Theory oj the Electron Microscope 147 



day electron microscopes, and can be transferred without much 

 alteration from light optics, it would be desirable to possess a 

 more complete diffraction theory which would take full account 

 of the peculiarities of electrons and may be a help in the inter- 

 pretation of doubtful structures, near the limit of resolution. 

 No attempt will be made here to develop such a theory, but it 

 may be useful to call attention to some features of the problem, 

 and to explain some statements made in previous chapters. 



In some ways electron wave optics is simpler and more com- 

 plete than light wave theory. As polarization effects, if they can 

 be detected at all, are practically negligible, free electrons can be 

 described by scalar waves, similar to sound waves. Optical dif- 

 fraction problems are also treated most often by substituting 

 scalar fields for the electromagnetic waves, but whereas in light 

 optics this substitution remains an often doubtful approximation, 

 it is entirely justified in electron optics. Another feature of opti- 

 cal diffraction theory which is open to objections is the assump- 

 tion of black, or at least partially absorbing surfaces, to which 

 reference has been made at the end of chapter 7. This difffculty 

 is very fully discussed in a monograph by B. B. Baker and E. T. 

 Copson.^- The orthodox optical method is to treat diffraction 

 as a field problem with boundary conditions. But it is easy to 

 see that a boundary in the mathematical sense, i.e., a surface, can 

 be transmitting or reflecting or both, but never absorbing. For 

 absorption a certain depth is needed, for full absorption of the 

 order of half a wavelength. The theory of electron diffraction, 

 however, is built up from the beginning as diffraction by spatially 

 extended fields. In principle we could therefore expect more 

 accurate solutions of the problems of the electron microscope as 

 in the case of the optical microscope, if the problem were not 

 complicated by the very large geometrical errors. 



It has been shown in chapter 6 and other places, how- the 

 very magnitude of these errors can be used to construct a simple 

 theory, by emphasizing the fact that in the case of uncorrected 

 objectives, contrast is mostly produced by the ''missing elec- 

 trons." It will be now attempted to give a wave-theoretical in- 

 terpretation of this geometrical concept. 



