Contrast by Scattering 47 



at angles of the order v3.10"^ radians or more. Such electrons 

 will be absorbed by physical objective apertures of the usual 

 dimensions. But if there is no physical aperture, the spherical 

 aberration will play much the same part as the chromatic aberra- 

 tion did in the case of inelastically scattered electrons. Figure 

 14b can be again used as an illustration. As the spherical aberra- 

 tion increases with the third power of the deflection, electrons 

 which have been scattered at appreciable angles by the object 

 will be distributed over a relatively wide area of the photographic 

 plate. Let us assume for instance that for an angle of 2.10"^ 

 radians, that is about 7 minutes of arc, the spherical aberration 

 is 10 A. This means that electrons deflected by 30' will be 

 distributed over a radius of about 800 A, those deflected by 1° 

 over about 6,400 A, which is practically equivalent to saying 

 that they will not have any perceptible efifect in the picture. The 

 effect is enhanced by the fact that elastically scattered electrons 

 will be in general deflected by wider angles than those which 

 have suffered losses. However, the number of elastically scat- 

 tered electrons is in general considerably less than that of the 

 other group. 



We can now understand the fact, mentioned without proof 

 at the end of the previous chapter, that a well collimated illum- 

 inating beam is, in effect, equivalent to a physical diaphragm. 



To sum up, electron microscopes without physical objective 

 aperture produce good pictures not so much in spite of, as rather 

 by virtue of, the lens defects. It can be said that micrographs, 

 especially of small and thin objects were produced prior to the 

 introduction of the physical objective aperture by an extraor- 

 dinary combination of lucky circumstances of which the workers 

 do not seem to have been aware. How these escaped attention 

 for such a long time, can be perhaps explained by the general 

 observation that unexpected difficulties are more stimulating to 

 efforts of understanding than unexpected successes. There is 

 also the reason, that the pioneers of the electron microscope were 

 guided mostly by the analogy of the optical microscope, and the 

 effects discussed are without a counterpart in optical microscopy. 

 A microscope with parallel illumination and uncorrected spheri- 



