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nar spacing. The diffraction pattern is a séries of spots in the Fourier, or focal, plane of the lens. A filter placed in the focal plane serves to limit the résolution by limiting the bandwidth of the image, but it also can serve to sélect certain parts of the Fourier spectrum in the image. The simplest examples of this, as used in optical microscopy, are bright-field and dark-field imaging. In the former the unscattered beam is allowed to reach the image, in the latter it is not. For the optical microscope, diffraction phenomena are not very useful in obtaining information about the microstructure of spécimens, since the wavelength of light is large on the scale of most ordered interatomic spacings. (One beautiful exception to this is the liquid crystal, in which light microscope images very similar to TEM images hâve been observed). 1 Since électrons hâve wave-

Figure 1. Ray diagrams show the principes of (a) diffraction contrast and (b) phase-contrast (high-resolution) imaging in the transmission électron microscope.

MRS BULLETIN/MARCH 1991

lengths much less than the typical interatomic spacing, and since suitably cohérent sources exist on microscopes for effectively monochromatic, parallel illumination on the spécimen, diffraction effects are very important. By filtering a spécifie Bragg peak and allowing it to reach the image, a diffraction contrast image is forrned, such as shown for the dark-field case in Figure la. If the microstructure changes in such a way to perrurb the periodicity or direction of atomic ordering, then the local intensity of a Bragg reflection will change, giving diffraction contrast. This is a very powerful way to image defects such as dislocations and faults, and polycrystalline or mulriphase boundaries. The diffraction contrast image is an example of filtering in Fourier space and observing the effect in real space. The opposite technique is also very useful in TEM. An aperture is placed in the plane of the object, or typically a conjugate plane in a multilens microscope. The lenses are then adjusted so that the diffraction plane is focused on the viewing screen. The diffraction pattern then arises only from the filtered portion of real space, and the method is known as selected-area diffraction. This is particularly useful in identifying the structure of précipitâtes and the diffraction conditions appropriate to the study of diffraction contrast images from defects. The ultimate real-space resolution of the diffraction contrast method and the Fourier-space resolution of the selectedarea diffraction pattern are limited intrinsically by the need to filter in the opposite Fourier domain. This is simply a conséquence of the uncertainty principle, which was expostulated for the optical case before the discovery of quantum mechanics by Abbe. If a filter of numerical aperture angle 6 is inserted in the Fourier plane, and the illumination is cohérent, then the image must be limited in resolution to d ~ 0.61 X/sin(0). The most obvious ramification of this is that atomic-level resolution can