Encircled energy
Encyclopedia
The optics term encircled energy refers to a measure of concentration of energy
in an optical image
, or projected laser at a given range. If a single star is brought to its sharpest focus
by a lens
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
of the PSF. Circles of increasing radius
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
dimension, typically in micrometer
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 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
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.
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
in an optical image
Image
An image is an artifact, for example a two-dimensional picture, that has a similar appearance to some subject—usually a physical object or a person.-Characteristics:...
, or projected laser at a given range. If a single star is brought to its sharpest focus
Focus (optics)
In geometrical optics, a focus, also called an image point, is the point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by...
by a lens
Lens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...
giving the smallest image
Image
An image is an artifact, for example a two-dimensional picture, that has a similar appearance to some subject—usually a physical object or a person.-Characteristics:...
possible with that given lens (called a point spread function
Point spread function
The point spread function describes the response of an imaging system to a point source or point object. A more general term for the PSF is a system's impulse response, the PSF being the impulse response of a focused optical system. The PSF in many contexts can be thought of as the extended blob...
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
Centroid
In geometry, the centroid, geometric center, or barycenter of a plane figure or two-dimensional shape X is the intersection of all straight lines that divide X into two parts of equal moment about the line. Informally, it is the "average" of all points of X...
of the PSF. Circles of increasing radius
Radius
In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...
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
Linear
In mathematics, a linear map or function f is a function which satisfies the following two properties:* Additivity : f = f + f...
dimension, typically in micrometer
Micrometre
A micrometer , is by definition 1×10-6 of a meter .In plain English, it means one-millionth of a meter . Its unit symbol in the International System of Units is μm...
s. When divided by the lens or mirror focal length, this gives the angular
Angular
The angular is a large bone in the lower jaw of amphibians and reptiles , which is connected to all other lower jaw bones: the dentary , the splenial, the suprangular, and the articular...
size of the PSF, typically expressed in arc-seconds
Minute of arc
A minute of arc, arcminute, or minute of angle , is a unit of angular measurement equal to one sixtieth of one degree. In turn, a second of arc or arcsecond is one sixtieth of one minute of arc....
when specifying astronomical 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
Aperture
In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture of an optical system is the opening that determines the cone angle of a bundle of rays that come to a focus in the image plane. The aperture determines how collimated the admitted rays are,...
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.