White-light optical implementation of the fractional fourier transform with adjustable order control

Optical implementation of iterative fractional Fourier transform algorithm

An optical implementation of iterative fractional Fourier transform algorithm is proposed and demonstrated. In the proposed implementation, the phase-shifting digital holography technique and the phase-type spatial light modulator are adopted for the measurement and the modulation of complex optical fields, respectively. With the devised iterative fractional Fourier transform system, we demonstrate two-dimensional intensity distribution synthesis in the fractional Fourier domain and three-dimensional intensity distribution synthesis simultaneously forming desired intensity distributions at several multi-focal planes.

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.

Fractional Fourier transform optical system with programmable diffractive lenses

We present experimental results for a fractional Fourier transform (FRFT) system implemented with programmable lenses written onto a liquid-crystal spatial light modulator (LCSLM). Because the focal length can be changed, different orders of the FRFT can be obtained without changing the optical setup. The LCSLM can very easily implement more complicated operations, including the realization of simultaneous orders of the FRFT and anamorphic transforms.

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.

Parallel fractional correlation: an optical implementation

An optical setup to obtain all the fractional correlations of a one-dimensional input in a single display is implemented. The system works as a multichannel parallel correlator for a continuous set of fractional orders and presents a variable shift variance. Some experimental results together with computer simulations are performed to illustrate the performance of our proposal.