42 The Electron Microscope 



inelastically scattered electrons. We assume a small object which 

 either hangs unsupported in space or is supported by a mem- 

 brane of negligible thickness. It will be shown later that the 

 very thin organic membranes used for this purpose in electron 

 microscopy fulfill the condition that most of the electrons of the 

 original beam pass through them without collisions, and there- 

 fore can be considered as of negligible thickness. 



For simplicity, we consider the problem as one of geometrical 

 electron optics, i.e., we consider the electrons as particles, neglect- 

 ing diffraction effects. We can also for a start neglect the 

 divergence of the illuminating beam, and consider it as parallel. 

 If the object were not present, the illuminating beam would 

 produce uniform blackening of the photographic plate. The 

 object becomes visible by its scattering effect. In the case of 

 elastically scattered electrons, obviously only those will make a 

 difference in the image which are scattered outside the objective 

 aperture. Those which are deflected by less than the aperture 

 angle will produce the same density as if they had not been 

 deflected at all, because, if the lens is assumed to be perfect, it 

 will focus them in the image point 'T" on the photographic plate. 



Recapitulating the argument, the object is made visible by 

 those electrons which are missing from the beam, because they 

 have been absorbed by the physical aperture of the objective. 

 This is unimpeachable ij we assume an objective free from 

 chromatic and spherical aberration. It is not admissible to con- 

 sider this as the basis of a general theory of contrast, as most 

 authors have assumed. We have seen that if the physical aper- 

 ture is made sufficiently small, the spherical aberration can be 

 practically eliminated. This is not sufficient to eliminate the 

 chromatic error. However homogeneous the primary beam, the 

 scattered beam will contain electrons of different velocities, 

 unless we assume against the evidence of Ruthemann's experi- 

 ments, and against the evidence of the theory of collisions that 

 most of the electrons will be scattered elastically. If this theory 

 were complete, it would be useless to smooth out the illuminat- 

 ing beam within limits of about 1 volt, if scattering produces 

 differences of the order of 10-30 volts. 



