Inverse scattering problems and restoration of a function from the modulus of its Fourier transform (Q1109237)

The author solves the following inverse problem: given a bounded domain \(\Omega\) in \({\mathbb{R}}^ n\), recover the function \(f\in C({\bar \Omega})\) from the knowledge of \[ g(x)=| \int_{\Omega}e^{-i<x,\xi >}f(\xi)d\xi |^ 2\quad (x\in {\mathbb{R}}^ n). \] Uniqueness theorems (up to ``rotations'') are proved, generalizing previous work by H. A. Ferweda, B. J. Hoenders, A. M. J. Huiser, and E. Wolf. The results have been announced earlier in Dokl. Akad. Nauk SSSR 279, No.6, 1348-1351 (1984).