根据实际光学元件的畸变波前建立了畸变波前模型,分析了位相均方根梯度计算过程中,三种波前数据处理方式的各自特点及优劣,并得出最佳处理方式,即对波前边缘增添零采样点、加汉宁窗处理、傅里叶变换、低通滤波、傅里叶逆变换、乘上逆汉宁窗,最后截取原始长度的数据.讨论了畸变波前边缘增添零采样点的个数、波前口径、波前抽样间距与均方根误差之间的相互关系.计算证明,对于口径为300 mm×300 mm、抽样间隔为0.5 mm的随机波前,当取截止频率为33 mm^-1、初始波前两边分别添14个点即波前尺寸扩大7 mm长时,其均方根误差最小,此时该值为 0.008 λ,恢复的波前最理想,计算所得的位相均方根梯度也最合理.

A distorted wavefront model is set up, according to the practical distorted wavefront of the optical components. In the calculation of phase RMS gradient, three different ways to handle the distorted wavefront are introduced.They are handling directly, Hanning window handling and the best one is the Hanning window handling, Fourier transformation, low-filter, inverse Fourier transformation, inverse Hanning window are accomplished in order after adding the zero-sampling points to the original distorted wavefront edges, finally a modelled distorted wavefront is cut off with the same size as the original one on the distorted wavefront gotten. RMS error of phase gradient of the wavefront can be the least. The correlations between the number of adding zero-sampling points,the size of wavefront and the sampling space of wavefont and the RMS error are discussed.The caculated phase RMS gradient is 0.046 λ·mm^-1 and that of experiment is 0.048 λ·cm^-1.