Geometrical Electron Optics 15 



The highest intensity available in light optics is that of sun- 

 light. The solar constant, i.e., the solar radiation which falls on 

 a square cm outside the terrestrial atmosphere is 1.94 cal/min 

 or 0.135 watts. This corresponds to a black body temperature 

 of 5770 °K, and to an energy flow of 2,000 watts/cm^ steradian. 



On the other hand a barium cathode, as assumed above, 

 again with an accelerating voltage of 60,000 volts, can produce 

 2.6 X 10^ watts/cm^ steradian, that is, more than a million times 

 more. With a tungsten cathode it is possible to realize a ten 

 times higher figure, and with a point discharge from a cold 

 cathode at least ten thousand times more again. The factor of a 

 million, which can be realized with barium cathodes under or- 

 dinary circumstances, sufficiently explains why electron optics 

 could score such successes in spite of the most primitive lenses. 

 We shall see later that by now electron microscopy has about 

 exhausted its enormous initial advantage ; further progress is 

 likely to be achieved along lines similar to those of light optics. 



The high intensity of electron beams explains why it was 

 possible in electron microscopy to cut down the numerical aper- 

 tures to one hundredth or even one thousandth of the values 

 which are used in light microscopy. The spherical aberration 

 increases with the cube of the aperture angle, therefore, it could 

 be very effectively reduced by this simple expedient. Reducing 

 the aperture is far less efifective in the case of the second im- 

 portant lens error, the chromatic aberration, as this is only in 

 direct proportion to the aperture angle. Everybody who has 

 looked through cheap pocket microscopes will have noticed that 

 though their aperture may be so small as to make satisfactory 

 illumination very difficult, the chromatic fringes still remain 

 rather disturbing. To solve this difficulty, another simple artifice 

 has been adopted in electron microscopy : strictly monochromatic 

 illumination by electrons of very homogeneous velocity. But 

 before discussing this further, it will be necessary to consider 

 the other side of the analogy between mechanics and optics. 



