104 The Electron Microscope 



point object, produced by the combination of spherical and 

 chromatic aberration in a magnetic lens 



/ 2E\ 



rf,, = /afCa2~-^j (29) 



and this is zero if we make 



E^iCa^V (30) 



i.e., if we give the outer electrons so much excess energy. As C 

 is usually near unity this means about E = 3 ev if V = 60 kev 

 at a ^ 10"~ radian. From the point of view of geometrical elec- 

 tron optics the idea is entirely correct, and it could be realized, 

 e.g., by imaging on the object a cathode with a suitable radial 

 potential drop. But in the electron microscope the wave nature 

 of the electrons manifests itself very noticeably, and if we. ir- 

 radiate the object with different electrons at different angles, 

 we must expect very strong diffraction, as each electron uses 

 only, as it were, a small fraction of the aperture. Kompfner 

 suggested to overcome this difficulty by producing coJierent 

 electrons of different velocities. His project is explained in 

 figure 38a. The electron swarm emitted by the cathode is 

 chopped into thin slices, and these slices traverse an accelerating 

 space between two concentric grids, which is operated with the 

 chopping frequency in such a phase that the outer electrons, 

 which reach the grids later, are more accelerated than the inner 

 ones. But, unfortunately, even if we assumed that the great 

 technical difficulties could be overcome, the diffraction error 

 in this arrangement would be much larger than Kompfner's 

 estimate of 1.5 A. 



Heisenberg showed, in 1928, that the basic facts of quantum 

 theory could be derived from what he called the Principle of 

 Indeterminacy. It is meaningless to talk of an electron as a 

 particle with a certain position and a certain velocity, as there 

 is no possible or thinkable experiment by which these two 

 quantities could be ascertained simultaneously. The mathemati- 

 cal formulation of this principle in a general form, and the 



