摘要：分數(shù)傅里葉變換作為一種新的研究工具在光學領域迅速得到應用。1993年9月，H.M.Ozaktas和D.Mendlovic首次利用平方率負梯度折射率(GRIN)介質(zhì)在光學上實現(xiàn)了分數(shù)傅里葉變換，并利用分數(shù)傅里葉變換進行分數(shù)傅里葉變換域濾波。隨后人們闡釋了分數(shù)傅里葉變換的物理意義，并基于給出了實現(xiàn)分數(shù)傅里葉變換的物理結構。至此，分數(shù)傅里葉變換開始引起光學界的廣泛關注，尤其在光學信息領域受到充分的重視。目前，分數(shù)傅里葉光學己經(jīng)發(fā)展成為現(xiàn)代光學的一個重要分支。

　　　本文先對復高斯方程的展開方式，分數(shù)傅里葉變換的發(fā)展和內(nèi)容以及菲涅爾衍射做了闡述，然后應用這些理論得到貝塞爾-高斯光束通過帶雙光闌限制的分數(shù)傅里葉變換的光學系統(tǒng)在柱坐標系中的一個近似解析式，從而進一步對貝塞爾-高斯光束通過帶雙光闌限制的分數(shù)傅里葉變換光學系統(tǒng)的特性以及影響因素進行研究。

關鍵詞：分數(shù)傅里葉變換 貝塞爾-高斯光束 硬邊光闌  傳輸特性

Abstract:Fractional Fourier transform as a new tool for research in the field of optics has been applied rapidly. In September 1993, H.M.Ozaktas and D.Mendlovic use square rate negative gradient refractive index (GRIN) medium realized fractional Fourier transform in optical for the first time, and by the fractional Fourier transform they realized fractional Fourier transform domain filter. Then the physical meaning of fractional Fourier transform was explained, and based on which the physical structure of the fractional Fourier transform was obtained. So far, wide attention was paid to the fractional Fourier transform in optical industry, especially in the field of optical information. At present, fractional Fourier optics has been developed into an important branch of modern optics.

This paper discusses the development and content of the complex Gauss equation, the fractional Fourier transform and the Fresnel diffraction theory at first. And then with those theories, an approximate analytic formula in cylindrical coordinates of the propagation property of Bessel-Gauss beam through fractional Fourier transform system with two circular apertures is obtained. So, further factors on the propagation property of Bessel-Gauss beam through fractional Fourier transform system with two circular apertures could be studied. 

Key words: fractional Fourier transforms   Bessel-Gauss beam   hard-edge aperture   Propagation properties