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BELL SYSTEM TECHNICAL JOURNAL 



Similar limitations apply to magnetic lenses, and in the end we find that 

 because of the simplest form of aberration, spherical aberration, best def- 

 inition is achieved in electron microscopes with /numbers of 100 or greater, 

 while the / number of a light microscope objective corrected for spherical 

 aberration and other defects as well may be around unity. Thus the elec- 

 tron microscope is severely handicapped, and this handicap is overcome 

 only because electron waves are much less than 1/100 the length of light 

 waves. 



W2= 2Le, 



e,w= Q^2 



a 



rV 



'2L 



Fig. 2 — Approximate relation between beam size and angular spread. 



Thermal Velocities or Electrons 



In many electron-optical systems, and particularly in such devices as 

 cathode ray tubes, it is desirable to focus an electron beam into a small 

 area, so as to produce a very small spot on a fluorescent screen, or to pass a 

 considerable current through a small aperture. We might think at first 

 that if our focusing system were good enough, that is, if it had very small 

 aberrations, we could focus a current from a cathode of given area into as 

 small a space as we desired. This, unfortunately, is not so. The obstacle 

 is the thermal velocities of the electrons emitted by the cathode. 



A simple example will show the sort of thing we should expect to take 

 place. Figure 2 shows a plane cathode and near to it a positive grid so 

 fine as to cause no appreciable deflections of the electrons which pass through 

 it. Farther on we have an aberrationless electron lens designed to focus 



