Phase problems, HREM

Zou, X. D. (1999) On the Phase Problem in Electron Microscopy The Relationship Between Structure Factors, Exit Waves, and HREM lmages . Microscopy Research and Technique 46,202-219. 

XD Zou. On the phase problem in electron microscopy the relationship between structure factors, exit waves, and HREM images. Microsc. Res. Tech. 46 202-219,... 

At present the only technique available for specific (sometimes called real-space) structure determination is high resolution electron microscopy (HREM). At first sight this appears to be an ideal method, as the direct imaging of the structure avoids the phase problem normally associated with diffraction methods, and can be applied to all materials, whatever their state of long range order. Compared with diffraction methods, however, the accuracy is relatively poor, as the available resolution is limited to not much better than 2S, well above the theoretical limit. Furthermore, severe problems of image interpretation occur, but within certain limitations, these can be overcome and the technique applied successfully. The object of this paper is to illustrate the use of these direct imaging methods in systems with possible catalytic application. 

In principle, HREM is a very single technique for structure determination and with electron wavelengths currently used, atomic detail should, in theory, be easily resolvable, without any "phase problem" However, the practical difficulties are by now well known and characterised (2) and a brief summary of the relevant points will be given here. 

Although there is no inherent phase problem in the HREM technique it is replaced by an "instrumental" phase problem arising from the relatively imperfect nature of electromagnetic lenses. Spherical aberration is the chief limitation, and its effect can be coupled with that of deviation from the Qatissian focus into a phase factor which can be considered to act upon the diffracted amplitudes before re-combination by the lens to produce the initial image amplitude, namely ... 

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