Application of the Wigner distribution function in optics

This contribution presents a review of the Wigner distribution function and of some of its applications to optical problems. The Wigner distribution function describes a signal in space and (spatial) frequency simultaneously and can be considered as the local frequency spectrum of the signal. Although derived in terms of Fourier optics, the description of a signal by means of its Wigner distribution function closely resembles the ray concept in geometrical optics. It thus presents a link between Fourier optics and geometrical optics. The concept of the Wigner distribution function is not restricted to deterministic signals; it can be applied to stochastic signals, as well, thus presenting a link between partial coherence and radiometry. Some interesting properties of partially coherent light can thus be derived easily by means of the Wigner distribution function. Properties of the Wigner distribution function, for deterministic as well as for stochastic signals (i.e., for completely coherent as well as for partially coherent light, respectively), and its propagation through linear systems are considered; the corresponding description of signals and systems can directly be interpreted in geometric-optical terms. Some examples are included to show how the Wigner distribution function can be applied to problems that arise in the field of optics

A flexible heterogeneous video processor system for television applications

A new video processing architecture for high-end TV applications is presented, featuring a flexible heterogeneous multi-processor architecture, executing video tasks in parallel and independently. The signal flow graph and the processors are programmable, enabling an optimal picture quality for different TV display modes. The concept is verified by an experimental chip design. The architecture allows several video streams to be processed and displayed in parallel and in a programmable way, with an individual signal qualit

Radar matched filtering using the fractional fourier transform

Abstract-A matched filter is the optimal linear filter for maximizing the signal to noise ratio (SNR) in the presence of additive noise. Matched filters are commonly used in radar systems where the transmitted signal is known and may be used as a replica to be correlated with the received signal which can be carried out by multiplication in the frequency domain by applying Fourier Transform (FT). Fractional Fourier transform (FrFT) is the general case for the FT and is superior in chirp pulse compression using the optimum FrFT order. In this paper a matched filter is implemented for a chirp radar signal in the optimum FrFT domain. Mathematical formula for a received chirp signal in the frequency domain and a generalized formula in the fractional Fourier domain are presented in this paper using the Principle of Stationary Phase (PSP). These mathematical expressions are used to show the limitations of the matched filter in the fractional Fourier domain. The parameters that affect the chirp signal in the optimum fractional Fourier domain are described. The performance enhancement by using the matched filter in the fractional Fourier domain for special cases is presented

The spatially averaged electric field in the near field and far field of a circular aperture

This paper presents a theoretical and numerical investigation of the spatially averaged electric field in the beam of a circular aperture. The investigation leads to closed-form analytical expressions, based on scalar diffraction theory, which describe the spatially averaged electric field in the Fresnel region of a circular aperture excited by a spatially uniform, harmonic plane wave. The expressions ultimately permit rapid, practical, and efficient prediction of certain routine electromagnetic measurements. Because the expressions are valid in the Fresnel region, they are also valid in the near field, the far field, and the Fraunhofer region of a circular aperture. In fact, it is shown that the closed-form expressions contain, as special cases, classic on-axis and far-field results associated with a circular aperture. The analytical expressions are based on a generalization of Fresnel diffraction originally developed by Lommel in the late 1800s. Hence, a thorough review of the literature on the Lommel diffraction formulation is presented. Finally, it is shown that results obtained from the closed-form expressions compare quite favorably to results obtained from the exact solution computed via the dyadic Green\u27s function approach

A study of digital holographic filter generation

Problems associated with digital computer generation of holograms are discussed along with a criteria for producing optimum digital holograms. This criteria revolves around amplitude resolution and spatial frequency limitations induced by the computer and plotter process