摘要：分数傅里叶变换作为一种新的研究工具在光学领域迅速得到应用。1993年9月，H.M.Ozaktas和D.Mendlovic首次利用平方率负梯度折射率(GRIN)介质在光学上实现了分数傅里叶变换，并利用分数傅里叶变换进行分数傅里叶变换域滤波。随后人们阐释了分数傅里叶变换的物理意义，并基于给出了实现分数傅里叶变换的物理结构。至此，分数傅里叶变换开始引起光学界的广泛关注，尤其在光学信息领域受到充分的重视。目前，分数傅里叶光学己经发展成为现代光学的一个重要分支。

　　　本文先对复高斯方程的展开方式，分数傅里叶变换的发展和内容以及菲涅尔衍射做了阐述，然后应用这些理论得到贝塞尔-高斯光束通过带双光阑限制的分数傅里叶变换的光学系统在柱坐标系中的一个近似解析式，从而进一步对贝塞尔-高斯光束通过带双光阑限制的分数傅里叶变换光学系统的特性以及影响因素进行研究。

关键词：分数傅里叶变换 贝塞尔-高斯光束 硬边光阑  传输特性

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