TF CT3 - Transfer Function - Complex, Binary 3D

PURPOSE

To compute the phase contrast transfer function for bright-field electron microscopy. For literature, see Notes. The 'TF CT3' option produces a binary or two-valued (-1,1) transfer function in complex 3D form. This can be applied, by using the 'MU' operation, to the Fourier transform of an object for correcting of the phase of bright-field weak phase contrast.

SEE ALSO

TF	[Transfer Function - Defocus dependent]
TF C	[Transfer Function - Complex]
TF C3	[Transfer Function - Complex 3D]
TF CT	[Transfer Function - phase flipping, Complex, Binary]
TF CTS	[Transfer Function - 2D & 3D CTF correction]
TF D	[Transfer Function - Display]
TF DDF	[Transfer Function - Determine DeFocus & amplitude contrast]
TF DEV	[Transfer Function - Determine Envelope function]
TF DNS	[Transfer Function - Determine and delete Noise background]

USAGE

.OPERATION: TF CT3

.OUTPUT FILE: TFC001
[Enter name of file that will store the computed function.]

.CS [MM]: 2.0
[Enter the spherical aberration constant.]

.DEFOCUS(ANGSTROEMS), LAMBDA(ANGSTROEMS): 2000,0.037
[Enter the amount of defocus, in Angstroems. Positive values correspond to underfocus (the preferred region); negative values correspond to overfocus. Next, enter the wavelength of the electrons. The value used in this example corresponds to 100kV. A table of values is listed in the glossary under lambda.]

.NUMBER OF SP. FREQU. PTS.: 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 [A-1]: 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=0.15/64) is calculated.]

.SOURCE SIZE [A-1], DEFOCUS SPREAD [A]: 0.005,250
[Enter the size of the illumination source in reciprocal Angstroems. 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.]

.AMPLITUDE CONTRAST RATIO [0-1], GAUSSIAN ENVELOPE HALFWIDTH[1/A]: 0.1,0.15
[Enter ACR and GEH. The envelope parameter specifies the 2 sigma level of the Gaussian (see note 2 for details).]

.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.]

The transfer function is now computed in complex 3D form, compatible with the Fourier transform format.

NOTES

1. Theory and all definitions of electron optical parameters are as in: J. Frank (1973) Optik 38:519, and R. Wade & J. Frank (1974) Optik 49:81. Internally, the program uses the generalized coordinates defined in these papers.

2. In addition, an optional cosine term has been added with a weight. The complete expression is:
   TF(K) = [(1-ACR)*sin(GAMMA) - ACR*cos(GAMMA)]*ENV(K)]

3. To apply the transfer function to a model structure, use 'TF CTS' operation.

4. Operation can produce volume of any dimensions (need not be power-of-two); consult 'FT MR' manual chapter for the exclusions.

SUBROUTINES

TRAFCT3, TRAFD, TRAFC, TFD

CALLER

UTIL1