ELECTRON IMICKOSCOI'Y 



transmission specimens. It was stated that 

 the resokition should be higher than usual 

 since the energy spread of electrons diff- 

 fracted at a Bragg angle would be smaller 

 than that of inelastically scattered electrons. 

 A resolution of 80 A Avas obtained experi- 

 mental! J^ 



Kushnir and Der-Schwarz (1958) dis- 

 cussed various problems in reflection elec- 

 tron microscopy and described some experi- 

 mental results. They dealt with the spatial 

 intensity distribution and velocity spectrum 

 of electrons scattered at a massive object, 

 the correction of chromatic aberration and 

 geometrical distortion, and the effects of ob- 

 jective aperture displacement. 



Further use has been made of the possibil- 

 ity of carrying out experiments on a specimen 

 whilst observing it in a reflection electron 

 microscope. Halliday and Rose (1959) de- 

 scribed the direct observation of wear proc- 

 esses in this way. There was also an earlier 

 paper by Takahashi, Takeyama, Ito, Ito, 

 Mihama, and Watanabe (1956) describing a 

 hot stage for reflection electron microscopy 

 and some results obtained from this. 



Equations 



A number of equations relevant to the 

 interpretation of reflection electron micro- 

 graphs and the use of the instrument follow. 

 The magnifications in directions parallel to 

 and perpendicular to the plane of incidence 

 are related by 



The magnification along a line in the image 

 at azimuth ^p is 



m^' = 



VI X sin d-i sec f 



I / ^ .ill ,. , ■ — 



(4) 



and a circle in the specimen will be imaged 

 as an ellipse. The height of an asperity h is 

 related to the length of the shadow it casts 

 L (measured in the image) by 



h = 



L sin di 



m± sin (di + Bo) 



(5) 



If the validity of this equation is not to be 

 affected by penumbra, a restriction must be 

 imposed on the angular spread of the inci- 

 dent electron beam 



2Aai < 



5 J. sin^ di 

 h sin $2 



(6) 



Thus good collimation becomes important 

 for small ^i . Other factors affecting the 

 validity of equation 5 have been listed on 

 page 225. The depth of field is approximately 



rtSx/of, 



(7) 



where a is the semi-angular aperture of the 

 objective lens. The chromatic aberration of 

 the objective lens limits the resolution to 



aCy, 



(8) 



m\\ = mx sin do , 



(1) 



and the resolutions in these directions by 

 a similar equation 



5|| = 5 J. /sin $2 



(2) 



Angular relationships in the image are dis- 

 torted because of the foreshortening. A line 

 in the specimen at azimuth cp (measured to a 

 line in the specimen in the plane of incidence) 

 will be imaged as a line at azimuth cp' where 



tan <p' = tan <p/sin 02 



(3) 



where C is the chromatic aberration coeffi- 

 cient of the objective lens, AV the half-width 

 of voltage spread of the scattered electrons, 

 and V the accelerating voltage. With present 

 instruments, other aberrations are negligible 

 compared with chromatic aberration and, 

 therefore, a should be made as small as pos- 

 sible. There will be an optimum value of a 

 when diffraction becomes important, but 

 this is of no practical significance since it 

 corresponds to an image which is too faint to 

 be focused or recorded. 



In a three lens electron microscope the 

 chromatic field aberrations can be kept to a 

 minimum by correct choice of the interme- 

 diate lens current and by exciting lenses in 



228 



