122 The Electron Microscope 



keep present-day objectives constant within - . But it must 



be remembered that the short focal length of the suggested 

 objective has been obtained not by a reduction of geometrical 

 dimensions, but by a sort of compensation between two large 

 systems. Fluctuations in the driving voltage will produce in it 

 a new phenomenon which deserves special attention. 



Space charge region 



Fig. 44. Achromatic condition 



It can be easily shown that fluctuations of the driving voltage 

 will produce relative variations of the focal length of the com- 

 posite lens of the same order as the relative fluctuation of the 

 voltage. Because of the very short focal length, its absolute 

 variation will be entirely negligible. But the new phenomenon 

 arises that unless special measures are taken, the focal point 

 will shijt along the axis by about the same amount as the varia- 

 tion of the focal length of either of the two component lenses, 

 taken by itself. Assuming that the constancy of the driving volt- 

 age is not better than in present-day microscopes, the shijt in the 

 above example would be about ten times the focal depth, and 

 would frustrate the superior resolution. Instead of calculating 

 the shift, we can at once indicate the measures to compensate it. 

 The intercept of the tangent to the trajectory where it enters the 

 space charge lens is 



b^(-\ =LeCothL (50) 



and if -^ is large, this will be very nearly 



