We study fractional Fourier transformation in the metaxial regime of geometric optics. Two commonly used optical arrangements that perform fractional Fourier transformation are a symmetric thick lens and a length of graded-index waveguide. By means of Lie methods in phase space, we can correct some of their aberrations: for the first, through deforming the lens surfaces to a polynomial shape, and for the second, by warping the output screen at the end of the waveguide. We correct the planar cases to third, fifth, and seventh aberration orders; checks are provided on the convergence of aberration series in phase space. We add some comments on the usefulness of these corrected devices for fractional transformers in scalar wave optics.

© 1999 Optical Society of America

[Optical Society of America ]

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

Related Journal Articles

• Reassessing the theoretical accuracy of the crossed-cylinder aberroscope technique (JOSAA)
• Accurate computation of mean power and astigmatism by means of Zernike polynominals (JOSAA)
• Scalar integral diffraction methods: unification, accuracy, and comparison with a rigorous boundary element method with application to diffractive cylindrical lenses (JOSAA)
• Charged-particle-beam propagator in wave-electron optics: phase-space and tomographic pictures (JOSAA)
• Fractional Fourier transformers through reflection (JOSAA)

Related Conference Papers

• New Optics Using Negative Refraction
• The role of spherical aberration on THz pulse propagation
• Third-Order Aberrations of an AGRIN Thin Lens as a Function of the Shape Factor and Conjugate Variable
• Numerical Integration of the Profile of Aspheric Surfaces
• Panomorph Lens: A New Type of Panoramic Lens