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
Original Manuscript: January 12, 2004
Revised Manuscript: May 7, 2004
Manuscript Accepted: May 7, 2004
Published: October 1, 2004
Jésus Lancis, Gladys Mı́nguez-Vega, Enrique Tajahuerce, Vicent Climent, Pedro Andrés, and José Caraquitena, "Chromatic compensation of broadband light diffraction: ABCD-matrix approach," J. Opt. Soc. Am. A 21, 1875-1885 (2004)