Accurate one-dimensional inverse scattering using a nonlinear renormalization technique
Accurate one-dimensional inverse scattering using a nonlinear renormalization technique
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使用非线性重正化技术进行精确的一维逆散射
DOI：
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发表时间：
1985
期刊：
影响因子：
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通讯作者：
Y. Kim
中科院分区：
文献类型：
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作者：
D. Jaggard;Y. Kim
本文提出了一种基于Riccati方程反演的非线性方法来求解一维非色散反散射问题。该方法避免了困扰大多数线性化的幅度和相位中的显著误差（例如，Born或其变体）反演方案。相反，Riccati方程的非线性近似用于从反射数据准确确定折射率振幅。该信息随后用于拉伸坐标，以便去除相位累积误差。由此产生的折射率重建，因此是准确的振幅和纵向的位置证明了良好的比较与精确的理论。该方法适用于连续和不连续的折射率分布，并支持实验测量。
A nonlinear method based on the inversion of the Riccati equation is presented here for the one-dimensional nondispersive inverse-scattering problem. This method avoids the significant errors in both amplitude and phase that plague most linearized (e.g., Born or its varients) inversion schemes. Instead, a nonlinear approximation to the Riccati equation is used for the accurate determination of the refractive-index amplitude from reflection data. This information is subsequently used to stretch the coordinates so as to remove the phase-accumulation error. The resulting refractive-index reconstructions are therefore accurate both in amplitude and in longitudinal placement as evidenced by the excellent comparison with exact theory. The method is applicable to both continuous and discontinuous refractive profiles and is supported by experimental measurements.