Scherzer Expression /Point Resolution/Limit
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This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.



The point resolution, determined by Cs and the wavelength λ, is given by the Scherzer expression d0 = 0.66 Cs1/4 λ3/4. That means the Scherzer resolution only depends on the electron wavelength and spherical aberration coefficient, and may be improved by reducing either.

For modern median voltage TEMs, the Scherzer point resolution is lower than the information limit, which is controlled by the temporal coherence of the electron source.

Based on Cs correction, extending Scherzer’s point resolution to information limit of the microscope can optimize the positive phase contrast from a weak-phase object. Assuming gSch = gmax and a defocus of ZSch = -8/(3λg2max) , one can obtain, [1]

         Scherzer Expression /Point Resolution/Limit ---------------------- [4261a]

The resulting contrast delocalization is given by,

         Scherzer Expression /Point Resolution/Limit ---------------------- [4261b]

In this case, the atoms are observed in dark contrast with respect to the background.





[1] Lentzen, M., Jahnen, B., Jia, C.L., Thust, A., Tillmann, K. & Urban, K. (2002). High-resolution imaging with an aberrationcorrected
transmission electron microscope. Ultramicroscopy 92, 233–242.



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