Conditional phase probability distributions of structure factors in a Karle-Hauptman matrix

From the joint probability distribution of all structure factors in a Karle-Hauptman matrix new phase probability distributions are obtained. These calculations lead to a reformulation of the maximum-determinant rule for phase determination. In addition a new function is derived whose maximum corresponds to the most probable values for the phases of an arbitrary subset of the structure factors in a Karle-Hauptman matrix. This function accounts for the interaction among phases in a Karle-Hauptman matrix through triple products and quartets simultaneously.