Space–bandwidth product of optical signals and systems

The space–bandwidth product (SW) is fundamental for judging the performance of an optical system. Often the SW of a system is defined only as a pure number that counts the degrees of freedom of the system. We claim that a quasi-geometrical representation of the SW in the Wigner domain is more useful. We also represent the input signal as a SW in the Wigner domain. For perfect signal processing it is necessary that the system SW fully embrace the signal SW.

Space-variant simultaneous detection of several objects by the use of multiple anamorphic fractional-Fourier-transform filters.

A fractional correlator that is based on the anamorphic fractional Fourier transform is defined. This new, to our knowledge, correlator has been extended to work with multiple filters. The novelty introduced by the suggested system is the possibility of the simultaneous detection of several objects in different parts of the input scene (when anamorphic optics are dealt with), thereby permitting an independent degree of space invariance in two perpendicular directions. Computer experiments as well as experimental optical implementation are presented.

Wavelength-multiplexing system for single-mode image transmission

The expanding use of optical communication by means of optical fibers and the situation of drastically increasing amounts of data to be transmitted urge the exploration of novel systems permitting the transmission of large amounts of spatial information by fiber with smaller spatial resolution. An optical encoding and decoding system is suggested for transmitting one- or two-dimensional images by means of a single-mode fiber. The superresolving system is based on wavelength multiplexing of the input spatial information, which is achieved with diffractive optical elements. Preliminary experimental results demonstrate the capabilities of the suggested method for the one- and two-dimensional c…

Optical illustration of a varied fractional Fourier-transform order and the Radon-Wigner display.

Based on an all-optical system, a display of a fractional Fourier transform with many fractional orders is proposed. Because digital image-processing terminology is used, this display is known as the Radon–Wigner transform. It enables new aspects for signal analysis that are related to time- and spatial-frequency analyses. The given approach for producing this display starts with a one-dimensional input signal although the output signal contains two dimensions. The optical setup for obtaining the fractional Fourier transform was adapted to include only fixed free-space propagation distances and variable lenses. With a set of two multifacet composite holograms, the Radon–Wigner display has b…

Variable fractional Fourier processor: a simple implementation

A new set of optical implementations of the fractional Fourier transform (FRT) is developed by use of Wigner matrix algebra. The reinterpretation of some elementary operations that synthesize a rotation in the phase-space domain allows us to propose a lensless setup for obtaining the FRT. This compact configuration is also very flexible, because the fractional degree of the transformation can be varied continuously by shifting the input and the output planes along the optical axis by proper amounts. The above results permit one to build an optical FRT processor formed by two FRT systems in cascade, with a spatial filter between them. We present the design of such a variable FRT processor, w…

Variable fractional Fourier processor: a simple implementation: erratum

Flexible optical implementation of fractional Fourier transform processors. Applications to correlation and filtering

Abstract Recently, in the field of fractional Fourier transforms (FRT) an operation coined “fractional correlation” has been proposed and investigated experimentally. In this paper we propose a new setup for obtaining the fractional correlation, which presents several advantages from the experimental point of view. The fractional filter plane can be adjusted accurately with the help of converging beam illumination and using an adjusting device consisting of a combination of Fresnel zone plates. Moreover the scaling factor between the input pattern and the filter can be adjusted at will. This degree of freedom is of special interest when using SLMs. In addition we present a configuration, ba…