52 The Electron Microscope 



given by the authors as 5.10"^, i.e., a total beam divergence of 

 10"*. It can be seen that the observation of Fresnel fringes gives 

 a useful method for measuring the very small illuminating angles 

 used in modern electron microscopes. 



Fresnel fringes are invaluable for ascertaining that the objec- 

 tive was really focused on the object. It will be shown in the 

 next section that focusing to maximum contrast will almost 

 invariably result in focusing a little off the object. But Fresnel 

 fringes disappear entirely at exact focus, and by this fact give 

 a very sensitive and reliable criterion. This is particularly 

 clearly shown by the series of photographs, reproduced in figure 

 15b which were kindly sent to the author by Dr. James Hillier. 

 All three photographs show the edge of a collodion film with 

 colloidal gold particles sputtered on it. The photograph at the 

 left was taken with an objective which was too weak, the central 

 one with correct focus, the last one with too strong a lens 

 current. It is remarkable that the contrast at the edge appears 

 worst at best focus. An operator who had only the general 

 appearance of the picture to guide him would have almost cer- 

 tainly chosen a somewhat defocused position. 



Another interesting feature of this series is the way in which 

 the appearance of the colloidal gold particles varies with varying 

 focus. Similar phenomena are well known to every user of light 

 microscopes. In the absence of any knowledge of the object, it 

 would have been difficult to decide which of the three pictures is 

 the closest representation of the original. 



In the hands of Hillier and Ramberg the observ^ation of 

 Fresnel fringes has proved an invaluable tool for the detection 

 and measurement of the most tenacious of lens errors : astig- 

 matism in the center, due to ellipticity of the magnetic field. 

 The central figure shows that it was not possible to focus a 

 magnetic objective, which would have been considered as a very 

 good one by any other test, simultaneously on a vertical and 

 on a horizontal edge. It will be described in a later chapter 

 how these authors used these observation methods for improv- 

 ing the objective, and finally achieved the best performance of 

 which any electron miscroscope of the present type is capable. 



