20 The Electron Microscope 



ondary waves can destroy one another in certain directions, and 

 that the resulting intensity is no longer a simple sum of the 

 component intensities. 



This problem of coherent light emission was first investigated 

 by Ernst Abbe who published his solution, in 1873. Abbe con- 

 sidered only the somewhat over-simplified special case of parallel 

 illumination and showed that in this case the microscopic image 

 is produced by an optical mechanism essentially different from 

 the one which operates in the case of self-luminous objects. 

 Abbe's theory of the microscope had the bad luck of finding 

 ardent protagonists who claimed for it validity far beyond the 

 limits in w^hich it was proved, and by this did much toward start- 

 ing a violent controversy which went on for almost forty years.* 

 But for the present we can leave aside the mechanism of image 

 formation, as Abbe's theory leads to the resolution limit 



f/A = 0.5^^ (16) 



sm a 



which for the small apertures used in electron microscopy gives 

 much the same result as Airy's equation (15). Airy's original 

 formula, w^hich was valid for small angles only, was also ex- 

 tended to large apertures by Rayleigh and other authors. It is 

 rather fortunate that the suffix "A" can mean equally well 

 "Airy" or "Abbe." 



The equations (15) or (16) explain at once the second great 

 intrinsic advantage of electron optics, which enabled the con- 

 struction of highly successful microscopes with entirely uncor- 

 rected lenses. In light microscopy it was possible to make sin a 

 as large as 0.9, and, by immersing the object into a medium with 

 a refractive index of about 1.6, the resolution limit could be 

 brought down to about one third of the vacuum wavelength. 

 The wavelength of yellow light, however, is about 0.6 fx or 

 6,000 A, and for ultraviolet light as used in microscopy about 

 0.28 ^ or 2,800 A. Therefore, the visual resolution limit re- 

 mained about 2,000 A, and even photographically it could not 

 be made better than about 1,000 A. 



* Cf. Appendix on Diffraction Theory of the Microscope. 



