Abstract

Compensation of chromatic dispersion for the optical implementation of mathematical transformations has proved to be an important tool in the design of new optical methods for full-color signal processing. A novel approach for designing dispersion-compensated, broadband optical transformers, both Fourier and Fresnel, based on the collimated Fresnel number is introduced. In a second stage, the above framework is fully exploited to achieve the optical implementation of the fractional Fourier transform (FRT) of any diffracting screen with broadband illumination. Moreover, we demonstrate that the amount of shift variance of the dispersion-compensated FRT can be tuned continuously from the spatial domain, which is totally space variant, to the spectral domain, which is totally space invariant, with the chromatic correction remaining unaltered.

© 2004 Optical Society of America

Wavelength-compensated Fourier and Fresnel transformers: a unified approach

J. Lancis, G. Mínguez-Vega, E. Tajahuerce, M. Fernández-Alonso, V. Climent, and P. Andrés
Opt. Lett. 27(11) 942-944 (2002)

Achromatic Fourier transforming properties of a separated diffractive lens doublet: theory and experiment

Enrique Tajahuerce, Vicent Climent, Jesús Lancis, Mercedes Fernández-Alonso, and Pedro Andrés
Appl. Opt. 37(26) 6164-6173 (1998)

Broadband space-variant Fresnel processor

G. Mínguez-Vega, J. Lancis, E. Tajahuerce, V. Climent, J. Caraquitena, and P. Andrés
Opt. Lett. 27(21) 1926-1928 (2002)

All-incoherent dispersion-compensated optical correlator

P. Andrés, V. Climent, J. Lancis, G. Mínguez-Vega, E. Tajahuerce, and A. W. Lohmann
Opt. Lett. 24(19) 1331-1333 (1999)

Chromatic compensation in the near-field region: shape and size tunability

G. Mínguez-Vega, M. Fernández-Alonso, E. Tajahuerce, J. Lancis, Z. Jaroszewicz, and P. Andrés
Appl. Opt. 44(32) 6933-6939 (2005)