The

optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultrav ...

term encircled energy refers to a measure of concentration of

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 hea ...

in an optical image, or projected

laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fi ...

at a given range. If a single star is brought to its sharpest

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 ...

by a

lens A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements ...

giving the smallest image possible with that given lens (called a point spread function or PSF), calculation of the encircled energy of the resulting image gives the distribution of energy in that PSF. Encircled energy is calculated by first determining the total energy of the PSF over the full image plane, then determining the

centroid In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. The same definition extends to any ...

of the PSF. Circles of increasing

radius In classical geometry, a radius ( : radii) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', meaning ray but also the ...

are then created at that centroid and the PSF energy within each circle is calculated and divided by the total energy. As the circle increases in radius, more of the PSF energy is enclosed, until the circle is sufficiently large to completely contain all the PSF energy. The encircled energy curve thus ranges from zero to one. A typical criterion for encircled energy (EE) is the radius of the PSF at which either 50% or 80% of the energy is encircled. This is a

linear Linearity is the property of a mathematical relationship ('' function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear ...

dimension, typically in

micrometer Micrometer can mean: * Micrometer (device), used for accurate measurements by means of a calibrated screw * American spelling of micrometre The micrometre ( international spelling as used by the International Bureau of Weights and Measures; ...

s. When divided by the lens or mirror focal length, this gives the angular size of the PSF, typically expressed in arc-seconds when specifying

astronomical Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, galaxi ...

optical system performance. Encircled energy is also used to quantify the spreading of a laser beam at a given distance. All laser beams spread due to the necessarily limited

aperture In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane. An ...

of the optical system projecting the beam. As in star image PSF's, the linear spreading of the beam expressed as encircled energy is divided by the projection distance to give the angular spreading. An alternative to encircled energy is ensquared energy, typically used when quantifying image sharpness for digital imaging cameras using

pixels In digital imaging, a pixel (abbreviated px), pel, or picture element is the smallest addressable element in a raster image, or the smallest point in an all points addressable display device. In most digital display devices, pixels are the sm ...

References

*Smith, Warren J.
''Modern Optical Engineering'', 3rd ed.
pp. 383–385. New York: McGraw-Hill, Inc., 2000. {{ISBN, 0-07-136360-2 Geometrical optics Physical optics Engineering concepts Optics

See also

References