grazing Angle High Frequency Rough Interface Scattering
NAVAL OCEAN RESEARCH AND DEVELOPMENT ACTIVITY STENNIS SPACE CENTER MS
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The first Born approximation is an effective method for the prediction of scattering from rough interfaces. This calculation arises from retaining only the first term in the Neumann series of the solution of an inhomogeneous integral equation of the second kind. This method yields adequate results for some geometries and frequencies. However, it cannot account for the multiple scattering which is expected to occur at low grazing angles for sufficiently rough and appropriately spaced rough surfaces. The reason for this is that multiple scattering is not included in the mathematics of the first Born approximation. However, second and higher order terms do allow for secondary, tertiary, etc., scattering and should prove to be a good predictive tool for low grazing angles for some geometries and all grazing angles for other cases. In the study presented here, we develop a technique for calculating higher order Born terms iteratively by a numerically efficient method. The formulation is then used to study the effects of scattering from rough interfaces for a variety of interesting cases for the first two Born terms.