**PURPOSE**- Generate the phase contrast transfer function for for bright-field electron microscopy. Produces a straight transfer function (or its square, the envelope function). Outputs this function and the radii in text form in a doc file. Do not use this operation to form a binary phase flipping CTF correction file for use with 'FD', it will not give the desired results. 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**[Transfer Function - Generate image showing effect of defocus on CTF] **TF D**[Transfer Function - Generate image showing effect of astigmatism on CTF]

**USAGE**- .OPERATION: TF L

- .CS [MM]: 2.0

[Enter the spherical aberration constant in millimeters.].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 FREQUENCY POINTS: 128

[Enter the length of the 1D array. (This is the size of the square image that will be CTF corrected.)].MAX 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, 0

[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.].AMPLITUDE 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.].OUTPUT DOCUMENT FILE: TFL_DOC_001

[Enter the name of the document file that will store the computed function.]

**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]*3 The input parameters for this operation can be determined using 'CTF FIND','TF DDF' and 'TF DEV'.

**SUBROUTINES**- TFD, TRAFL

**CALLER**- UTIL1

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