Numerical approximation of the Bai distribution function

Yushi Zheng; Min Wan; John J. Healy

doi:10.1117/12.3022148

18 June 2024 Numerical approximation of the Bai distribution function

Yushi Zheng, Min Wan, John J. Healy

Proceedings Volume 12998, Optics, Photonics, and Digital Technologies for Imaging Applications VIII; 129981I (2024) https://doi.org/10.1117/12.3022148
Event: SPIE Photonics Europe, 2024, Strasbourg, France

Conference Poster

Abstract

In recent years, many novel phase space distributions have been proposed and one of the more independently interesting is the Bai distribution function (BDF). The BDF has been shown to interpolate between the instantaneous auto-correlation function and the Wigner distribution function, and to link the geometrical and wave optical descriptions in the Fresnel domain. Currently, the BDF is only defined for continuous signals. However, for both simulation and experimental purposes, the signals must be discrete. This necessitates the development of a BDF analysis workflow for discrete signals. In this paper, we will analyse the sampling requirements imposed by the BDF, and demonstrate their correctness by comparing the continuous BDFs of continuous test signals with their numerically approximated counterparts. Our results will permit more accurate simulations using BDFs, which will be useful in applying them to problems in, e.g., partial coherence.

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Yushi Zheng, Min Wan, and John J. Healy "Numerical approximation of the Bai distribution function", Proc. SPIE 12998, Optics, Photonics, and Digital Technologies for Imaging Applications VIII, 129981I (18 June 2024); https://doi.org/10.1117/12.3022148

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KEYWORDS

Wigner distribution functions

Autocorrelation

Fourier transforms

Transform theory

Partial coherence

Wave propagation

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