CHAPTER 8 i 



THE DETECTION LIMIT OF THE 

 UNCORRECTED ELECTRON MICROSCOPE 



THE size of the smallest particle which can be detected in 

 an electron microscope of the bright-field, transmission 

 type is closely connected with its resolution. Let us imagine 

 a small disk-shaped object of diameter d which absorbs all elec- 

 trons falling on it. The absorbed electrons will be missing in 

 the picture of the uniform background, and the missing intensity 

 (deficit), will be distributed according to a certain law, com- 

 pounded of spherical aberration, variation of the driving voltage, 

 and diffraction. In first approximation, let us assume the deficit 

 to be uniformly distributed over a disk of a diameter equal to 

 the resolution limit d^. The particle will be visible if the contrast, 

 defined as the ratio of deficit to background intensity is more 

 than a certain minimum, say 10 per cent. This means that the 

 small object will be visible if 



c^min = \M^r = 0.316^^ (27a) 



For a resolution limit of 30 A, as in von Ardenne's photo- 

 graph shown in figure 16, this is 9.5 A, in good agreement with 

 the experimental value which was about 10 A. 



In second approximation, we must take into account the 

 peaked character of the distribution of the intensity in the error 

 figure. This need not take us into a detailed investigation of 

 the actual distribution, as the correction is small and rather 

 insensitive to the actual shape. If we assume the distribution 

 in the shape of a probability distribution, the resolution limit 

 would be approximately the diameter on which the intensity has 

 dropped to half the peak value. The minimum between two 



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