Optical fibers have been widely used in various industries, national defense, and information technology due to their flexibility, low transmission loss, small size, and light weight. To avoid phase changes in optical fibers caused by environmental vibrations and temperature drift, a combination of fibers and free space optics is often used to construct a circulator device in typical applications, such as Doppler wind lidar and laser Doppler vibrometer systems. Alignment error is the main source of decreased coupling efficiency between fibers and free space optics. Many theoretical studies have examined the impact of mismatch factors on coupling efficiency, such as tilt and misalignment of fibers on coupling efficiency. However, few methods exist for detecting the relative spatial position information of optical fiber such as tilt and dislocation. Conventional detection methods, including the energy monitoring method and far-field coincidence monitoring method, cannot quantitatively analyze fiber mismatch factors. The coupling efficiency is related to the wavefront correlation coefficient between the two fibers, which is determined by their relative position. Monitoring the correlation between the two fiber wavefronts can guide assembly and quantitatively evaluate the coupling efficiency of this type of circulator. The phase detection technology based on Hertz-level frequency-shifting heterodyne interferometry can theoretically determine the wavefront correlation coefficient of the two fibers, which is related to the PV (Peak to valley) value of the interference wavefront.

Based on the theory of Hertz-level frequency-shifting heterodyne interferometry, the sources affecting the demodulated value of the interferometric phase are analyzed. The acousto-optic modulator (AOM) frequency is further segmented into fixed and random frequency for analysis. The parameters related to the detector including fixed frame frequency deviation and shot noise are analyzed.

A linear relationship is found between transverse displacement and PV value, with a slope of 0.139λ μm^-1. The change in PV value, δ_PV<0.002λ, caused by the fixed deviation of AOM frequency, within the range of ±0.2 Hz from the nominal value, is two orders of magnitude smaller than the PV value caused by the relative spatial position of the optical fiber. Similarly, when the fixed deviation of frame rate is within the range of ±1 Hz, the PV change is also two orders of magnitude smaller. The impact of shot noise on PV variation is generally less than 10^-3λ, mainly influenced by factors such as the quantum efficiency, pixel size, and bandwidth of the detector. Based on the simulation results, the selection of experimental devices is carried out. Lumentum 1103P He-Ne laser tube is used for the laser. The low-frequency heterodyne drive circuit with a 5 Hz frequency offset is self-developed. The frequency offset measurement data of the drive circuit shows a frequency range of (5±0.1) Hz. The visible camera SUA230 of Hua-Teng Vision is selected for the detector, with an image area size of 7 mm×7 mm and a pixel size of 5.86 μm. The parameter α related to the shot noise is calculated to be 3.3 calculated based on quantum efficiency and other parameters. In an experiment with 50 consecutive measurements, the mean PV value is 0.2167λ with a standard deviation of 0.0059λ.

The influence of frequency deviation of the acousto-optic frequency shifter, the frame frequency deviation of the detector, and shot noise on the measurement accuracy of the heterodyne wavefront detection system are studied, and the influence formula is derived. The effects of the fixed frequency deviation of the acousto-optic frequency shifter, random frequency deviation of the acousto-optic frequency shifter, fixed frame rate deviation of the detector, and detector shot noise on measurement accuracy are simulated and analyzed. When the wavefront PV caused by transverse displacement is within one wavelength, the PV value change due to fixed and random frequency deviations of the acousto-optic frequency shifter is within ±0.2 Hz. When the fixed frame rate deviation of the detector is within the range of ±1 Hz, the PV value change caused by it is also in the order of 10^-3λ. The impact of shot noise on the wavefront is mainly related to the working bandwidth, quantum efficiency, and pixel size of the detector, and the PV value change caused by it is generally not more than 10^-3λ. According to the analysis results, the heterodyne wavefront detection device is built, and the measurement resolution is better than 0.01λ, which verifies the relevant theory. The detection device can accurately characterize the correlation between the two wavefronts, providing a technical means for the quantitative characterization of this type of circulator, and effectively improve the performance of LIDAR and laser Doppler vibrometers using this type of circulator.