CTF (Contrast Transfer Function) is the function which modulates the
amplitudes and phases of the electron diffraction pattern formed in the back
focal plane of the objective lens. It can be represented as:
Clearly, it will be a complicated curve which will depend on:

Cs (the quality of objective lens defined by spherical aberration
coefficient)
 
l
(wavelength defined by accelerating voltage)
 
D
f
(the defocus value)
 
k (spatial frequency)

The figures below show typical CTF plotted for an imaginary 200 keV
microscope:
Important points to notice:

CTF is oscillatory: there are "passbands" where it is
NOT equal to zero (good "transmittance") and there are
"gaps" where it IS equal (or very close to) zero (no
"transmittance").
 
When it is negative, positive phase contrast occurs, meaning that
atoms will appear dark on a bright background.
 
When it is positive, negative phase contrast occurs, meaning that
atoms will appear bright on a dark background.
 
When it is equal to zero, there is no contrast (information
transfer) for this spatial frequency.

Other important features:

CTF starts at 0 and decreases, then

CTF stays almost constant and close to 1 (providing a broad band
of good transmittance), then

CTF starts to increase, and

CTF crosses the kaxis,
and then

CTF repeatedly crosses the kaxis
as k increases.

CTF can continue forever but, in reality, it is modified by envelope
functions and eventually dies off. Effect of the
envelope functions can be represented as:
where Ec is the temporal coherency envelope (caused by chromatic
aberrations, focal and energy spread , and instabilities in the high
tension and objective lens current), and Ea is spatial coherency
envelope (caused by the finite incident beam convergence).
Yet more to note:
[ Home ] [ Effect of Defocus ] [ Effect of Cs ] [ Effect of High Voltage ] [ Envelope Functions ] [ Point Resolution ] [ Information Limit ] [ Spatial Coherency ] [ Passbands ]
