Phaseless inverse scattering and the phase problem in optics
Phaseless inverse scattering and the phase problem in optics
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DOI：
10.1063/1.529990
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发表时间：
1992-11
影响因子：
1.3
通讯作者：
M. Klibanov;P. Sacks
中科院分区：
文献类型：
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作者：
M. Klibanov;P. Sacks
考虑了两个相关问题：(i)半线上支持的势V(x)的逆散射问题，当给定数据为‖R−(k)‖时，反射系数的振幅；（ii）半线上支持的函数g(t)的确定当给定数据为‖g(k)‖时，g的傅里叶变换的振幅。在V或g的某些条件下，证明了唯一性定理并开发了计算方法。给出了从‖R−(k)‖中恢复V(x)的一个数值例子。
Two related problems are considered: (i) the inverse scattering problem for a potential V(x) supported on the half‐line {x≥0}, when the given data is ‖R−(k)‖, the amplitude of the reflection coefficient and (ii) determination of a function g(t) supported on the half‐line {t≥0} when the given data is ‖g(k)‖, the amplitude of the Fourier transform of g. Under certain conditions on V or g, uniqueness theorems are proved and computational methods are developed. A numerical example of recovery of V(x) from ‖R−(k)‖ is given.