Numerical Algorithm For The Inverse Scattering Problem Of Infinite Surface Based On Phaseless Near-Field Data

This thesis studies the inverse scattering problem about the infinite surface in twodimensional space.Given the incident field ui,the incident field ui produces scattering due to the infinite surface,which helps us obtain the scattered field us,the near-field u:=ui+us at the space Ω above the rough surface.We first establish two kinds of partial differential equation models for the direct scattering problem.The first one is that for a sound-soft infinite surface,the nearfield u satisfies the Helmholtz equation Δu+κ2u=0 in the upper space Ω and the Dirichlet boundary condition at the infinite surface Γ,which is called the direct scattering problem of the sound-soft infinite surface.The second one is the direct scattering problem of the impedance type infinite surface,i.e.,the near-field u satisfies the Helmholtz equation in the upper space Ω and the third kind boundary condition(?)u/(?)v+iκβu=0 at the infinite surface Γ.The well-posedness of the above two direct scattering problems depend on the boundary equation of the scattered field us and the density function ψ.Furthermore,we develop a Nystr(?)m method for the boundary equation of density function ψ.Next,we propose the the translation invariance of phaseless data and the methods to break the the translation invariance.Finally,we adopt a nonlinear integral equation method with phaseless near-field data to reconstruct the sound-soft and impedance type infinite surface by a sum of several point sources.The numerical examples of this two type infinite rough surface indicate that a nonlinear integral equation method of the phaseless near-field data produced by a sum of point sources uniquely determines the shape and position of the infinite surface.