Spatial Coherency

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Up Level
Effect of Defocus
Effect of Cs
Effect of High Voltage
Envelope Functions
Point Resolution
Information Limit
Spatial Coherency

The spatial coherency is one of the major factors which impose a limit on the resolution of a microscope.

The spatial coherency is defined by the incidence half-angle a ( or convergence) of the incoming electrons which can be expressed as:

where M is magnification, j is charge density, B is brightness, and t is exposure time.

For a given microscope the value of a can be improved to some extent by lowering magnification, increasing the exposure time (by spreading the beam), using smaller spot size and/or condenser aperture. Consequently the information limit of a microscope can be significantly improved. (take a look)

The convergence also depends on the brightness of the electron source. Since the brightness of an FEG is at least 100 times higher than a LaB6 source, FEG sources provide a very strong improvement in spatial coherency extending the information limit to very high frequencies.

The most striking effect of FEG influence on high resolution performance is low-magnification high-resolution microscopy which is often used in structural biology. In such applications the magnifications as low as x50000 and very high underfocus values are used to extend the information transfer at the high spatial frequencies as far as possible. The price we pay for this is fast oscillations in CTF. (take a look)


LaB6 microscope at high magnification


LaB6 microscope at lower magnification (10 times lower than above)


LaB6 microscope at low magnification and high underfocus (~40 scherzer)


FEG microscope at low magnification and high underfocus (~40 scherzer)