4 research outputs found
Rough surface backscatter and statistics via extended parabolic integral equation
This paper extends the parabolic integral equation method, which is very
effective for forward scattering from rough surfaces, to include backscatter.
This is done by applying left-right splitting to a modified 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. In addition, the form of
this Green's function allows the mean field and autocorrelation to be found
analytically to second order in surface height. These may be regarded as
backscatter corrections to the standard parabolic integral equation method
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Rough surface reconstruction from phaseless single frequency data at grazing angles
We develop a method for the reconstruction of a perfectly reflecting rough surface from phaseless measurements of a field arising from single frequency scattering at grazing angles. Formulations are given for both Dirichlet and Neumann boundary conditions, and numerical experiments are presented in which close agreement is found with the exact solution. The approach is a marching method based on the parabolic integral equation, which recovers the surface progressively in range, and is iterated a small number of times to produce the final result. It is found that the approach is robust with respect to spatially localized perturbations and to measurement noise