10 



The Electron Microscope 



Field linzs Ar = const. 





/ Lines A ^ consC 

 (equivalent poteritial lines j 



Fig. 3. Magnetic lens 



This at once explains the lens effect of axially arranged coils. 

 By its definition (3) the vectorpotential A is zero at the axis and 

 increases approximately linearly with the radius r. This means 

 that the equivalent potential decreases outside the axis and that 

 the magnetic field has a repellent effect, i.e., it drives the elec- 

 trons back, toward the axis. Therefore, a magnetic lens is always 

 a condensing lens. An example is shown in the lower half of 

 figure 3. Increasing equivalent potential is indicated by increas- 

 ing density of shading. 



Having shown that axially symmetrical fields act as lenses, it 

 remains to investigate whether they are good lenses. Of the 

 numerous defects which lenses can have, only three are of in- 

 terest in microscopy : the spherical aberration, the chromatic 

 aberration, and the coma. 



Spherical aberration, the most important of the lens defects 

 in electron microscopy, is illustrated in figure 4. An axial point 

 is imaged as a point strictly speaking only while the imaging 

 rays are infinitesimally close to the axis. These are called 

 paraxial rays, and their intersection with the axis is the paraxial 

 or Gaussian image. At larger angles a, the intersection moves 

 away from the Gaussian point by a distance which is called the 

 longitudinal spherical aberration, and which in first approxima- 

 tion is proportional to a^. If a screen p is placed at the Gaussian 

 point, the bundle will intersect it instead of in a point in a disk 

 of a diameter proportional to a^. This diameter is called the 



