The phase problem and its relation to the spin-glass problem

The maximum-entropy method of image reconstruction is discussed in the context of the crystallographic phase problem. Entropy is the function to be maximized in a space of phases which has dimension equal to the number of structure-factor constraints. The function ∫ [1 − exp (−ρ/ρ0)] dV is proposed as a suitable one. An analogy between the phase problem and the spin-glass problem of condensed-matter physics is discussed. This analogy has instigated a study of the geometry of the entropy surface in the space of unknown phases for a simple model and preliminary results are presented.