Contrast transfer function CTF

B1.17.5.1 IMAGING OF PROJECTED STRUCTURE—THE CONTRAST TRANSFER FUNCTION (CTF) OF TEM... 

In HREM images of inorganic crystals, phase information of structure factors is preserved. However, because of the effects of the contrast transfer function (CTF), the quality of the amplitudes is not very high and the resolution is relatively low. Electron diffraction is not affected by the CTF and extends to much higher resolution (often better than lA), but on the other hand no phase information is available. Thus, the best way of determining structures by electron crystallography is to combine HREM images with electron diffraction data. This was applied by Unwin and Henderson (1975) to determine and then compensate for the CTF in the study of the purple membrane. 

H(u) is the Fourier Transform of h(r) and is called the contrast transfer function (CTF). u is a reciprocal-lattice vector that can be expressed by image Fourier coefficients. The CTF is the product of an aperture function A(u), a wave attenuation function E(u) and a lens aberration function B(u) = exp(ix(u)). Typically, a mathematical description of the lens aberration function to lowest orders builds on the Weak Phase Approximation and yields the expression ... 

It is well known that under the weak-phase-object approximation (WPOA) [19], the image intensity function is linear to the convolution of the projected potential distribution function cpt (x, y) and the inverse Fourier transform (FT) of the contrast transfer function (CTF) r(u) of the electron microscope ... 

As mentioned in section 6, the structure factors F(u) are proportional to the Fourier components lim(u) of the HREM image and the projected potential is proportional to the negative of the image intensity, if the image is taken Scherzer defocus where the contrast transfer function T(u) -1. In general, the Fourier components lim(u) are proportional to the structure factors F(u) multiplied by the contrast transfer function (CTF). The contrast transfer function T(u) = D(u)sinx(u) is not a linear function. It contains two parts an envelope part D(u) which dampens the amplitudes of the high resolution components ... 

Within the weak-phase object approximation, the effect of the aberrations is most conveniently described by the Contrast Transfer Function (CTF), which gives the phase factor as a function of spatial frequency (diffraction angle). 

Figure 2.6. An example of a contrast transfer function (CTF). The calculated CTF of a 200CX HRTEM at Scherzer defocus and Cs = 1.2 mm. The first zero is arrowed (corresponding to 0.23 nm resolution) and the resolution in angstrdms is shown on the horizontal axis. A-D are envelope functions plotted as a function of convergence angle (0) of the beam and beam energy spread (A V). Parallel illumination is necessary for high resolution (after Boyes et al 1980).

Conserved core genes, large viruses and, 382 Contrast transfer function (CTF), 94-95 cryoelectron microscopy and, 44 E function simulation and, 96 in subnanometer resolution reconstruction, 104... 

Subnanometer resolution reconstruction, contrast transfer function (CTF) in, 104... 

In addition, there are various technical corrections that must be made to the image data to allow an unbiased model of the structure to be obtained. These include correction for the phase-contrast transfer function (CTF) and, at high resolution, for the effects of beam tilt. For crystals, it is also possible to combine electron diffraction amplitudes with image phases to produce a more accurate structure (7), and in general to correct for loss of high resolution contrast for any reason by "sharpening" the data by application of a negative temperature factor (22). 

Unfortunately, electron images do not give a direct rendering of the specimen density distribution. The relationship between image and specimen is described by the contrast transfer function (CTF), which is characteris-... 

Figure 14.5. Representative plots of the contrast transfer function (CTF) as a function of spatial frequency, for two different defocus settings (0.7 and 4.0 fxm underfocus) and for a field emission (light curve) or tungsten (dark curve) electron source. AH plots correspond to electron images formed in an electron microscope operated at 200 kV and with objective lens aberration coefficients, Cg =...

The corresponding functions which do contain information over a range of dimensions are the contrast transfer function, CTF, and the Wiener spectrum, or noise content of the deposit as a function of spatial frequency (8). These functions also have been found to contain information which correlates to the particle size distribution, as will now be discussed. 

The use of a large aperture corresponds to the bright-field (BF) mode. The images obtained in BF mode are interference images dne to the coherent contrast transfer function (CTF) of the object They provide atomic structure lattice fringes (LFs) or atom imaging. The resolntion obtained is 3.2 A for 100 kV and 1.16 A for 400 kV. 

The contrast transfer function (CTF) describes the performance of a TEM and is determined by the electron energy, coherence of the beam as well as focus and... 

This means that great care is required in comparing results from different sources. The most complete method of defining resolution is to measure the ratio (contrast in the image)/ (contrast in the object) as a function of detail separation. This is the modulation transfer function (MTF), also called the contrast transfer function (CTF), which describes how the modulation or contrast in the object is transferred to the image. Qearly, when MTF falls to some very smaU value, no object detail is reproduced in the image. 

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