TF C - Transfer Function - Complex

PURPOSE

To compute the phase contrast transfer function for bright-field electron microscopy. The 'TF C' operation produces the transfer function in complex form so that it can be applied (by using 'MU') to the Fourier transform of a model object, for simulations of bright-field weak phase contrast. For literature, see Notes.

SEE ALSO

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

.OUTPUT FILE: TFC001
[Enter the name of the output 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.]

.DIMENSIONS OF OUTPUT ARRAY: 128, 128
[Enter the dimensions of the (real) 2D array, whose Fourier transform you plan to multiply by the complex output of TF C.]

.MAXIMUM SPATIAL FREQUENCY [1/A]: 0.15
[Enter the spatial frequency limit in 1/Angstroem units. The maximum spatial frequency is 1/(2*pixelsize), where pixelsize is the size of the pixel in Angstroems.]

.SOURCE SIZE[1/A], 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 range due to axial astigmatism. The value given indicates a defocus range of +/- 400A around the nominal value as the azimuth is varied. 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 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, 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) 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, and an ad hoc Gaussian fall off function has been added as discussed in Stewart et al., EMBO J. 12 (1993) 2589-2599. The complete expression is:
   TF(K) = [(1-ACR)*sin(GAMMA) - ACR*cos(GAMMA)]*ENV(K)*exp[-(K/GEH)^2
   In an array of size N, the halfsize H = (N/2)+1. Each element of the array (K) corresponds to a spatial frequency
   Kx = (K-H) * DK
   where DK is the maximum spatial frequency.]

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

TRAFC, TFD

CALLER

UTIL1