Supennicroscopes 37 



reduces the obtainable resolution by a factor of three or more, 

 that is, below the value obtainable without a physical aperture. 

 Therefore, the diaphragm has been again discarded in most 

 electron microscopes operating at the present time. 



It appears at first sight that such microscopes without a physi- 

 cal aperture present an entirely different pr()l)lem. Most in- 

 vestigators have indeed assumed that as the divergence of the 

 electron beam scattered by the object is several times the di- 

 vergence of the original beam, these microscopes could be 

 considered as operating with parallel illumination, and they 

 explained image formation by Abbe's theory, applicable to such 

 cases. ^^' ^- If this were so, it would be hard to understand why 

 the physical aperture improved the definition only by a factor 

 of about two. Even if the electrons were scattered only to twice 

 the original divergence, the spherical aberration which grows 

 with the cube of the angle ought to reduce the resolution by a 

 factor 8. This paradox will be explained in the next chapter. 

 For the present, it will be sufficient to note without proof that 

 there is no very essential difference between the limitation of the 

 aperture by a physical diaphragm and limitation by the illuminat- 

 ing beam. The effect of an illuminating beam, collimated as well 

 as possible, is much the same as using a physical objective aper- 

 ture corresponding to a little more than the root mean square 

 divergence angle of thermal origin, calculated above. 



It was mentioned in chapter 2 that even with apertures of 

 the order of 10-^ radians, very steady driving voltages are re- 

 quired in order to reduce the chromatic aberration to the same 

 level as the diffraction error and the spherical aberration. The 

 power of a magnetic lens can be wTitten 



1 P 



j=const.^ (18) 



where / is the focal length and J the current through the coil. A 

 variation of / will have two effects. One is the chromatic change 

 of focus which will cause the image of a point on the axis to 

 appear as a disk. The other is the chromatic change of magnifica- 



