空间插值在功率谱密度计算中的应用

为了提高光学元件波前中频PSD计算的精度和有效频谱宽度，提出了填补波前无效数据的双线性插值法和抑制欠采样噪声的六采样点插值法。模拟计算和实验结果表明：双线性插值法有效地保证了填充数据与真实数据的一致性,抑制了零填充方法引入的虚假中高频信息,使得填补后的PSD与原始PSD较好地吻合；六采样点插值法有效地分离了信号和欠采样噪声，使得有效PSD频谱上限从1/2 Nyquist频率提高到Nyquist频率。

Application of spatial interpolation to calculation of power spectrum density

To improve the precision and effective spectrum width of wavefront power spectrum density(PSD) at mid-spatial scale, double linear interpolation and six-sample-wide interpolation are proposed to patch invalid points and reduce aliasing noise, respectively. Double linear interpolation reduces discrete discontinuities and retains spectral structure of the valid areas, without adding visible middle and high spatial frequency errors existing in zero-filled method. Six-sample-wide interpolation effectively separates the signal from the aliasing noise and thus increases the effective spectrum upper limit of PSD from half of Nyquist frequency to Nyquist frequency. The validity of double linear interpolation and six-sample-wide interpolation is verified by computer simulation and experiment.