A note on iterative fourier transform phase reconstruction from magnitude

In this correspondence, a well-known iterative procedure for Fourier transform phase reconstruction from magnitude (usually referred to as the Gerchberg-Saxton-Fienup procedure) is revisited. The convergence of this algorithm has raised some controversy in the recent literature. In this correspondence we first point out a potential source of error in the numerical implementation of the algorithm. Then, we present a conjecture which would explain why this algorithm sometimes fails.