In optics, a pencil or pencil of rays is a geometric construct used to describe a beam or portion of a beam of electromagnetic radiation or charged particles, typically in the form of a narrow beam (

conical A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines conn ...

cylindrical A cylinder (from ) has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infini ...

). 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 Focusing may refer to: * Adjusting an optical system to minimize defocus aberration * Focusing (psychotherapy), a psychotherapeutic technique See also *Focus (disambiguation) Focus, or its plural form foci may refer to: Arts * Focus or Focus Fe ...

action of a lens is often described in terms of pencils of

ray Ray may refer to: Fish * Ray (fish), any cartilaginous fish of the superorder Batoidea * Ray (fish fin anatomy), a bony or horny spine on a fin Science and mathematics * Ray (geometry), half of a line proceeding from an initial point * Ray (g ...

s. In addition to conical and cylindrical pencils, optics deals with astigmatic pencils as well. In electron optics, scanning electron microscopes use narrow pencil beams to achieve a deep

depth of field The depth of field (DOF) is the distance between the nearest and the furthest objects that are in acceptably sharp focus in an image captured with a camera. Factors affecting depth of field For cameras that can only focus on one object dist ...

Ionizing radiation Ionizing radiation (or ionising radiation), including nuclear radiation, consists of subatomic particles or electromagnetic waves that have sufficient energy to ionize atoms or molecules by detaching electrons from them. Some particles can travel ...

used in radiation therapy, whether photons or charged particles, such as

proton therapy In medicine, proton therapy, or proton radiotherapy, is a type of particle therapy that uses a beam of protons to irradiate diseased tissue, most often to treat cancer. The chief advantage of proton therapy over other types of external beam ra ...

and

electron therapy Electron therapy or electron beam therapy (EBT) is a kind of external beam radiotherapy where electrons are directed to a tumor site for medical treatment of cancer. Equipment Electron beam therapy is performed using a medical linear accelerato ...

machines, is sometimes delivered through the use of pencil beam scanning. 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

A 1675 work describes a pencil as "a double cone of rays, joined together at the base." 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".

References

Geometrical optics Antennas (radio) Radiation therapy {{optics-stub