The solution of the one-dimensional sign problem for Fourier transforms

An iterative procedure for the determination of the signs of scattering amplitudes is considered. It is assumed that the scattering density is a one-dimensional antisymmetric function with a limited range of definition. The convergence of the method to a rigorous solution is proved. The stability of the procedure with respect to various experimental errors is shown in model examples. The proof can be generalized for a one-dimensional phase determination of a continuous intensity distribution.