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纳米级和皮米级激光测距是光学技术中的重要一环,同时也是深空引力波探测实验所必须的技术。德国汉诺威的爱因斯坦研究所为此提出并实现了一种基于相位深度调制技术的外差式激光干涉仪,作为LISA计划测距系统的后备方案,在数值处理过程中使用了Levenberg-Marquardt非线性拟合方法作为干涉仪光学读出算法。探讨并展示了另外两种新的外差干涉仪光学读出拟合算法。第一种算法采用近似并迭代的数值方法将拟合过程分为两次迭代:第一次估算干涉仪的调制深度和调制相位,第二次线性迭代拟合干涉仪的相位和振幅。另外一种算法首先利用离散傅里叶变换计算频谱,然后从频谱中拟合出干涉仪的调制相位,之后采用高斯-牛顿迭代方法线性拟合调制深度、相位和振幅。在空气中长时间运行的结果显示,第一种拟合算法的连续测距误差小于0.24nm,第二种算法的误差在0.19nm左右,比原来的非线性拟合算法分析得到的误差小了5～6倍。
Nanometer and picometer laser ranging is an important part of optical technology, but also the necessary technology for the deep space gravity wave detection experiment. For this reason, the Einstein Institute in Hannover, Germany, proposed and implemented a heterodyne laser interferometer based on the phase-depth modulation technique. As a backup scheme of the LISA planned ranging system, Levenberg-Marquardt Linear fitting method as interferometer optical readout algorithm. Two new algorithms of optical readout fitting for heterodyne interferometer are discussed and demonstrated. The first algorithm uses an approximate and iterative numerical method to divide the fitting process into two iterations: the first one to estimate the modulation depth and the modulation phase of the interferometer, and the second one to fit the phase and amplitude of the interferometer. The other algorithm first uses the discrete Fourier transform to calculate the spectrum and then fits the interferometer’s modulation phase from the spectrum, then uses Gaussian-Newton iterative methods to linearly modulate the depth, phase and amplitude. The results of long run in air show that the first type of fitting algorithm has a continuous ranging error of less than 0.24 nm, the second one has an error of about 0.19 nm, which is smaller than the original non-linear fitting algorithm 5 to 6 times.