Practical Electron Microscopy and Database

Phase extension procedure, using the magnitudes of the structure factors from ED (electron diffraction) and starting phases from the corresponding EM (electron microscopy), can be employed to improve a high-resolution image. The tangent formula [1] is normally used as the basis of the phase extension,

         ---------------------- [3493a]

         ------------------------------------------ [3493b]

where,
          α_h -- The phase associated with the normalized structure factor E_h
          E_h -- The normalized structure factor
          F_h -- The conventional structure factor
          Σ -- The average value of |F_h|² for the scattering angle corresponding to h
          ε -- Usually equals unity but can be a small integer depending on the space group and the type of reflection and giving the effect that for all the reflections of that particular type <|E_h|²> = 1.

By substituting E_h with known phases into the right-hand side of Equation 3493a, originally unknown phases can be predicted according to the outcome on the left-hand side.