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 1.310-12 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 /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 wavelength uncertainty, the air refractive index uncertainty, the phase measurement uncertainty and the nonlinearity error are 3 pm, 300 pm, 6.3 pm and 118 pm, respectively. Finally, the performance evaluation shows that the combined uncertainty of the interferometer reaches 322 pm in a span of 100 mm, which is mainly due to the refractive index of air. The heterodyne interferometer meets the requirements for traceable trans-scale measurement with a sub-nanometer resolution, which can be widely used in instrument calibration, length standard making, and geometric measurement.

In this paper, a quasi-common-path method to improve the stability of laser measurement instruments is proposed. The method releases the strictness of the common-path structure and enables the compensation of errors caused by air turbulence. A wavefront measurement system is set up to simultaneously detect both the wavefronts of the quasi-common-path beams, of which the orthogonal distance varies from 0 to 4 times the beam diameter. The correlation coefficient between two wavefronts remains around 0.9 in turbulence, which verifies the feasibility. Based on the method, a three-axis interferometer whose measuring optical paths orthogonally split 30 mm is established, and the stability of the optical paths is evaluated. The standard deviations of the displacement and the displacement difference at the original point are about 0.31 μm and 0.006 μm, respectively, while these performance properties at 1 m are 1.14 μm and 0.02 μm, respectively. The experimental results show that quasi-common-path beams allow for stability improvement, which can also be widely used in the field of precision machine manufacturing.