**PURPOSE**- Generate the phase contrast transfer function for for bright-field electron microscopy. Produces a listing of the radii and CTF functions in a single doc file. The functions are the: the straight transfer function, the negative of the straight transfer function, a binary or two-valued (-1,1) phase fipping transfer function, a trapped straight transfer function with all values before the first minimum set to 1, the envelope function, and the diffractogram i.e. square of the straight transfer function. Note: Do not use the binary phase flipping listing with 'FD', it will not give the desired phase flipping results. Further info on CTF related operations in SPIDER. Example.

**SEE ALSO****TF L**[Transfer Function - Generate CTF, in doc file] **TF**[Transfer Function - Generate image showing effect of defocus on CTF] **TF CT**[Transfer Function - Generate a binary, phase flipping, complex, CTF correction image] **TF CTS**[Transfer Function - CTF correction with SNR, image/volume]

**USAGE**- .OPERATION: TF LIS

- .OUTPUT DOCUMENT FILE: TFLIS_DOC_001

[Enter the name of the document file that will store the computed functions. The doc file key is: radius, followed by registers for the radius in inverse pixels (1/PIX), radius in inverse Angstroms (1/A), the straight transfer function, the negative straight transfer function, the phase fipping transfer function, the trapped straight transfer function, the envelope function, and the diffractogram function.

A comment key line contains the defocus, the radius of the first minimum, and radius of the first zero crossing..SPHERICAL ABBERATION 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 FREQUENCY POINTS: 128

[Enter the length of the 1D array. This is the size of the square image that will be CTF corrected.].PIXEL SIZE [A]: 2.8

[Enter the number of Angstroms per pixel in the digitized micrograph.].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 spread corresponding to energy spread and lens current fluctuations.].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).]

**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'. - The first CTF extremum and first zero for each micrograph which are listed in the output doc file comments can be useful for filtering the images to the first phase reversal.

**SUBROUTINES**- TRAFL, TFD, GET_TF_INPUT

**CALLER**- UTIL1

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