Defocus imaging phase contrast

Deliberate defocusing enhances phase contrast at lower magnifications but it must be used with caution. If there is only random structure in the specimen, deliberate or accidental defocus may induce clearly visible structure unrelated to the specimen—artifacts. Thomas [59] discussed this in detail for polymer microscopy, quoting several TEM studies of polymers that were dominated by phase contrast artifacts. With care, artifacts can be recognized [63, 64] and phase contrast imaging can be successfully applied to polymer systems (e.g., [65]). Phase contrast at high resolution produces lattice images (see Section 2.4.4 and Section 3.1.5). 

For the high resolution case, the phase-contrast effects are automatically introduced owing to the combined effect of defocus and spherical aberration, which gives rise to an image of a structure complicated by the fact that also the amplitude term, resulting from the propagation process, interacts in a non-linear way with the phase term [16,89,90,96]. 

Figure 14.1. Schematic diagram showing the principle of image formation and diffraction in the transmission electron microscope. The incident beam/o illuminates the specimen. Scattered and unscattered electrons are collected by the objective lens and foeused back to form first an electron diffraction pattern and then an image. For a 2D or 3D crystal, the electron-diffraetion pattern would show a lattice of spots, eaeh of whose intensity is a small fraetion of that of the incident beam. In praetiee, an in-focus image has no eontrast, so images are recorded with the objeetive lens slightly defocused to take advantage of the out-of-focus phase-contrast mechanism.

In addition, this CTF is attenuated by an envelope or damping function, which depends on the coherence of the beam, specimen drift, and other factors (6,71,72). Figure 14.5 shows a few representative CTFs for different amounts of defocus on a normal and a FEG microscope. Thus, for a particular defocus setting of the objective lens, phase contrast in the electron image is positive and maximal only at a few specific spatial frequencies. Contrast is either lower than maximal, completely absent, or it is opposite (inverted or reversed) from that at other frequencies. Hence, as the objective lens is focused, the electron microscopist selectively accentuates image details of a particular size. 

This equation means that we can manipulate the amount of phase shift by defocusing the image. Formation of a phase contrast image requires that the wave function on the image plane satisfies the following condition. 

This condition can be obtained in a defocused condition of the objective lens. As a result, an image of phase contrast may be interpreted in terms of periodic structures of a crystalline solid. Such an image of phase contrast is called the interpretable structure image. 

We note from this formula that the image contrast closely depends on the phase contrast transfer function sin2jtx(M). As shown in Fig. 1.2, the value of m.2TX,x u) changes strongly depending on the defocus e. However, if such a condition as... 

F re 3.6 A montage of simulated phase contrast images of Rh/CeOj for two different defocus values and five different CeOj support thicknesses. (Courtesy of... 

Figure 3.7 (Above) A montage of model Rh/CeOj structures for five different Rh cluster sizes. (Below) Corresponding simulated phase contrast images for two different defocus values for the model structures. (Courtesy offf. Calvino, University of Cadiz, Spain). ...

In phase contrast scattered beams are allowed to pass through a large objective aperture and recombine with the unscattered beam to form the image. This would give no contrast if the objective lens was perfect, and perfectly in focus. The lens is not perfect, and often defocused, causing the scattered beams to be phase shifted. 

The spherical aberration of the objective lens and any defocus both add phase shifts to the diffracted beams that depend on the angle 26. From Fig. 6.9 it appears that phase shifts will move the image laterally. If the scattering is weak, the transmitted wave acts as a reference phase, and the phase of the diffracted beam is naturally 90 ° to this. Then, as for phase contrast generally, there will be no contrast in a perfectly formed image. As d decreases 26 increases and the phase shift x due to defocus and aberration increases. This will cause the image contrast to appear and strengthen, then disappear at... 

Periodic structures can also be imaged by phase contrast (defocus) techniques, but these require care as artefacts are easily produced, especially from non-periodic structures, and it has been suggested that some reports concerning polyurethanes have been misinterpreted (Roche and Thomas 1981). 

The analogous light microscope method uses a phase plate to produce a phaseshift. Defocusing the objective lens is the method used to produce this phaseshift in the electron microscope. The situation is quite complex. The nature of the defocus-phaseshift relation must be well known in order to interpret the resulting images accurately. Phase contrast is always present, but can often be ignored except at high resolution or deliberate defocus [40,49, 63] (Section 3.1.4). 

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