ELECTRON MICROSCOPY 



simple sliape gives results of adequate ac- 

 curacy for practical purposes (Archard 1954). 



The relations between the geometric fac- 

 tors, applied excitation and the focal proper- 

 ties and aberrations have been calculated 

 and measured by many different workers 

 (e.g., Glaser, 1941, Ramberg, 1942, Lenz 

 1950, Liebmann andGrad, 1951). The results 

 are now well established and it is more rele- 

 vant to describe these results than the meth- 

 ods for deriving them. The results are more 

 complete for the magnetic than for the elec- 

 trostatic lens, but those for the latter are 

 adequate to show its inferiority. All the rele- 

 vant properties are given in a series of uni- 

 versal curves derived from data calculated 

 by Liebmann and Grad (1951). 



The first order focal properties of impor- 

 tance are the focal length (Jo , for objective 

 and/i , for projector) and focal distance (zq). 

 These parameters can be expressed in the 

 simple universal curves of Figure 2 in terms 

 of the ratios /o/(>S -f D), fi/(S + D), Zo/ 

 (S + D) and the excitation parameter Vr/ 



(Niy where eVr is the relativistically cor- 

 rected electron energy, and NI the effective 

 ampere-turn excitation of the lens. By effec- 

 tive is meant the ampere-turn excitation 

 drop across the lens gap. The dotted line in 

 the figure represents the thin lens approxima- 

 tion given by 



/ = 25 VriS + D)/{Niy (2) 



It is seen that the projector focal length 

 passes through a minimum. This is of im- 

 portance in that it determines the maximum 

 magnification which can be obtained with a 

 given stage length. 



Of paramount importance is the spherical 

 aberration of the objective lens which sets 

 the ultimate limit of resolving power. The 

 spherical aberration is defined by the con- 

 stant Cs where Cs a^ gives the radial error 

 in position of a ray leaving the object at 

 angle a with the axis, the distance being 

 measured in object space. 



The value of Cs/f is given within an error 

 of ± 10 % for values of the ratio S/D between 

 0.2 and 2 by the full curve of Figure 3. The 



16 



Cs/f 



14 



12 



lO 



0-2 



0-4 



0-6 



08 



lO 



1-4 



1-6 1-8 



f/(Si-D) 

 Fig. 3. Variation of the ratio CJj with// (5 -h Dy. 



20 



150 



