For example, 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.
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.
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.