The inversion of three-beam intensities for scalar scattering by a general centrosymmetric crystal

It is shown that, for the general centrosymmetric crystal, both the signs and magnitudes of all structure amplitudes may be obtained uniquely and explicitly from an analysis of the variation with angle of incidence of the three-beam elastic intensities. The solution derives from certain symmetries which are shown to be inherent in the three-beam dynamical wavefunction.