Pencil (optics)

In optics, a pencil or pencil of rays, also known as a pencil beam or narrow beam, is a geometric construct (pencil of half-lines) used to describe a beam or portion of a beam of electromagnetic radiation or charged particles, typically in the form of a cone or cylinder.

Antennas which strongly bundle in azimuth and elevation are often described as "pencil-beam" antennas. For example, a phased array antenna can send out a beam that is extremely thin. Such antennas are used for tracking radar, and the process is known as beamforming.

In optics, the focusing action of a lens is often described in terms of pencils of rays. In addition to conical and cylindrical pencils, optics deals with astigmatic pencils as well.^[1]

In electron optics, scanning electron microscopes use narrow pencil beams to achieve a deep depth of field.^[2]

Ionizing radiation used in radiation therapy, whether photons or charged particles, such as proton therapy and electron therapy machines, is sometimes delivered through the use of pencil beam scanning.^[3]

In backscatter X-ray imaging a pencil beam of x-ray radiation is used to scan over an object to create an intensity image of the Compton-scattered radiation.

History

In 1675, a pencil was interpreted as a double cone of rays, as from an object point, through a lens, to an image point.

A 1675 work describes a pencil as "a double cone of rays, joined together at the base."^[4] In his 1829 A System of Optics, Henry Coddington defines a pencil as being "a parcel of light proceeding from some one point", whose form is "generally understood to be that of a right cone" and which "becomes cylindrical when the origin is very remote".^[5]

References

^ Edward L. Nichols & William S. Franklin (1903). The Elements of Physics: A College Text-book. Macmillan Co. p. 77.
^ Nick Johnson (19 May 1983). "The art of seeing the very small". New Scientist. 98 (1358): 472.^{[permanent dead link‍]}
^ Faiz M. Khan (2009). The Physics of Radiation Therapy (4th ed.). Lippincott Williams & Wilkins. pp. 521–522. ISBN 978-0-7817-8856-4.
^ Bailey, Nathan (1675). "An Universal Etymological English Dictionary". Retrieved 24 November 2022.
^ Coddington, Henry (1829). A System of Optics: A treatise on the reflexion and refraction of light. -pt.2 A treatise on the eye and on optical instruments. J. Smith. Retrieved 24 November 2022.

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