Phase Extension Procedure
- Practical Electron Microscopy and Database -
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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,

        tangent formula as basis of the phase extension ---------------------- [3493a]

        tangent formula as basis of the phase extension ------------------------------------------ [3493b]

          αh -- The phase associated with the normalized structure factor Eh
          Eh -- The normalized structure factor
          Fh -- The conventional structure factor
          Σ -- The average value of |Fh|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 <|Eh|2> = 1.

By substituting Eh 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.






[1] Karle J, Hauptman H. 1956. A theory of phase determination for the four types of non-centrosymmetric space groups 1P222, 2P22, 3P12, 3P22. Acta Cryst 9:635–651.




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