激光外差干涉快速超精密测量模型研究

为了精确地描述激光外差干涉在快速超精密测量中的位移测量．建立了激光外差干涉快速超精密测量模型。传统外差干涉测量模型采用舍去高阶误差的方法，便于分析与快速计算，但存快速纳米精度测量中，高阶误差已经影响到测量精度．根据多普勒频移公式，通过分析激光外差干涉的测量原理．在已有的激光干涉测量模型上增加了u^2/c的积分项．相当于将传统测量模型进行了高阶误差补偿。通过理论分析可知，当最高测量速度为1m/s，运行位移为3m时，该测量模型能够减小约18nm的测量误差，解决了传统测量模型存存的残余误差累计问题，从而为激光外差干涉在快速超精密测量领域的应用提供了一种理论依据。

Study on Fast Ultra-Precision Measurement Model in Laser Heterodyne Interferometry

In order to describe accurately laser heterodyne interferometer measurement in fast ultra-precision, a new model is proposed. The laser heterodyne interferometer measurement theory is analyzed, and laser interferometer fast ultra-precision model based on the Doppler frequency shift model is deduced. In the model, the integral of v2/c is added, the part is ignored in laser heterodyne interferometer conventional model. With this model, when the highest measurement speed is up to 1 m/s and the displacement is up to 3 m, about 18 nm of measurement error is reduced, and the residual error is removed, the fast ultra-precision measurement is realized.