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Fourier transform in metaxial geometric optics

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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 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

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