We consider lattice dynamics with a small stochastic perturbation of order ε and prove that for a space-time scale of order ε the Wigner function evolves according to a linear transport equation describing inelastic collisions. For an energy and momentum conserving chain the transport equation predicts a slow decay, as 1/ √ t, for the energy current correlation in equilibrium. This is in agreem...

The Wigner distribution is used to model the PSF of an aperture mask at different defocus planes. Algorithmic methods of determining an optimal mask pattern for a desired set of impulse responses are investigated. ©2010 Optical Society of America OCIS codes: 110.7348, 070.7425

We study crystal dynamics in the harmonic approximation. The atomic masses are weakly disordered, in the sense that their deviation from uniformity is of order √ ε. The dispersion relation is assumed to be a Morse function and to suppress crossed recollisions. We then prove that in the limit ε → 0 the disorder averaged Wigner function on the kinetic scale, time and space of order ε, is governed...

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 an...

The Wigner distribution (WD) can be decomposed into a linear combination of elementary WDs. Slow-oscillatory elementary WDs and fast-oscillatory elementary WDs mainly contribute to auto-terms and cross-terms, respectively. Using a weight function to keep slow-oscillatory elementary WDs and attenuate fast-oscillatory elementary WDs, one can balance auto-term resolution and cross-term suppression...

Cross-terms lie between two auto-components and are oscillatory, with their frequencies increasing with increasing distance in time-frequency between the two components. The cross-terms can have a peak value as high as twice that of the auto-components. A Wigner distribution of a two-component signal is shown in Figure 1. In this figure, it is easy to separate the auto-components from the cross...

This paper presents an analysis of the representation of instantaneous frequency using time-frequency distributions of energy density domain. Similarity to the ”ideal” instantaneous frequency presentation is chosen as a criterion for comparison of various distributions. Although all the commonly used distributions suffer from the artifacts along frequency axis, it is shown that the Wigner distr...

The Wigner distribution of rotationally symmetric partially coherent light is considered and the constraints for its moments are derived. While all odd– order moments vanish, these constraints lead to a drastic reduction in the number of parameters that we need to describe all even–order moments: whereas in general we have (N + 1)(N + 2)(N + 3)/6 different moments of order N , this number reduc...