外差式激光干涉仪光学读出的两种新算法的设计与实现

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。

Design and implementation of two new fitting algorithms for optical readouts of a heterodyne interferometer

Nanometer and picometer laser metrology is an important part of optical technology. It is also required in the space gravitational wave detection experiments. Deep modulation has been developed and demonstrated for this purpose in experiments of increasing complexity in Hannover,it also served as a fallback option for LISA,Levenberg-Marquardt nonlinear fitting algorithm has been used for data reduction. Two new improved fitting algorithms are presented and explored for Hannover deep internal phase modulation interferometers. The first one employs appropriate and simple functional relationship to fit the demodulated phase in two stages:firstly,it determines the modulation depth and the modulation phase; secondly,it fits the demodulated phase together with the amplitudes. The other one,which applies a Discrete Fourier Transform at first,determines modulation phase at the first stage,then uses a Gauss-Newton Method to fit the modulation depth,the demodulation phase and the amplitudes linearly. Using the first method,the RMS residuals for measurement in the air are demonstrated to be 0.24 nm,and the second method 0.19 nm,about 5 to 6 times better than the old one.