ELECTROSTATIC ELECTRON-OPTICS 



19 



The required paths of the two rays must in general be determined 

 either by a series or step-by-step integration of the differential equation 

 for A, or else by actual measurements on the physical lens.^^ 



FIRST 

 RAY 



FIRST PRINCIPAL I FOCAL |POINTS 



SECOND 

 RAY 



SECOND 

 PLANE 



Fig. 11 — The cardinal points of a lens. 



Magnification 



Electron object and electron image are defined as their optical 

 analogies. The electron object may be an actual source of electrons, 

 or the real image of such a source, or it may be a virtual image from 

 which the electrons are apparently coming as they enter a lens. 



The magnification by an electron lens may be treated in the following 

 manner. Let Si be the size of an electron object located at a distance 

 Di from the first principal plane of a lens. Two electron rays from 

 the edge of the object are considered— as shown in Fig. 12. The ray 



PRINCIPAL 



PLANES 



FIRST SECOND 



Fig. 12 — Magnification. 



entering the lens parallel to the axis may be regarded as passing on to 

 the second principal plane and then bending sharply to pass through 

 the second principal focal point ; the ray through the first principal 

 focal point may be considered as passing on to the first principal 

 plane and then proceeding parallel to the axis. The intersection of 

 the two rays locates the electron image and determines its size 52. 

 The magnification M is defined as S2/S1, and it follows from simple 

 geometry that 



D2 - F2 Fi 



M = 



Di- Fx 



(65) 



^' Other step-by-step methods can be used when a map of the equipotential 

 surface is available. 



