The Detection Limit 63 



overlapping distributions would just about vanish if the centers 

 were approached to this distance. Calculation gives a value of 

 1.10 for the peak factor, i.e., to the ratio of the peak intensity to 

 the intensity obtained by distributing it uniformly over the half- 

 value diameter. If, however, we assume the distribution to have 

 the same law as in the Airy diffraction figure, and imagine it 

 replaced by a uniform distribution over 0.67 of the diameter of 

 the central disk, which is the same assumption as we have made 

 in the previous chapter, the peak factor becomes 1.13. Therefore, 

 either of these two assumptions gives almost exactly 



''miu 



= 0.3(/r (27b) 



for the diameter of the smallest object which can be detected in 



a bright-field electron microscope of resolution d^. 



d^ 

 So far, we have assumed the cross section tt -^ to be absorbing. 



But as we have seen in chapter 6, inelastic scattering has prac- 

 tically the same eflfect as absorption, whether the electrons which 

 have suffered energy losses ultimately reach the photographic 

 plate or not. The case of elastic scattering is somewhat more 

 complicated, but at least in the case of small physical apertures 

 most of these electrons will also contribute to the contrast. We 

 can, therefore, with good approximation replace absorbing cross 

 section by scattering cross section. 



J. Hillier,^^ who was the first to attempt an evaluation of the 

 detection limit of the electron microscope, followed an argument 

 similar to the above, but was led to the paradoxial conclusion 

 that the uncorrected microscope with small aperture should be 

 able to detect a single atom of atomic number exceeding 25, i.e., 

 heavier than manganese, if the atom would not move during the 

 exposure. He found that taking account of the atomic electrons 

 did not materially alter the lower limit to the atomic number 

 of an atom that could be detected with the electron microscope. 

 The difference in the laws of scattering will be explained in 

 more detail in chapter 13. Though the uncorrected microscope 

 cannot see single atoms, its detection limit is rather impressive. 

 Von Ardenne's gold particles contained only about thirty atoms 



