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Related Experiment Video

Updated: Jun 23, 2026

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating

Published on: October 11, 2016

Rays, beams and diffraction in a discrete phase space: Wilson bases.

|May 20, 2009

Summary

High-frequency fields can be efficiently represented using phase-space methods, potentially reducing computational costs for wave propagation calculations. This study explores the Windowed Fourier Transform for optimal discrete basis generation.

Area of Science:

Computational physics
Wave propagation theory
Applied mathematics

Background:

High-frequency fields possess localized phase-space representations.
This localization offers potential for significant computational cost reduction in propagator calculations.

Purpose of the Study:

To investigate the application of phase-space representations for high-frequency fields.
To explore the Windowed Fourier Transform (WFT) for wavefield analysis in diffraction theory.
To develop an optimal discrete basis for numerical evaluations.

Main Methods:

Utilizing the Windowed Fourier Transform (WFT) to represent continuous wavefields.
Parameterizing wavefields in phase-space along ray trajectories.
Generating a discrete Wilson basis through optimal phase-space sampling of the WFT.

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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Related Experiment Videos

Last Updated: Jun 23, 2026

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating

Published on: October 11, 2016

$Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene$

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene

Published on: August 22, 2017

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Main Results:

Demonstrated strong localization of coefficients in phase-space for high-frequency fields.
Observed noncanonical WFT coefficients due to WFT non-uniqueness.
Developed an optimal discrete sampling method for generating a minimal orthogonal basis.

Conclusions:

Phase-space representations, particularly using the WFT, are effective for analyzing high-frequency fields.
The discrete Wilson basis provides an optimal, computationally efficient representation for numerical analysis.
This approach holds promise for reducing computational costs in wave propagation problems.