Einzel lens

Theory

The equation for the change in radial velocity for a particle as it passes between any pair of cylinders in the lens is:

\Delta v_r = \int \frac{qE_r(r,z)}{m v_z} dz,

with z axis passing through the middle of the lens, and r being the direction normal to z. If the lens is constructed with cylindrical electrodes, the field is symmetrical around z. E_r(r,z) is the magnitude of the electric field in the radial direction for a particle at a particular radial distance and distance across the gap, m is the mass of the particle passing through the field, v_z is the velocity of the particle and q is the charge of the particle. The integral occurs over the gap between the plates. This is also the interval where the lensing occurs.

The pair of plates is also called an electrostatic immersion lens, thus an einzel lens can be described as two or more electrostatic immersion lenses. Solving the equation above twice to find the change in radial velocity for each pair of plates can be used to calculate the focal length of the lens.

Application to television tubes

The einzel lens principle in a simplified form was also used as a focusing mechanism in display and television cathode ray tubes, and has the advantage of providing a good sharply focused spot throughout the useful life of the tube's electron gun, with minimal or no readjustment needed (many monochrome TVs did not have or need focus controls), although in high-resolution monochrome displays and all colour CRT displays a (technician-adjustable) focus potentiometer control is provided.

References

References

1. "Radio and Television" by C. A. Quarrington, 1952–1963.
2. "Television Receiver Servicing" by E. A. W. Spreadbury, 1953.