IIVIAGE FORMATION MECHANISM 



and diffraction elements as manifested by the 

 instrument developed by Cowley and Rees 

 in 1952. 



Boersch has contributed greatly to the 

 understanding of the physical optics of elec- 

 tron microscopical phenomena. First he had 

 shown, in 1936, the correlation between dif- 

 fraction diagram and the electron optical 

 image. Recognition of this fact was essen- 

 tially responsible for the development of all 

 modern combined electron microscopical 

 and diffraction instrumentation. In 1941, he 

 showed the correlation between image prop- 

 erties of crystalline objects and Bragg reflec- 

 tion. Then, in 1943, he discovered the exist- 

 ence of Fresnel diffraction in electron 

 microscopical images. This discovery led in 

 1946 to the observation of phase contrasts 

 by Hillier and Ramberg and to the method 

 called "microscopy by reconstructed wave- 

 fronts" invented by Gabor in 1948. 



Electron interferometry started with a 

 proposal by Marton in 1952. Following this 

 proposal, Marton, Simpson, and Suddeth 

 built a three-crystal, wide beam interferome- 

 ter in 1953. About the same time, accidental 

 interferences had been observed in electron 

 microscope images by Rang. The use of Fres- 

 nel biprisms for electron interferometry was 

 introduced in 1954 by Mollenstedt and 

 Diiker. 



L. Maeton 



IMAGE FORMATION MECHANISM 



Two criteria are commonl}- used for judg- 

 ing an image formed by an optical system: 

 one is resolution, and the second is contrast. 

 Some of the factors governing both are com- 

 mon, and for this reason the ensuing discus- 

 sion will consider both. The essential mecha- 

 nism, responsible for both qualities, is 

 scattering of electrons in the broadest phys- 

 ical sense. It is customary, however, to desig- 

 nate the coherent effects of scattering from an 

 aggregate of atoms by the term "diffraction," 

 reserving thus the expression "scattering" to 



the manifestations of localized electron- 

 specimen interaction at the atomic or quasi- 

 atomic level. These two effects constitute the 

 major contributions to resolution and con- 

 trast in the image. Two minor contributions 

 are called "refraction" and "absorption." 

 Refraction is that process in which the major 

 change brought about by the scattering is 

 limited to a change in the phase of the wave 

 function, while in absorption there is a large 

 change in the amplitude of the wave func- 

 tion due to the scattering. 



In this discussion of image formation, we 

 will consider only those effects which arise 

 from the interaction of the electrons with 

 the object and those modifications of these 

 effects which are produced by the proper- 

 ties and defects of the optical system. How- 

 ever, the general effect of the optical proper- 

 ties of the system on image formation will 

 not be treated. 



Diffraction is due to the wave nature of 

 the electron which produces deviations from 

 the simple geometrical model of energy 

 propagation. These deviations are manifested 

 by the appearance of dark and bright bands, 

 the Fresnel diffraction fringes. The least re- 

 solved distance of an optical instrument 

 (most commonly called resolving power) can 

 be taken to be the distance at which the 

 first diffraction maximum from a point-like 

 object coincides with the zeroth diffraction 

 maximum of the next object. Using this so- 

 called Ra3^1eigh criterion in the Abbe rela- 

 tion, we obtain 



5 = 



0.61X 



n sin a 



(1) 



where 8 is the least resolved distance, X is 

 the wave length of the electron (X = h/p, 

 where h is the Planck constant and p is the 

 momentum of the electron), and a is the 

 aperture angle of the optical system, n is the 

 refractive index of the electron optical me- 

 dium wliich for many applications can be as- 

 sumed to be unity. The numerical constant 

 0.61 changes if another criterion is substi- 



159 



