**PURPOSE**- Generate the phase contrast transfer function for for bright-field electron microscopy. Produces the straight transfer function (or its square, the envelope function) for a specified defocus and astigmatism using specified electron optical parameters. Output is in form of SPIDER image. Further info on CTF related operations in SPIDER. Example.

**SEE ALSO****TF**[Transfer Function - Generate image showing effect of defocus on CTF] **TF C**[Transfer Function - Generate a straight, complex, CTF correction image] **TF C3**[Transfer Function - Generate a straight, complex, CTF correction volume] **TF CT**[Transfer Function - Generate a binary, phase flipping, complex, CTF correction image] **TF CT3**[Transfer Function - Generate a binary, phase flipping, complex, CTF correction volume] **TF CTS**[Transfer Function - CTF correction with SNR, image/volume] **TF DDF**[Transfer Function - Determine Defocus & amplitude contrast] **TF DEV**[Transfer Function - Determine Envelope function] **TF DNS**[Transfer Function - Delete noise background] **TF L**[Transfer Function - Generate CTF, in doc file]

**USAGE**- .OPERATION: TF D

- .OUTPUT FILE: TFD001

[Enter the name of the file that will store the CTF correction image.].CS [MM]: 2.0

[Enter the spherical aberration coefficient.].DEFOCUS [A], ELECTRON VOLTAGE [Kev]: 20000, 300

[Enter the amount of defocus, in Angstroms. Positive values correspond to underfocus (the preferred region); negative values correspond to overfocus. Next, enter the energy of the electrons in Kev.

(Note: operation still accepts the legacy input of electron wavelength lambda [A] instead of voltage)]..NUMBER OF SPATIAL FREQ. POINTS: 128

[Enter the dimension of the 3D array. In our example, each element of the array (K,I) corresponds to a spatial frequency

*Kx = (K-65) * DK*

*Ky = (I-65) * DK*

where*DK*is defined by the next input.].MAXIMUM SPATIAL FREQUENCY [1/A]: 0.15

[Enter the spatial frequency radius corresponding to the maximum radius ( = 128/2 in our example) of pixels in the array. From this value, the spatial frequency increment (*DK = 0.15/128*) is calculated.].SOURCE SIZE [1/A], DEFOCUS SPREAD [A]: 0.005,250

[Enter the size of the illumination source in reciprocal Angstroms. This is the size of the source as it appears in the back focal plane of the objective lens. A small value results in high coherence; a large value, low coherence. Enter the estimated magnitude of the defocus variations corresponding to energy spread and lens current fluctuations.].ASTIGMATISM [A], AZIMUTH [DEG]: 400, 30

[Enter the defocus variation due to axial astigmatism. The value given indicates a defocus range of*+/- 400 A*around the nominal value as the azimuth is changed. Then, enter the angle, in degrees, that characterizes the direction of astigmatism. The angle defines the origin direction in which the astigmatism has no effect.].AMPL CONTRAST RATIO [0-1], GAUSSIAN ENVELOPE HALFWIDTH: 0.1, 0.15

[Enter the ACR and the GEH. The Gaussian envelope parameter specifies the 2 sigma level of the Gaussian (see note 2 for details).].DIFFRACTOGRAM, ENVELOPE or STRAIGHT (D/E/S): D

[Either the transfer function is put into the array directly as computed (option 'S'), or its square (option 'D') is stored, or else the envelope function describing the attenuation of the transfer function due to partial coherence effects (option 'E') is stored.]

**NOTES**

- Theory and all definitions of electron optical parameters are according to:

Frank, J. (1973). The envelope of electron microscopic transfer functions for partially coherent illumination.

*Optik*, 38(5), 519-536.

and

Wade, R. H., & Frank, J. (1977). Electron microscope transfer functions for partially coherent axial illumination and chromatic defocus spread.

*Optik*, 49(2), 81-92.

Internally, the program uses the generalized coordinates defined in these papers. - In addition, an optional cosine term has been added with a weight,
and an ad hoc Gaussian falloff function has been added as discussed
in Stewart et al. (1993)
*EMBO J.*12:2589-2599.

The complete expression is:

*TF(K) = [(1-ACR )* sin(GAMMA) - ACR * cos(GAMMA)] * ENV(K) * exp[-GEP * K**2]*

**SUBROUTINES**- TRAFD, TFD

**CALLER**- UTIL1

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