基于广义惠更斯-菲涅耳衍射积分公式, 以LohmannⅠ型光学系统为例, 推导出Bessel光束通过含光阑的球差分数傅里叶变换系统后的场分布表达式, 通过数值模拟计算了Bessel光束在理想分数傅里叶变换系统中的传输特性以及光阑和球差对光束传输的影响规律。研究表明: Bessel光束通过分数傅里叶变换系统后不再保持其传输不变性; 系统只含光阑时, 可在常规傅里叶变换面上获得空心光束; 系统同时存在光阑和球差时, 正球差下输出面可获得聚焦性更好、中心光强更强的光束; 光阑较小时, 轴上光强分布主要受光阑影响, 光阑达到一定数值后, 轴上光强分布主要受球差影响。

Based on the generalized Huygens-Fresnel diffraction integral formula, field distribution expressions of Bessel beams passing through a spherical aberration fractional Fourier transform system with an aperture are derived when we take Lohmann Ⅰ type optical system as an example. Propagation characteristics of Bessel beams in ideal fractional Fourier transform system and the influence rule of aperture and spherical aberration on beam propagation are calculated by numerical simulation. The results show that Bessel beams do not maintain propagation invariability after passing through a fractional Fourier transform system. When the system only contains an aperture, a hollow beam can be obtained at the conventional Fourier transform plane. When the system contains aperture and spherical aberration, beams with good focusing property and high central light intensity can be obtained with positive spherical aberration. Light intensity distribution on the axis is mainly affected by the aperture when the aperture size is small, and it is influenced by spherical aberration when the aperture size exceeds a critical value.