International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2010 
International Tables for Crystallography (2010). Vol. B, ch. 1.3, p. 91

Sayre (1952a) derived his `squaring method equation' for structures consisting of equal, resolved and spherically symmetric atoms by observing that squaring such an electron density is equivalent merely to sharpening each atom into its square. Thuswhere is the ratio between the form factor common to all the atoms and the form factor for the squared version of that atom.
Most of the central results of direct methods, such as the tangent formula, are an immediate consequence of Sayre's equation. Phase refinement for a macromolecule by enforcement of the squaring method equation was demonstrated by Sayre (1972, 1974).
References
Sayre, D. (1952a). The squaring method: a new method for phase determination. Acta Cryst. 5, 60–65.Sayre, D. (1972). On leastsquares refinement of the phases of crystallographic structure factors. Acta Cryst. A28, 210–212.
Sayre, D. (1974). Leastsquares phase refinement. II. Highresolution phasing of a small protein. Acta Cryst. A30, 180–184.