148 The Electron Microscope 



Let us consider a small object under the microscope illumi- 

 nated by a parallel beam of electrons with energy E, which may 

 be represented, as usual, by a plane wave in the z-direction 



lAie"^ =:Ioe^\E }J 



where i/^i is Schrodinger's complex amplitude, j ^ V — 1 the 

 imaginary unit, and A the de Broglie wavelength. The suffix i 

 means incident or illiuninating. When the electron beam is scat- 

 tered at the object, two sorts of waves will originate from it, both 



falling off at large distances like -. One shall be represented by 



r 



the amplitude \pc, and called the coherent ivave. It corresponds 

 to the same value of energy, E, as the incident beam. The other 

 shall have the amplitude «//«, and the energy constant E'. This 

 corresponds to electrons scattered with losses appreciable enough 

 to make them incapable of interfering with the incident wave. 

 The criterion of incoherence will be discussed later. The result- 

 ing wave at some point, e.g., at the photographic plate, will be 

 represented by an expression 



2jdht 2jtjht 



(l/^i-j-i//e)e E -f ^,e E' 



The resulting electron density is obtained by taking the square of 

 the absolute value and averaging it over a long time interval. 

 The electron current or intensity is given by a formula of similar 

 build. As we want to indicate the essentials only, we replace this 

 by squaring, as if the xp^ were real, and obtain the following 

 scheme for the resulting intensity or photographic density : 



{^p, + ^,)' + "As' = h^ + (2^5^o + .Ac') + «As' (60) 



(Background) (Missing electrons) (Incoherent 



scattered 

 electrons) 



Filling in this scheme promises to be rather laborious. The 

 large material on atomic collisions worked out and collected es- 

 pecially by Mott and Massey ^^ is not quite sufficient for this 

 purpose. In collision experiments, and even in the greater part 

 of electron diffraction or rather interfraction experiments, only 

 the scattered electrons matter. Kikiichi lines are an exception. 



