基于平面对称光学系统的波像差理论，给出了鱼眼镜头各类像差的波像差计算表达式，利用自相关积分法计算了它的调制传递函数，采用8节点的高斯-勒让德数值积分方法求解了其自相关积分；分析了鱼眼镜头倍率色差对确定空间频率光栅的相位改变量，给出了C(656.3 nm)、D(589.3 nm)、F(486.1 nm)离散光谱的倍率色差的调制传递函数计算表达式.利用本文方法和Zemax快速傅里叶变换法分别计算两个鱼眼镜头系统的调制传递函数,并进行了对比.结果表明，对于中小孔径的鱼眼镜头成像系统，本文方法和仿真得到的结果较好地吻合.

Based on the aberration theory of plane symmetric optical systems, the expressions of each type of wave aberration of fisheye lens were formulated. The autocorrelation integral was used to calculate the modulation transfer function of the fisheye lens. The 8-node Gauss-Legendre integral was applied to solve the complicated integral. On the other hand, the phase change value of a grating of certain spatial frequency resulted from the lateral color aberration was analyzed, the expression of the modulation transfer function of the lateral color aberration with discrete spectral of C(656.3 nm), D(589.3 nm), F(486.1 nm) light was derived. Finally, the proposed method was used to calculate the modulation transfer function curves of two fisheye lens systems; and the results were compared with those obtained by Zemax program. The study results show that the proposed method is valid for calculation of a fisheye lens with a moderate/small pupil.