TF CT - Transfer Function - phase flipping, Complex, Binary

PURPOSE

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

SEE ALSO

TF	[Transfer Function - Defocus dependent]
TF C	[Transfer Function - Complex 2D]
TF C3	[Transfer Function - Complex 3D]
TF CT3	[Transfer Function - Complex, Binary 3D]
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 CT

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

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

.DEFOCUS [A], LAMBDA [A}: 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 SPATIAL FREQ. POINTS: 128
[Enter the dimension of the 2D 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. Next, 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 here 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 where the astigmatism has no effect.]

.AMPLITUDE RATIO CONTRAST [0-1]: 0.2
[Enter ACR. See below for definition.]

.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, use sign switch -1.)

The transfer function is then computed in complex form compatible with the Fourier transform format.

NOTES

1. Theory and all definitions of electron optical parameters are as in: J. Frank (1973) '/I>Optik38:519 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 2D structure, use the following steps:
   (i) Use 'FT' to compute the Fourier transform of the model structure,
   (ii) Use 'TF C' 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

TFD, TRAFD

CALLER

UTIL1