Envelope Functions

Back ] Next ]


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

CTF does not continue forever and the higher spatial frequencies are effectively damped out by envelope functions. The point where envelope functions damp the CTF to zero corresponds to the information limit of the microscope.

Effect of the envelope functions can be represented as:

where Ec is the temporal coherency envelope (caused by chromatic aberrations, focal and energy spread,instabilities in the high tension and objective lens current), and

Ea is spatial coherency envelope (caused by the finite incident beam convergence).

 

CTF with only temporal coherency envelope applied

Philips Tecnai F20 ST
Voltage: 200 keV
Cs: 1.2 mm
Cc: 1.2 mm
Energy Spread: 0.7 eV
Convergence: 0 mrad
Focal Spread: 4.2 nm

 

 

CTF with only spatial coherency envelope applied

Philips Tecnai F20 ST
Voltage: 200 keV
Cs: 1.2 mm
Cc: 1.2 mm
Energy Spread: 0 eV
Convergence: 0.25 mrad
Focal Spread: 0 nm

 

 

CTF with both envelopes applied

Philips Tecnai F20 ST
Voltage: 200 keV
Cs: 1.2 mm
Cc: 1.2 mm
Energy Spread: 0.7 eV
Convergence: 0.25 mrad
Focal Spread: 4.2 nm