Scanning transmission electron microscopy: Seeing the atoms more clearly
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ing with light Seeing is a commonly used word that we tend to take for granted, however it carries a wide variety of meanings. There is the ability to see with one’s eyes, to discern visually, the act of detecting the scene. There is also the ability to discern mentally after digesting the scene, to understand, as in the phrase “I see what you mean.” Another one that is especially relevant to the transmission electron microscope (TEM) is to see below the surface, which in everyday usage means to see all the ramifications of an issue and understand it in depth. In a similar vein, transmission electron microscopy “sees into” the bulk of a material, whereas scanning electron or scanning probe microscopies mostly “see” the surface. From the days of Anton van Leeuwenhoek in the Netherlands and Robert Hooke in the United Kingdom, both scientists and non-scientists alike have been fascinated by the optical microscope’s ability to see details that are invisible to the naked eye. As lenses improved, not only were smaller things made visible, but an understanding of the limits to resolution gradually grew. First was the realization that light has many colors, and simple lenses focus each color differently, a problem that was alleviated with the invention of the achromatic lens by Chester Moore Hall around 1730. The geometrical optics limit to resolution took almost another 150 years to appreciate, however. Ernst Abbe (1873)1 first realized the role of the lens aperture in
defining resolution by analogy with the action of a diffraction grating. If the diffracted light did not enter the aperture of the imaging lens, the grating could not be resolved. His famous formula states resolution is proportional to wavelength divided by numerical aperture. General objects could be viewed as an assembly of diffraction gratings of different sizes and spacings. A major advance in the understanding of image contrast came from Lord Rayleigh,2 who explained the role of coherence in optical microscopy. If an object is self-luminous, light emitted from different atoms will be incoherent (i.e., each emitted photon will have a random phase), and all we need to consider is the intensity distribution, as shown in Figure 1a. If, however, we need to illuminate an object, then there are two limiting situations referred to as coherent or incoherent imaging. For a nearly parallel beam (such as from a point source far away), as shown in Figure 1b, neighboring points on the object will be illuminated by wavefronts equal in phase. The images of the two points will also be in phase, and we must sum amplitudes before taking the square to find the intensity. This means that the light from the two points will interfere, and the resulting image is said to be coherent. As seen in Figure 1b, adding the amplitudes leads to a broad amplitude distribution that does not resolve the objects, and therefore neither does the intensity. Lord Rayleigh demonstrated this by taking two point sources and spacing them such that the peak in the intensity distribution
Stephen J. Penn
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