中文摘要：

提出了一种能够实现跨尺度测量具有亚纳米分辨力的可溯源外差干涉仪,利用小型化碘稳频532 nm激光器,将激光频率溯源至国际计量委员会推荐的复现米定义谱线之一的R（56）32-O（a10）上;使用双频激光空间分离的设计方法,抑制了双频激光混叠引起的测量位移非线性误差,补偿了光纤与声光调制器引入的相位噪声;通过高精度的相位测量技术,使相位测量分辨率达到了0.017°.干涉仪的不确定度评估结果显示,100 mm的量程内,其不确定度达322 pm,实现了跨尺度亚纳米分辨力可溯源的位移测量.

英文摘要：

In order to realize the traceable trans-scale displacement measurements with high resolutions in the fields of fundamental scientific research and ultra-precision machining,we demonstrate a trans-scale heterodyne interferometer with a sub-nanometer resolution,through assembling a compact iodine-stabilized laser at 532 nm.Using modulation transfer spectroscopy,the green laser is traced back to the transition line R（56）32-O（a10）,which is one of the recommended spectral lines for ‘meter＇ redefinition.The Allan standard deviation of the laser frequency is 1.3 × 10^-12 within an average time of 1 s.Compared with most He-Ne lasers,the green laser has a short wavelength and good stability,which leads to a higher resolution.We use two acoustic-optic modulators driven by a two-channel acoustic-optic driver sharing the same crystal oscillator to separate input beams spatially.The frequency of one beam is shifted by 80 MHz and the other is shifted by 82 MHz,which results in a beat frequency of 2 MHz.As a result,the nonlinearity caused by source mixing substantially is reduced.The phase noises of the fibers and two acoustic-optic modulators are well compensated.In order to minimize the difficulty in adjusting the optical path and the error of the measurement,we integrate the interferometry components and design a monolithic prism.The optical resolution of the interferometer reaches to λ/4.The experiment is carried out in a vacuum environment to reduce the influence of the refractive index of air.High-precision phase measurement technology is used to improve the accuracy of the interferometer.The errors of the interferometer can be classified as random and systematic errors.Random errors include the error from the frequency instability of the laser and the error due to environmental effects.Systematic errors include the phase measurement error and the nonlinearity error.To verify the performance of the interferometer,these errors must be evaluated.In a span of 100 mm,the measurement uncertainties caused by laser