Wigner distribution transformations in high-order systems

By combining the definition of the Wigner distribution function (WDF) and the matrix method of optical system modeling, we can evaluate the transformation of the former in centered systems with great complexity. The effect of stops and lens diameter are also considered and are shown to be responsible for non-linear clipping of the resulting WDF in the case of coherent illumination and non-linear modulation of the WDF when the illumination is incoherent. As an example, the study of a single lens imaging systems illustrates the applicability of the method.Comment: 16 pages, 7 figures. To appear in J. of Comp. and Appl. Mat

Field weed population models: a review of approaches and application domains

We evaluated models of weed population dynamics based on an analysis of their assumptions, biological rationale, flexibility, documentation, accessibility, demand for parameter estimation and documented validity. We arrived at general recommendations regarding which modelling approach should be applied in order to address different application domains

Wide angle near-field diffraction and Wigner distribution

Free-space propagation can be described as a shearing of the Wigner distribution function in the spatial coordinate; this shearing is linear in paraxial approximation but assumes a more complex shape for wide-angle propagation. Integration in the frequency domain allows the determination of near-field diffraction, leading to the well known Fresnel diffraction when small angles are considered and allowing exact prediction of wide-angle diffraction. The authors use this technique to demonstrate evanescent wave formation and diffraction elimination for very small apertures

Transitional free convection flows induced by thermal line sources

In the present study the usefullness of a large eddy simulation for transition is examined. Numerical results of such simulations are presented from a study to determine the characteristics of a flow induced by a thermal line source. The first bifurcation to time dependent motion and the route to chaos are considered. Qualitatively these features are in good agreement with theory. The governing equations, the concept of large eddy simulation and the numerical code that was used are described extensively. Also the results from a literature survey are presented. Special attention is paid to analytical solutions for the boundary layer equations for laminar flow and the stability of these solutions. It includes also overall conservation principles for turbulent plumes and results obtained by experiments

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

Gabor's expansion and the Zak transform for continuous-time and discrete-time signals : critical sampling and rational oversampling

Gabor's expansion of a signal into a discrete set of shifted and modulated versions of an elementary signal is introduced and its relation to sampling of the sliding-window spectrum is shown. It is shown how Gabor's expansion coefficients can be found as samples of the sliding-window spectrum, where - at least in the case of critical sampling - the window function is related to the elementary signal in such a way that the set of shifted and modulated elementary signals is bi-orthonormal to the corresponding set of window functions. The Zak transform is introduced and its intimate relationship to Gabor's signal expansion is demonstrated. It is shown how the Zak transform can be helpful in determining the window function that corresponds to a given elementary signal and how it can be used to find Gabor's expansion coefficients. The continuous-time as well as the discrete-time case are considered, and, by sampling the continuous frequency variable that still occurs in the discrete-time case, the discrete Zak transform and the discrete Gabor transform are introduced. It is shown how the discrete transforms enable us to determine Gabor's expansion coefficients via a fast computer algorithm, analogous to the well-known fast Fourier transform algorithm. Not only Gabor's critical sampling is considered, but also the case of oversampling by a rational factor. An arrangement is described which is able to generate Gabor's expansion coefficients of a rastered, one-dimensional signal by coherent-optical means

Error Reduction In Two-Dimensional Pulse-Area Modulation, With Application To Computer-Generated Transparencies

The paper deals with the analysis of computer-generated half-tone transparencies that are realised as a regular array of area-modulated unit-height pulses and with the help of which we want to generate [via low-pass filtering] band-limited space functions by optical means. The mathematical basis for such transparencies is, of course, the well-known sampling theorem [1], which says that a band-limited func-tion y(x), say, [with x a two-dimensional spatial column vector] can be generated by properly low-pass filtering a regular array of Dirac functions whose weights are proportional to the required sample values yey(Xm) [with X the sampling matrix and m=(mi,m2)t an integer-valued column vector; the superscript t denotes transposition]