Dr. Min Wan Profile

Dr. Min Wan

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Proceedings Article | 18 June 2024 Poster + Paper

Numerical approximation of the Bai distribution function

Yushi Zheng, Min Wan, John Healy

Proceedings Volume 12998, 129981I (2024) https://doi.org/10.1117/12.3022148

KEYWORDS: Autocorrelation, Fourier transforms, Transform theory, Wave propagation, Partial coherence, Wigner distribution functions

Read 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.

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