UNIQUENESS OF THE COMPLEX DIFFRACTION AMPLITUDE IN X-RAY BRAGG-DIFFRACTION

The concept of the complex diffraction amplitude for x-ray Bragg diffr action is discussed in terms of a unique product of its zeros. This fo rmalism allows the inverse scattering problem in x-ray Bragg diffracti on to be solved unambiguously. The phase-retrieval technique, via a lo garithmic dispersion relation, has associated with it the problem of l ocalization of zeros of the complex diffraction amplitude. The mathema tical approach predicts an infinite number of zeros of the complex dif fraction amplitude. However, a physical (discrete) representation of t he inversion technique limits the number of zeros that should be consi dered and allows one to obtain a unique solution for the structure-fac tor profile. Practical examples of the analytical continuation of the complex diffraction amplitude are presented. Distinctions between the artificial, mathematical, and the true, physical, features of the anal ytical continuation are elucidated.