Simulating contrast transfer functions

A thorough dicussion of the mathematics of CTFs can be found in the literature (Brydson, 2011). Briefly, to simulate a CTF as seen in experimental electron micrographs, we need to model the following as functions of spatial frequency ($\bf{u}$):

• Squared phase function, $\chi(\bf{u})^2$
• Aperture function, $A(\bf{u})$
• Spatial coherence envelope, $S(\bf{u})$
• Temporal coherence envelope, $E_t(\bf{u})$

Where $AST$ is the envelope damping function, $E(\bf{u})$. The simulated CTF is the product of these functions:

$$ CTF^2 = E(\bf{u})\chi(\bf{u})^2 $$

Currently, simulated CTFs allow modelling of the following geometric lens aberrations: - Defocus - Spherical aberration - Twofold astigmatism

Other modelled parameters: - Accelerating voltage - Focal spread - Chromatic aberration