60 The Electron Microscope 



view to improving the resolution but in order to investigate 

 thicker objects. At 60 kv, which can be roughly considered as 

 the optimum, the resolution becomes (with the strongest objec- 

 tive that can be realized) 



d\^ = 90A (26) 



Thus ultimately, the resolution depends on the numerical 

 coefficient C, which characterizes the spherical aberration. On 

 the basis of Scherzer's theory of the spherical aberration, 

 R. Rebsch ^^ obtains a minimum value of C ^ 0.1 for the opti- 

 mum shape of the lens field. Rebsch's value is based partly on 

 a somewhat too optimistic estimate of the minimum distance at 

 which two aberration figures merge into one, and 0.2 appears 

 to be a better founded theoretical value. With this equation (29) 

 gives a value of 6 A for the resolution limit as determined by 

 spherical aberration and dififraction. 



Until very recently, there was a rather large discrepancy 

 between this theoretical limit and the practical achievements. 

 Several authors tried to explain this by values of C much larger 

 than the theoretical optimum, and this seemed to be confirmed 

 by attempts to measure the spherical aberration directly, which 

 never gave values of less than about two. But J. Hillier and 

 E. G. Ramberg, in a most important paper, still unpublished at 

 the time of writing, proved conclusively that the discrepancy 

 between theory and practice was in fact not due to large de- 

 partures of the magnetic field in the axis from the theoretically 

 recommended law, but to minute yet important departures from 

 axial symmetry. The eUipticity of the field need be only of the 



order of TTwyyS' ^^^^ ^^ ^^ ^"^Y^ ^^^^ departure from circular 



symmetry need not be more than one caused by a deformation 

 of the round bore in the pole pieces of this magnitude, in order to 

 prevent the achievement of resolving powers better than two to 

 three times below the theoretical limit. The astigmatisms en- 

 countered within good magnetic lenses were in fact so small as 

 to escape direct observation by any other method than that 



