CTF correction

An example of CTF correction

CTF parameters in SPIDER and single particle reconstruction

CTF graphical tools

References

The image formation in bright field electron microscopy
can be described
by the action of the contrast transfer function (CTF) H(**k**).
Accordingly, the relationship between the object o(**r**) and the
image contrast i(**r**) can be written as
i(**r**) = o(**r**)* h(**r**), where * stands for the
convolution
operation, and h(**r**) is the point spread function, which is the
Fourier transform of H(**k**). Thus, following the convolution
theorem, I(**k**) = O(**k**)H(**k**).

The shape of the CTF, H(**k**), depends on several parameters (for
details, see Frank, 2006):

*defocus* [A] - which describes the deviation in the focus of
the objective lens from the "Gaussian focus."

*spherical aberration coefficient* [mm] - which describes the
(third order) spherical aberration of the wave front in the objective lens.

*source size* [1/A] - which describes the illumination divergence,
expressed as a size in the back focal plane (hence a quantity in reciprocal space).

*defocus spread* - which describes the spread of defocus due to
the spread of electron energies or to the fluctuation of lens current.

The only parameter being varied in the experiment is the defocus.
Depending on the defocus setting, different features of the object
appear enhanced or suppressed in the image. This is because the
CTF oscillates between -1 (negative contrast transfer) and +1
(positive contrast transfer) as we go from low to high spatial
frequencies. The exact locations of the zero crossings (where
no contrast is transferred, and information is lost) depends on
the defocus.
[For examples of CTFs at different defocus settings, click here.]

The *Wiener filter* is the least square solution to the problem
of signal recovery in the presence
of noise. Let's assume we have N images i_{n} (**r**)
(with Fourier transforms I_{n}(**k**)) whose CTFs are H_{n}(**k**).
In that case, the best estimation of the object transform O(**k**) is

- several procedure files: 1) compute the power spectra of the micrographs, 2) estimate defocus, and 3) assign micrographs to defocus groups.
- CTF parameters are estimated with the the SPIDER operation TF ED.
- CTF correction is applied during 3D reconstruction, via the TF CTS operation.
- In this approach, 3-dimensional CTF correction is carried out for each defocus group, creating a volume for each defocus group. These volumes are combined to form a single, CTF-corrected volume. For details, see Penczek et al.,1997.

- ctfdemo.py : a graphical interface that lets you experiment with the various CTF parameters used in SPIDER.
- ctfmatch.py : a tool for analyzing the output from SPIDER's TF ED operation.
- ctfgroup.py : graphically assign micrographs to defocus groups.

Updated Jan. 18, 2006