108 The Electron Microscope 



f quantities which by means, known at present, cannot be re- 

 duced below certain Hmits, but they figure in the -r power, so 



that only very radical improvements can appreciably reduce the 

 resolution limit. The suggestion of the author, to be now de- 

 scribed, seems to ofifer at least a possibility of reducing Cj very 

 considerably. Though the factors C and / are intimately con- 

 nected, it will be convenient to start with a discussion of the 

 focal length / by itself. 



It may be noted that a reduction of / appears not only desir- 

 able but also necessary in any scheme for an efficient reduction 

 of the resolution limit, as the error diameter caused by fluctua- 

 tions of the driving voltage in the magnetic lens 



4 = 2a/^ (20) 



is proportional to /. If we want to reduce d^., and at the same 

 time increase the aperture a in order to reduce the diffraction 



. AV 



error, we must very strongly reduce the fluctuation ^r^ or / or 



both. But it appears from Vance's investigations that a substan- 

 tial reduction of the fluctuation will be very difficult, and progress 

 in this direction is bound to stop anyway once the fluctuation 

 becomes of the order of the initial velocities of the electrons 

 emitted by thermionic cathodes. We must therefore look for 

 ways to reduce /. 



The problem of the short focus lens is illustrated in figure 39. 

 The focal length is given by the abscissa of the intersection be- 

 tween the initial tangent, starting from the focal point, and the 

 final tangent, which is parallel to the axis. Between these two 

 limits the trajectory can have dififerent shapes, and these will 

 strongly influence the spherical aberration. R. Rebsch has 

 shown,"*^ that if there were no limit to the field intensities which 

 we can produce, the spherical aberration could be reduced below 

 any limit. It would be sufficient to produce an infinitely strong 

 field in an infinitesimally small interval near the focal point, 



