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J Opt Soc Am A Opt Image Sci Vis. 2006 Jun;23(6):1410-8.

Propagation of hollow Gaussian beams through apertured paraxial optical systems.

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Joint Research Center of Photonics of the Royal Institute of Technology and Zhejiang University, Zhejiang University, Hangzhou, China.


On the basis of the generalized Collins formula and the expansion of the hard-aperture function into a finite sum of complex Gaussian functions, an approximate analytical formula for a hollow Gaussian beam propagating through an apertured paraxial stigmatic (ST) ABCD optical system is derived. Some numerical examples are given. Furthermore, by using a tensor method, we derive approximate analytical formulas for a hollow elliptical Gaussian beam propagating through an apertured paraxial general astigmatic ABCD optical system and an apertured paraxial misaligned ST ABCD optical system. Our results provide a convenient way for studying the propagation and transformation of a hollow Gaussian beam and a hollow elliptical Gaussian beam through an apertured general optical system.

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