Contrast by Scattering 45 



trons have suffered energy losses in the object. These electrons 

 will be missing from the beam which in the absence of the object 

 would produce a uniform background on the photographic plate. 

 If the object had absorbed them, or if it had scattered them all 

 outside the physical aperture, there would be an area of zero 

 photographic density corresponding to the image of the object. 

 Some, or most of these electrons may be scattered inside the 

 physical aperture. Because of the chromatic defect of the lenses 

 they will be focused not on the photographic plate, but at V, 

 nearer to the lens, and they will fall on the plate inside a disk, 

 with a radius corresponding to the chromatic error. An ele- 

 mentary consideration shows that as the focal length of a mag- 

 netic lens is inversely proportional to the electron energy V, the 

 diameter of this disk will be, expressed in terms of equivalent 

 object size 



d, = 2af^ (20) 



where a is the aperture angle and AV the energy loss suffered by 

 the electrons. In the illustration it is assumed for simplicity that 

 their distribution is uniform over this disk. If a is large this 

 assumption is not admissible, as the electrons may be scattered 

 in a much narrower cone. In this case, their distribution will 

 approach a shape similar to the probability law, without a sharp 

 outer edge. As an example, let us assume a = 1 ° as mean angle 

 of scattering, V = 60,000 volts, AV = 20 volts, and a focal 

 length of 0.5 cm. This gives dc = 560 A, which is more than ten 

 times the resolution limit obtained with microscopes without 

 physical objective aperture. Figure 14 shows immediately that 

 this large aberration does not interfere at all with the definition 

 of the object. It merely produces a slightly darker border around 

 the image of the object, the density difference at the edge of the 

 object has remained unchanged, that is, it has the same value 

 as if all the electrons which have been scattered by the object had 

 been absorbed, irrespective of the size of the aperture. In 

 photography contrast is measured as the ratio of the densities 

 or the difference of their logarithms, therefore strictly speaking 



