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

**SEE ALSO****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 D**[Transfer Function - Generate image showing effect of astigmatism on CTF] **TF DDF**[Transfer Function - Determine Defocus & amplitude contrast] **TF DEV**[Transfer Function - Determine Envelope function] **TF DNS**[Transfer Function - Delete noise background]

**USAGE**- .OPERATION: TF

- .OUTPUT FILE: TRA001

[Enter the name of the image file where the transfer function is to be stored.].CS [MM]: 3.5

[Enter the spherical aberration coefficient.].WAVELENGTH LAMBDA [A]: 0.037

[Enter the wavelength of the electrons. The value used in this example corresponds to 100kV. Other values are listed in the glossary under lambda.].LOWER DEFOCUS LIMIT [A]: -1800.

[Enter the lower defocus limit in Angstroms.].UPPER DEFOCUS LIMIT [A]: 3000.

[Enter the upper defocus limit in Angstroms.].NUMBER OF SPATIAL FREQ. POINTS and DEFOCUS POINTS: 120, 300

[Enter the number of spatial frequency grid points and the number of defocus grid points for the output plot. This sets the size of the output image.].MAXIMUM SPATIAL FREQUENCY [1/A]: 0.5

[Enter the spatial frequency limit in reciprocal Angstroms.].SOURCE SIZE: .005

[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.].DEFOCUS SPREAD [A]: 200.

[ Enter the estimated magnitude of the defocus variations corresponding to 1/e halfwidth energy spread and lens current fluctuations.].AMPLITUDE CONTRAST RATIO [0-1], GAUSSIAN ENVELOPE HALFWIDTH: 0.1, 0.15

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

[Either the transfer function is put into the image 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').].FRAME WANTED? (Y/N): Y

[Is a frame wanted around the plot image?]The specified function will then be generated, and stored in the output file.

**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**- TRAF, TF

**CALLER**- UTIL1

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