Electronic optics

Electronic optics is a field of theoretical and applied physics born from a series of experiments in which a beam of electrons produced the same diffraction phenomena of a beam of light rays. It was thus shown unequivocally the undulatory nature of the electron (and therefore also of other material corpuscles).

The electronic optics can then make use of the same methods used in physical optics, with the advantage (which in certain applications is crucial) that the wavelength of the waves associated with electrons can be much shorter than that of light radiation. In many cases, however, the approximations of geometric optics are sufficient: this happens when the wave aspect of the electron can be neglected.

The electrons can then be considered as point particles, having mass and charge, describing curved trajectories, in particular rectilinear. The deviation from the rectilinear propagation is caused by the presence of electric and magnetic fields; the phenomenon is analogous to the curvature of the trajectory of light rays that occurs when they cross a medium whose refractive index varies with continuity.

The laws of the motion of an electron inside electric and magnetic fields are those of mechanics and electromagnetism. In particular, the force exerted on an electron (but the same considerations are valid also for ions) in an electrostatic field is proportional to the charge of the particle and to the intensity of the field and is directed according to the flow lines of the field itself. The force exerted by a magnetic field on an electric charge moving inside it is instead the Lorentz force. If an electron moves in a non-uniform electric field, the laws of its motion can be expressed in a form analogous to Snell’s law, valid for the refraction of light rays.

If the electron moves in a magnetic field, the magnitude corresponding to the refraction index depends not only on the characteristics of the field, but also (for the same form of Lorentz law) on its velocity. Based on these considerations, electrostatic lenses and magnetic lenses are constructed. The electrostatic lens consists of two coaxial cylindrical electrodes placed one behind the other. The lines of force of the electric field deflect the electrons of the beam so as to obtain a focusing effect similar to that produced by a converging glass lens on a beam of light rays parallel to its axis. The magnetic lens, on the other hand, consists of a solenoid traversed by an electric current that produces a uniform magnetic field directed along its axis.

A beam of electrons entering the solenoid in a direction parallel to the axis is not deflected, because the component of the velocity in the direction normal to the axis is zero and the Lorentz force is proportional to this component. However, if they enter in an inclined direction with respect to the axis of the solenoid, then they are subjected to a force perpendicular to the axis the greater the component of velocity in this direction. This force forces them to describe trajectories that are the resultant of a uniform rectilinear motion and a uniform circular motion, that is spirals.

If the electrons of the beam have different normal components of velocity, they describe spirals of different radius: the overall effect of the field generated by the solenoid is to make them all converge in a single point of the axis. In this case we have a focusing effect similar to that of a converging lens. Both electrostatic lenses and magnetic lenses have aberrations similar to those that occur in the case of glass optics.

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