为了研究受硬边光阑约束及失调Lohmann光学系统对分数傅里叶变换的影响，采用了平顶多高斯光束模型模拟硬边光阑，推导了平面光波在受硬边光阑约束和系统透镜离轴时的Lohmann型分数傅里叶变换光学系统中传播的解析表达式；计算机模拟了受半径为7．696cm的硬边光阑约束和透镜离轴失调量时的输出。结果表明，在有硬边光阑约束和离轴失调时Lohmann两种结构并不等效。

To study the influence of hard-edge apertured and misaligned Lohmann's optical system on fractional Fourier transforms,the flat-topped multi-Gaussian beam model was adopted to simulate hard-edge apertures. The analytical expressions for transformation of plane wave in a hard-edge apertured and off-axis Lohmann's fractional Fourier transform optical system were derived. The numerical simulation for outputs when the system was apertured with aperture radius of 7.696cm and the lenses were off-axis was also given. It is shown that the two Lohmann's setups are not equivalent when they are apertured and misaligned.