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TF D - Transfer Function - Display

(10/23/96)

PURPOSE

Computes the phase contrast transfer function for bright-field electron microscopy. TF D produces the transfer function (or its square, the envelope function) in real, displayable form.

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, ternary]
TF CT3 [Transfer Function - complex, ternary 3D]
TF CTF [Transfer Function - CTF correction]
TF D [Transfer Function - display]
TF DDF [Transfer Function - determine defocus and amplitude contrast]
TF DEV [Transfer Function - determine envelope function]
TF DNS [Transfer Function - determine and delete noise background]
TF FL [Transfer Function - flip sign of Fourier transform]
TF MFL [Transfer Function - make filter file for 'TF FL']

USAGE

.OPERATION: TF D

.OUTPUT FILE: TFD001
[Enter the name of the 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. Other values are listed below:

 
                     keV           A 
                     100        0.03700 
                     200        0.02501 
                     300        0.01968 
                     400        0.01643                            ] 

.NUMBER OF SP. FREQU. PTS.: 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. It 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 difference due to axial astigmatism. The value given indicates a defocus range of +/- 400A around the nominal value as the azimuth is varied. Next, 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 PARAMETER: 0.2,100
[Enter ACR and GEP; see below for definitions.]

.(D)IFFRACTOGRAM/(E)NVELOPE/(S)TRAIGHT: D
[Either the transfer function is put into the array directly as computed (option 'S'), or its square (option 'D') is stored, or else the envelope function describing the attenuation of the transfer function due to partial coherence effects (option 'E') is stored.]

NOTES

  1. Theory and all definitions of electron optical parameters are according to: 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 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]

SUBROUTINES

TFD, TRAFD, TRAFC, TRAFC3

CALLER

UTIL1

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