Abstract
The Legendre transformation is used to describe limits of beams of light rays in homogeneous space and optical systems. It is shown that by means of a Legendre transformation, a light ray, a beam of rays and an envelope of beams of light rays are converted into a point, a set of points and a border of a set of points, respectively, in a phase space (phase portraits). Application of a Legendre transformation to an envelope of the beam of light rays passing through an optical fiber results in a border of the phase stop. It is found that phase portraits of beams of light rays simplify description of vignetting in high aperture and wide angle objectives.
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