Ray tracing the Wigner distribution function for optical simulations

Mout, Marco; Wick, Michael J.; Bociort, Florian; Petschulat, J.; Urbach, Paul

doi:10.1117/1.oe.57.1.014106

Cited by 3 publications

(1 citation statement)

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“…It describes a signal in space and spatial frequency simultaneously, and can be considered as the local spatialfrequency spectrum of the signal [20]. The WD has immediate applications in Fourier optics [21], geometrical optics [22], wave optics [23], ray optics [24], matrix optics [25], and radiometry [26]. Particularly, it is a powerful time-frequency analysis tool designed for the detection of linear frequency-modulated (LFM) signals.…”

Section: Introductionmentioning

confidence: 99%

Unique Parameters Selection Strategy of Linear Canonical Wigner Distribution via Multiobjective Optimization Modeling

Shi

Sun

et al. 2023

Chinese J. Elect.

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There are many kinds of linear canonical transform (LCT)-based Wigner distributions (WDs), which are very effective in detecting noisy linear frequency-modulated (LFM) signals. Among WDs in LCT domains, the instantaneous cross-correlation function type of Wigner distribution (ICFWD) attracts much attention from scholars, because it achieves not only low computational complexity but also good detection performance. However, the existing LCT free parameters selection strategy, namely a solution of the expectation-based output signal-to-noise ratio (SNR) optimization model, is not unique. In this paper, by introducing the variance-based output SNR optimization model, a multiobjective optimization model is established. Then the existence and uniqueness of the optimal parameters of ICFWD are investigated. The solution of the multiobjective optimization model with respect to one-component LFM signal added with zero-mean stationary circular Gaussian noise is derived. A comparison of the unique parameters selection strategy and the previous one is carried out. The theoretical results are also verified by numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Unique Parameters Selection Strategy of Linear Canonical Wigner Distribution via Multiobjective Optimization Modeling

Shi

Sun

et al. 2023

Chinese J. Elect.

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Simulation of diffraction and scattering using the Wigner distribution function

Pietersoone,

Létang,

Rit

et al. 2024

Opt. Lett.

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We present a new, to the best of our knowledge, method to simulate diffraction images accounting for both coherent and incoherent effects, based on the Wigner distribution function of the exit wave. This permits the simulation of wave and particle effects simultaneously and simulates images photon by photon. It is motivated by artifacts observed in x ray phase-contrast images after phase retrieval, present as noise in the low spatial frequency range, which can make analysis of such images challenging. Classical simulations have so far not been able to reproduce these artifacts. We hypothesize that these artifacts are due to incoherent scatter present in the images, hence the interest in developing a simulator that permits the simulation of both diffraction and incoherent scattering. Here, we give a first demonstration of the method by simulating the Gaussian double-slit experiment. We demonstrate the capability of combining diffraction and incoherent scattering, as well as simulating images for any propagation distance.

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