Representation of the Wigner distribution function for light beams passing through apertured optical systems

By introducing a method that a hard-edged aperture function can be expanded into an approximate sum of complex Gaussian functions with finite numbers, the analytical expression of Wigner distribution function for a Gaussian beam passing through a cylindrical symmetric and paraxial ABCD optical system with a hard-edged aperture is obtained. Numerical calculations show that the effect of an aperture on the Wigner distribution function is prominent. The analytical results are also compared with the integral calculation results and they show that this method of expanding a hard aperture into Gaussian functions with finite numbers is proper and ascendant. This method could also be extended to studying the Wigner distribution functions of other light beams passing through a paraxial ABCD optical system with a hard-edged aperture.

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