The theory of canonical transforms is applied to establish the mathematical foundations of the operator algebra method, leading to useful relations between geometrical ray optics and the operator representation of wave optics. The transfer operator of a general first-order system is expressed in terms of the elements of the ray-transfer <i>ABCD</i> matrix. The theory is exemplified through the discussion of basic operator subgroups and special types of systems: Fourier, Fresnel, imaging, and afocal.
© 1982 Optical Society of America
Moshe Nazarathy and Joseph Shamir, "First-order optics—a canonical operator representation: lossless systems," J. Opt. Soc. Am. 72, 356-364 (1982)