Abstract

The phase space of rays in geometric optics has a position coordinate on the screen that is unbounded, while its canonically conjugate momentum coordinate is bound by the local refractive index of the medium. The classical Fourier transform is a rotation of phase space by ½π; this is possible only in the Heisenberg-Weyl plane ℛ^2N of classical mechanics or, locally, near the optical axis and center. A point map of optical momentum, however, permits a definition of an optical Fourier transform that is global and canonical and matches the classical Fourier transform in the paraxial regime.

© 1991 Optical Society of America

Metaxial correction of fractional Fourier transformers

Kurt Bernardo Wolf and Guillermo Krötzsch
J. Opt. Soc. Am. A 16(4) 821-830 (1999)

Refracting surfaces between fibers

Kurt Bernardo Wolf
J. Opt. Soc. Am. A 8(9) 1389-1398 (1991)

Fractional Fourier transformers through reflection

Kurt Bernardo Wolf and Guillermo Krötzsch
J. Opt. Soc. Am. A 19(6) 1191-1196 (2002)

Symmetry-adapted classification of aberrations

Kurt Bernardo Wolf
J. Opt. Soc. Am. A 5(8) 1226-1232 (1988)

Structure of the set of paraxial optical systems

R. Simon and Kurt Bernardo Wolf
J. Opt. Soc. Am. A 17(2) 342-355 (2000)