Limit of Electron Microscopy 131 



microscope about twenty times beyond the limit of the uncor- 

 rected type. At 60 kev, for instance, a corrected objective would 

 have to be constructed with an aperture of about 0.1 radian or 

 5.7°. At 10 kev it would have to be about 14°. But even if this 

 could be achieved, a hydrogen atom would still remain invisible. 

 This was first pointed out by L. I. Schilf,'^^ though by an argu- 

 ment which requires some modifications. Schiff assumed a per- 

 fect lens, corrected for spherical aberration, though not necessarily 

 for chromatic aberration, as he takes only elastically scattered 

 electrons into account. In such an objective, contrast could be 

 produced only by those electrons which fail to pass the physical 

 aperture. But in order to produce the required definition, the 

 aperture at 10 kev would have to be opened up to about 14°, 

 and it can be seen from figure 46 that under such conditions 

 practically no contrast would be produced, as only a negligible 

 fraction of the electrons is deflected by more than 5°. This could 

 be remedied by oblique illumination, but the difiiculty arises 

 that the effective aperture of the lens is only the part actually 

 filled by scattered electrons, and this is not sufficient for the 

 required resolution. 



At this point the argument requires modification. It is hard 

 to see how the fact that the aperture is not filled by electrons 

 could produce a diffraction error, as diffraction in the aperture 

 arises from cutting out a part of the w^ave. Yet the result is 

 correct, as can be seen from the following reasoning. 



It has been explained in chapter 6 that in the transmission 

 type of electron microscope, small objects are not detected by 

 scattered electrons, but by the electrons which are missing from 

 the original beam. Inelastically scattered electrons are distributed 

 by the chromatic aberration over an area considerably larger 

 than the resolution disk, and can be considered as absorbed. 

 Elastically scattered electrons on the other hand will contribute 

 to the contrast in, a perfect microscope only if they are absorbed 

 by a physical diaphragm. Without going into the details of the 

 very complicated problem which involves diffraction, both at the 

 object and at the aperture, we can obtain an approximate esti- 

 mate by a direct application of the Principle of Indeterminacy. 



