SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 5467-5499, January 2020.
We consider the fixed angle inverse scattering problem and show that a compactly supported potential is uniquely determined by its scattering amplitude for two opposite fixed angles. We also show that almost symmetric or horizontally controlled potentials are uniquely determined by their fixed angle scattering data. This is done by establishing an equivalence between the frequency domain and the time domain formulations of the problem, and by solving the time domain problem by extending the methods of [Rakesh and M. Salo, Inverse Problems, 36 (2020), 035005] which adapts the ideas introduced in [A. Bukhgeim and M. Klibanov, Soviet Math. Dokl., 24 (1981), pp. 244--247] and [O. Imanuvilov and M. Yamamoto, Comm. Partial Differential Equations, 26 (2001), pp. 1409--1425] on the use of Carleman estimates for inverse problems.

中文翻译：

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固定角度逆散射，用于几乎对称或受控的扰动

SIAM数学分析杂志，第52卷，第6期，第5467-5499页，2020年1月。
我们考虑了固定角逆散射问题，并表明了一个紧密支撑的电势是由其在两个相对的固定角度的散射幅度唯一确定的。我们还表明，几乎对称或水平控制的电势由其固定角度散射数据唯一确定。这是通过在问题的频域和时域公式之间建立等价关系以及通过扩展[Rakesh and M. Salo，Inverse Problems，36（2020），035005]的方法来解决时域问题来完成的。适应了[A. Bukhgeim和M. Klibanov，苏联数学。Dokl。，24（1981），第244--247页]和[O. 伊曼努维洛夫（Imanuvilov）和山本M. [偏微分方程，26（2001），第1409--1425页]，关于使用Carleman估计来求解反问题。