加窗加权插值离散傅里叶变换在波长扫描干涉仪中的应用

Application of windowed weighted interpolation discrete Fourier transform in wavelength scanning interferometer

针对现有的波长扫描干涉仪在采样范围内信号周期数较少时含有比较严重的信号频谱泄漏,导致较大的恢复误差的问题,提出一种基于加窗加权插值离散傅里叶变换(DFT)的频率估计的光程差恢复算法,该算法在信号采样长度为2~3个周期时仍能很好地抑制频谱泄漏.仿真结果显示:当周期数较少时,该算法恢复精度相比于现有的傅里叶变换相位斜率法有很大提高.对平面镜及单刻线标准样板的测量实验显示:加窗加权插值离散傅里叶变换算法达到约10 nm的恢复精度,进一步验证了该算法在波长扫描干涉仪的光程差恢复中有很好的应用价值.

Existing wavelength scanning interferometers suffer serious signal spectral leakage when the number of signal periods in the sampling range is small,which leads to a larger recovery error.To address the above problem,an optical range difference recovery algorithm was proposed based on frequency estimation with windowed weighted interpolation discrete Fourier transform(DFT),which can still suppress the spectral leakage well when the signal sampling length is 2 to 3 cycles.Simulation results show that the recovery accuracy of this algorithm is greatly improved compared with the existing Fourier transform phase slope method when the number of cycles is small.The measurement experiments on the plane mirror and the single inscribed standard sample show that the windowed weighted interpolation DFT algorithm can achieve a recovery accuracy of about 10 nm,which further verifies the value of the algorithm in the optical range difference recovery of wavelength scanning interferometer.