Calculation of the point-by-point error in protein crystallographic electron-density functions

In protein crystallographic studies, the mean-square error at each point in the electron-density function is given, in space group P1, by σ²(x) = (1/V²) F²_o[1-m(h)²] + (1/V²) F²_o {m₂(h) exp [iα₂(h)] - m(h)² exp [2iα_B(h)]} exp (-4πih . x). Here, F_o is the observed structure-factor amplitude; m(h) exp [iα_B(h)] = ∫ P[α(h)] exp (iα) dα is the weighted phase factor in the 'best' Fourier coefficient of Blow & Crick; m₂(h) exp (iα₂) = ∫ P[α(h)] exp (2iα) dα is similar to a traditional second moment. P[α(h)] dα is the probability that the phase angle for a given reflection has value between α and α +dα.