64 The Electron Microscope 



each. He was also able to obtain pictures of single large organic 

 molecules, such as edestine. 



It may be noted that the simple argument which led to equa- 

 tion (27) requires more careful elaboration when applied to 

 microscopes in which the resolution is mainly limited by diffrac- 

 tion, i.e., in cases in which the diffraction error considerably 

 exceeds the two geometrical errors. In this case, the argument 

 which operates with electrons, or superposition of positive and 

 negative intensities may lead to appreciable errors. As a next 

 approximation, it may be replaced by the following : \\!^ consider 

 the inelastic scattering of an electron as absorption, followed by 

 reemission. The absorption can be also replaced by reflection, 

 because a black body cannot be exactly defined for the purposes 

 of wave theory. In fact, all theories of the microscope and other 

 optical instruments in which absorbing objects or diaphragms 

 occur are only approximations, for reasons explained in the 

 appendix. As regards re-emission, it is entirely justified to con- 

 sider a particle which scatters an electron with energy loss as 

 a self-luminous object. Moreover, as is shown in the appendix, 

 even in elastic scattering, electrons suffer sufficient energy losses 

 to make their waves incoherent in the sense of being imable to 

 interfere with the primary electron waves. In this approxima- 

 tion, we must therefore proceed as follows: Consider the object 

 first as absorbing or reflecting and calculate the diffraction figure 

 in the image plane of the microscope. It is well known that this 

 figure can have a wide variety of shapes. In many cases a bright 

 region will appear in the center of the image of a small dark 

 object. On this diffraction figure we must superimpose the Airy 

 figure, produced by diffraction of the reemitted electrons at the 

 objective aperture. Obviously, if two diffraction figures have 

 widely different characters, the minimum detectable diameter 

 might be appreciably different from the value given by equation 

 (27). But the problem is more of theoretical than practical in- 

 terest, as in present-day microscopes the geometrical errors are 

 of the same order as the diffraction error. 



