An einzel lens (from german: Einzellinse – single lens), or unipotential lens, is a

charged particle In physics, a charged particle is a particle with an electric charge. It may be an ion, such as a molecule or atom with a surplus or deficit of electrons relative to protons. It can also be an electron or a proton, or another elementary particle, ...

electrostatic lens An electrostatic lens is a device that assists in the transport of charged particles. For instance, it can guide electrons emitted from a sample to an electron analyzer, analogous to the way an optical lens assists in the transport of light in an o ...

that focuses without changing the energy of the beam. It consists of three or more sets of cylindrical or rectangular apertures or tubes in series along an axis. It is used in

ion optics An electrostatic lens is a device that assists in the transport of charged particles. For instance, it can guide electrons emitted from a sample to an electron analyzer, analogous to the way an optical lens assists in the transport of light in an op ...

to focus

ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...

s in flight, which is accomplished through manipulation of the

electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...

in the path of the ions. The electrostatic potential in the lens is symmetric, so the ions will regain their initial

energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...

on exiting the lens, although the

velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...

of the outer particles will be altered such that they converge on to the axis. This causes the outer particles to arrive at the

focus Focus, or its plural form foci may refer to: Arts * Focus or Focus Festival, former name of the Adelaide Fringe arts festival in South Australia Film *''Focus'', a 1962 TV film starring James Whitmore * ''Focus'' (2001 film), a 2001 film based ...

intersection slightly later than the ones that travel along a straight path, as they have to travel an extra distance.

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 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 tube A cathode-ray tube (CRT) is a vacuum tube containing one or more electron guns, which emit electron beams that are manipulated to display images on a phosphorescent screen. The images may represent electrical waveforms ( oscilloscope), pictu ...

s,"Television Receiver Servicing" by E. A. W. Spreadbury, 1953. 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 A monochrome or monochromatic image, object or palette is composed of one color (or values of one color). Images using only shades of grey are called grayscale (typically digital) or black-and-white (typically analog). In physics, monochrom ...

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

*{{Citation , doi = 10.1063/1.1686484 , title = Construction of an einzel lens capable of high voltage operation , year = 1974 , author = Aberth, William H. , journal = Review of Scientific Instruments , volume = 45 , pages = 1289, bibcode = 1974RScI...45.1289A , issue = 10 Electrostatics Mass spectrometry

Theory

Application to television tubes

See also

References