Estimation of the variance in any point of an electron-density map for any space group

In a recent paper [Giacovazzo & Mazzone (2011). Acta Cryst. A67, 210-218] a mathematical expression of the variance at any point of the unit cell has been described. The formulas were derived in P1 for any type of Fourier synthesis (observed, difference and hybrid) under the following hypothesis: the current phases are distributed on the trigonometric circle about the correct values according to von Mises distributions. This general hypothesis allows the variance expressions to be valid at any stage of the phasing process. In this paper the method has been extended to any space group, no matter whether centric or acentric. The properties of the variance generated by space-group symmetry are described; in particular it is shown that the variance is strictly connected with the implication transformations, which are basic for Patterson deconvolution. General formulas simultaneously taking into account phase uncertainty and measurement errors have been obtained, valid no matter what the quality of the model.