Wavelength-compensated Fourier and Fresnel transformers: a unified approach

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

We report a diffractive-lens triplet with which to achieve wavelength compensation in the near field diffracted by any aperture. On the one hand, the all-diffractive triplet allows us to tune, in a sequential way, the Fresnel-irradiance shape to be achromatized by changing the focal length of one diffractive lens. On the other hand, we can adjust the scale of the chromatically compensated Fresnel diffraction field by shifting the aperture along the optical axis. Within this framework, we present an extremely flexible white-light Fresnel-plane array illuminator based on the kinoform sampling filter. A variable compression ratio and continuous selection of the output pitch are the most appealing features of this novel application.

Chromatic compensation of broadband light diffraction: ABCD-matrix approach

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.

High-contrast white-light Lau fringes

We present a new optical assembly with which to achieve Lau fringes with totally incoherent illumination. Gratinglike codification of the spatially incoherent source combined with an achromatic Fresnel diffraction setup allows us to achieve Lau fringe-pattern visibility of almost 100% with broadband light. The white-light character to our proposed setup is in stark contrast to previous monochromatic implementations. Potential implications of this fact are identified.

Broadband space-variant Fresnel processor

We present a radically new class of optical setup working with white-light illumination, namely, a chromatically compensated processor operating in the Fresnel domain. The optical configuration is a hybrid (diffractive-refractive) three-lens system that exhibits an intermediate achromatic Fresnel plane and an output image plane without chromatic distortion. As a first application of this optical arrangement we develop a parallel space-variant color pattern-recognition experiment with white light.