A geometrically constrained phase refinement function: the derivation of a new modified tangent formula

A new phase refinement function that makes explicit use of the well resolved nature of the atomic peaks is presented. This function is first deduced for the one-dimensional case and then extended to the three-dimensional one. A new modified tangent formula can be derived from it. The effectiveness of this modified tangent formula is illustrated on the basis of some test structures. This function also seems to provide the XMY function of Debaerdemaeker & Woolfson [Acta Cryst. (1983), A39, 193-196] with a possible rational explanation.