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 . {{{`"CTF"(K)=sin(-pi*("defocus"*K^2-"Cs"*lambda^3*K^4/2.)-phi)*e^{(-1/4*"B_factor"*K^2)}`}}}
 . {{{`K=sqrt(K_x^2+K_y^2+K_z^2)`}}}
 . {{{`phi="atan"("Q"/(1-"Q"))`}}} [See reference 1 and 2]
 . When {{{`K=0`}}}, {{{`"CTF"(K)=sin(-phi)="amplitude_contrast_ratio"`}}}
 . {{{`CTF(K)=sin(-pi*("defocus"*K^2-"Cs"*lambda^3*K^4/2.)-A)*e^(-(K/(2*"B_factor"))^2)`}}}
 . where {{{`K=sqrt(K_x^2+K_y^2+K_z^2)`}}} and A is amplitude contrast.
 . When {{{`K=0`}}}, {{{`CTF(K)=sin(-A)="amplitude_contrast_ratio"`}}}
 . 2. The CTF is often written as:
 . {{{`CTF(K)=(sqrt(1-A^2)*sin(-pi*("defocus"*K^2-"Cs"*lambda^3*K^4/2.)) - A*cos(-pi*("defocus"*K^2-"Cs"*lambda^3*K^4/2.)))*e^(-(K/(2*"B_factor"))^2)`}}}

How to use CTF in SPARX

In SPARX, the EMAN CTF object are used to store and apply all CTF parameters.

  • To generate a CTF object, use function [:generate_ctf:generate_ctf(p)], here p is a list of parameters [defocus, cs, voltage, apix, bfactor, ampcont]. Their definitions are:

    defocus

    defocus in `µ`m. Positive number means underfocus.

    voltage
    microscope voltage in kV (default 300 kV).
    apix

    pixel size in `Å`.

    cs
    Spherical aberration constant in mm. (Default 2.0)
    amp_contrast
    Amplitude contrast ratio, unitless, given as percentage of (0,100). (Default 10%)
    bfactor

    B-factor defining exponential decay of Fourier amplitudes decay `Å^2`. (Default 0.0, i.e., no decay).

    Notice: In some other software packages, the defocus value is in Å and amplitude contrast ratio is in the range of (0, 1). This function will automatically determine whether these two CTF parameters are in this convention and convert them into our convention.

  • To apply CTF object to an image, use [:filt_ctf:filt_ctf(img, ctf)], where ctf is a CTF object.

  • To put a CTF object into the header of an image, it can be done in two ways:
    1. use function set_ctf(img, p), where p is a list of parameters [defocus, cs, voltage, apix, bfactor, ampcont].

    2. if the CTF object already exists, one can use img.set_attr("ctf", ctf) directly.

  • To recover the numerical values of CTF parameters from CTF object stored in the header of an image, use function p=get_ctf(img).

  • To access or set individual parameters in a ctf object, use:
  • bfactor = ctf.bfactor
  • ctf.bfactor = 200.0

Description

  • 1. The Contrast Transfer Function of electron microscope has the following form:
  • `CTF(K)=sin(-pi*("defocus"*K^2-"Cs"*lambda^3*K^4/2.)-A)*e^(-(K/(2*"B_factor"))^2)`

  • where `K=sqrt(K_x^2+K_y^2+K_z^2)` and A is amplitude contrast.

  • When `K=0`, `CTF(K)=sin(-A)="amplitude_contrast_ratio"`

  • 2. The CTF is often written as:
  • `CTF(K)=(sqrt(1-A^2)*sin(-pi*("defocus"*K^2-"Cs"*lambda^3*K^4/2.)) - A*cos(-pi*("defocus"*K^2-"Cs"*lambda^3*K^4/2.)))*e^(-(K/(2*"B_factor"))^2)`

Reference

1. J. Frank Optik (1973) 38:519

2. R. Wade & J. Frank Optik (1974) 49:81.

3. Z. Huang, P. R. Baldwin, S.Mullapudi, and P .A. Penczek, Automated determination of parameters describing power spectra of micrograph images in electron microscopy. J. Struct. Biol. 144 (2003), pp. 79-94.

CTF_info (last edited 2017-05-07 11:51:17 by penczek)