Theory oj flic Electron Microscope 143 



only 10 years after his death, in 1910, l)y his pupil, O. Lummer, 

 and by F. Reiche "^ who tried to establish it on the n.iost solid 

 foundation known at that time.* 



Abbe considered the simplest ol)ject, a grid or grating with 

 equal distribution of black and white, and the simplest method 

 of illumination : parallel light, i.e., a plane w^ave. This will give 

 rise to the well-known Fraunhofer diffraction phenomenon : At 

 a distance large in comparison with the grid constant, the trans- 

 mitted wave will consist approximately of a number of plane 

 waves of which one is in the original axial direction and the one 

 nearest it will be deflected by an angle 6, given by 



smO = ^ (58) 



d 



if d is the grid constant, as illustrated in figure 53. This is the 

 wave diffracted iii the first order. Abbe showed by theory and 

 by experiment that if the aperture of the objective is so small 

 as to admit only the axial, ::;ero order wave, the image will show 

 no trace of the grid structure of the object. Likeness to the 

 original begins to emerge only if the first order diffracted beam 

 is added to the zero order beam. If the first order is admitted, 

 but the zero order cut out, a spurious structure appears, the 

 image has twice as many bars as the original. This is illustrated 

 in figures 54 (a-c) which relate to the case of the grid with 

 ten bars. Interesting photographs, showing the apparent distor- 

 tion of diatomae by microscope objective apertures of various 

 shapes have been taken by Beck.'^ 



Whereas a microscope w^ith axial illumination cannot resolve 



a grid with a period finer than -^ — •, the resolution can be 



sin a 



improved if the illuminating beam forms an angle a with the 

 axis, so that, in addition to the undeflected beam, one of the first 



* Rather incomprehensibly, Lummer and Reiche omitted any reference 

 to the violent controversy on xA.bbe's theory, though they list in the 

 bibliography without comments several books and papers which contradict 

 their contentions. 



