The Resolution Limit 59 



and for the optimum resolution limit, as produced by the com- 

 bination of diffraction and spherical aberration by the rule of 

 geometrical addition 



1 3 



t/,A = 750(C/)*V-«A (24) 



where / has to be substituted in cm. This would be the best 

 resolution obtainable if the variation of the driving voltage 

 could be altogether suppressed. But obviously little would be 

 gained by this. If instead we make rfc = d^ the numerical factor 



of (24) is increased only by yl— = 1.12, i.e., to about 850 in- 

 stead of 750. 



Equation (24) shows that only three parameters of the elec- 

 tron microscope enter into the resolving power, provided that 

 the fluctuations of the driving voltage can be kept sufficiently 

 small. It appears from (24) that in order to obtain a high 

 resolution the most effective method is to raise the potential V. 

 This is really less effective than it appears, for two reasons. The 

 first is that in a given magnetic lens field the focal length f is 

 proportional to V. However, saturation of iron sets a limit to 

 the field intensities which can be realized. The usual focal length 

 for 60 kev electrons is about 0.5 cm, and the shortest which can 

 be realized is about 0.3 cm. Assuming such a lens of maximum 

 power we obtain 



J. JL 

 d',j, = 35C^V-^A (25) 



As the resolving power increases only with the I power of V, 

 the gain is very small. In reality, it will be even less profitable 

 to increase V beyond about 60 kv, as the penetrating power of 

 fast electrons rises so rapidly that very small particles can no 

 longer be detected for lack of contrast. High voltage electron 

 microscopes have been constructed by M. von Ardenne ^^ (200 

 kv), H. O. Muller and E. Ruska ^7 (220 kv), and by Y. K. 

 Zworykin, J, Hillier and A. W. Vance ^^ (300 kv), not with a 



