50 The Electron Microscope 



uneven spacing, at both sides of the true contour. Precisely the 

 same phenomenon is observed in electron microscopes under 

 suitable conditions. 



According to the elementary theory of Fresnel diffraction,* 

 the fringes are caused by the interference of the primary, parallel 

 wave, and an edge zvavc, that is to say, a cylindrical wave, start- 

 ing from the illuminated edge of the dark object, without loss 

 of phase. In a plane at a distance y from the plane of the object, 

 dark fringes of the order « appear in the bright field at a dis- 

 tance X from the "true shadow" according to the equation 



x^ = nyX 



w^here A is the wavelength. 



The distance between two consecutive fringes is 



A,r = V^'-^ ( V^^ — V^^ — 1 ) 



The fringes of order n — 1 and w will be separately visible only 



x 

 if the divergence of the illuminating beam is less than A-. If it is 



more, the fringes will merge into one another. 



Figure 15a shows exceptionally clear Fresnel diffraction pat- 

 terns, recently obtained in the R.C.A. laboratory by J. Hillier 

 and E. G. Ramberg. The distance of the 1st order dark fdnge 

 from the edge is about 80 A. As the wavelength of 60 kev elec- 

 trons is about 0.05 A, the photograph must have been taken 

 w4th a defocusing of about 1 -3.10'^ "^ A or 13 [i. In the original, 

 fringes are Ansible up to the 7th or even 8th order, with a spacing 



of only about 14 A corresponding to an angle A -of only about 

 1 -1.10"^. This agrees very well with the half-illuminating angle 



* Cf. e.g. R. W. Wood, Physical Optics, Macmillan, New York, 2d ed., 

 p. 220-223. 



t To avoid misunderstanding, please note that the raised period between 

 numbers stands for a decimal point and the lower period, for a multi- 

 plication sign, i.e., 1 SAO^ is 1.3 X 10^, 



