**PURPOSE**- Generate the phase contrast transfer function for bright-field electron microscopy. Produces a two-valued (-1,1) transfer function in cubic complex form used for phase flipping of cubic volumes. The output CTF function can be used to correct the phase of a cubic bright-field weak phase contrast volume using the 'TF COR' or 'TF CTS' operations. Further info on CTF related operations in SPIDER. Example.

**SEE ALSO****TF**[Transfer Function - Generate image showing effect of defocus on CTF] **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 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 CT3

- .OUTPUT FILE: TFC001

[Enter name of file that will store the computed function. The transfer function is computed in complex form compatible with the Fourier transform format.].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 dimension of the cubic 3D volume which you wish to CTF correct.].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 is calculated.].SOURCE SIZE [1/A], DEFOCUS SPREAD [A]: 0, 0

[Enter the size of the illumination source in reciprocal Angstroms. Note: the source size has no effect on outcome for this operation.

Next enter the estimated magnitude of the defocus spread corresponding to energy spread and lens current fluctuations. Note: A non-zero value for the spread will diminish phase flipping for high frequencies which is probably not desirable!

.ASTIGMATISM [A], AZIMUTH [DEG]: 0, 0

[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.].AMPLITUDE CONTRAST RATIO [0-1]: 0.1

[Enter the ACR.].SIGN [+1 or -1]: -1

[Application of the transfer function results in contrast reversal if underfocus (*DZ*positive) is used. To compensate for this reversal and make the modified structure displayable by surface representation, use the sign switch -1 above.]

**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'. - To apply the transfer function to a model 3D structure, use
'TF CTS' or 'TF COR'.
- Alternatively use the following steps to apply the transfer function
to a model 3D structure:

(i) Use 'FT' to compute the Fourier transform of the model structure,

(ii) Use 'TF C3' to compute the transfer function in complex format,

(iii) Use 'MU' to multiply the Fourier transform with the complex transfer function,

(iv) Use 'FT' to compute the inverse Fourier transform.

**SUBROUTINES**- TRAFC, TFD

**CALLER**- UTIL1

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