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Double Wigner distribution function of a first-order optical system with a hard-edge aperture
1Department of Physics, Zhejiang University of Science and Technology, Hangzhou 310023, China. welcome.pan@163.com
Applied Optics
|December 25, 2007
Summary
This study analyzes how apertured optical systems affect Wigner distribution. Researchers derived double Wigner distribution functions for systems with hard apertures, offering accurate analytical results for Gaussian beam spatial filtering.
Area of Science:
- Optics and Photonics
- Quantum Optics
- Mathematical Physics
Background:
- The Wigner distribution function (WDF) is crucial for analyzing optical systems, especially those with apertures.
- Understanding the impact of apertures on WDF is essential for advanced optical designs and signal processing.
Purpose of the Study:
- To develop a method for expressing the effect of apertured optical systems on the Wigner distribution.
- To derive the double Wigner distribution functions for optical systems with hard apertures.
- To obtain analytical expressions for the Wigner distribution of a Gaussian beam through a spatial filtering system.
Main Methods:
- Representing the hard aperture function as a finite sum of complex Gaussian functions.
- Utilizing superposition integrals to describe the transformation of the Wigner distribution.
- Deriving analytical expressions for double Wigner distribution functions.
Main Results:
- The effect of an apertured optical system on WDF is shown to be a superposition integral.
- Analytical expressions for double Wigner distribution functions of first-order optical systems with internal and external hard apertures were derived.
- Accurate analytical expressions for the Wigner distribution of a Gaussian beam passing through a spatial filtering system with an internal hard aperture were obtained.
Conclusions:
- The derived analytical method accurately represents the Wigner distribution transformations in apertured optical systems.
- The analytical results demonstrate superiority and accuracy when compared to numerical integration methods.
- This work provides a valuable tool for the analysis and design of optical systems involving apertures and Gaussian beams.
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