基于分数傅里叶域信号处理的迈克尔逊干涉法测量波长

Wavelength Measurement by Michelson Interferometry Based on Fractional Fourier Transform Signal Processing

建立了迈克尔逊干涉法测量波长所得条纹图的数学模型,揭示了其线性调频信号(chirp信号)特性,提出了基于分数傅里叶变换信号处理方法对迈克尔逊干涉条纹进行处理,实现了激光波长测量。实验结果表明:该测量方法具有可行性,对于波长范围为400~635 nm的激光,波长测量的平均相对误差约为0.39%。在干涉条纹图被高斯白噪声污损情况下,波长测量的平均相对误差仍然小于1%。

The mathematical model of the fringe pattern obtained by Michelson interferometric measurement of wavelength is established,its linear frequency modulation signal(chirp signal)characteristics are revealed,and Michelson'ss interferometric fringe processing based on the fractional Fourier transform signal processing method is proposed to realize the laser wavelength measurement.The experimental results show that the proposed wavelength measurement method is feasible.The average relative error of wavelength measurement is about 0.39%for lasers in the wavelength range of 400 nm to 635 nm.The average relative error in wavelength measurement is still less than 1%when the interferogram is contaminated by Gaussian white noise.