Three-dimensional (3D) laser Doppler micro-vibration measurement technology is widely applied in the research on dynamic characteristics of microstructures. Its two off-axis optical paths are employed to receive signal light containing in-plane vibration information. The optical fiber coupling efficiency in optical paths will directly affect the vibration measurement accuracy of the system. At present, the factors affecting the coupling efficiency of optical fiber mainly include optical system aberration, atmospheric turbulence, amplitude distribution type of signal light and local light, and optical system parameters. The effect of gravity, temperature, or mechanical deformation of optical elements during installation on the coupling efficiency is not considered. In addition, most of the current research focuses on one-dimensional laser Doppler detection system, and there is a lack of research on 3D laser Doppler micro-vibration measurement system, especially the off-axis optical path. To this end, based on the diffraction propagation theory and the fiber coupling principle, the optical transmission and coupling model of the off-axis signal receiving optical path in the 3D micro-vibration measurement system is built in this paper. The mechanical deformation of typical optical components in the system is analyzed, and the influence of these mechanical deformations on the fiber coupling efficiency is studied. In addition, the maximum tolerances of different mechanical deformations are given. The research is of guiding significance for the design and installation of 3D laser Doppler micro-vibration measurement system.

The detection optical path of the 3D micro-vibration measurement system includes the main axis optical path and off-axis optical path. The main axis optical path is overlapped with the z axis. Its function is to incident the laser onto the object to be measured and receive the reflected signal light containing the vibration component information of the object in the z direction. The two off-axis optical paths are in the y-z plane and the x-z plane respectively, and the angle between them and the main axis optical path is 40°. They are employed to receive the reflected signal light containing the information of the vibration component of the object in the x and y directions. The object plane is inclined to the off-axis coupling lens plane, so the diffraction propagation between the two inclined planes needs to be considered. In this paper, the optical transmission model of the off-axis signal is built. Firstly, the optical field of the original object plane signal is projected onto the reference plane parallel to the coupling lens plane by the frequency domain coordinate rotation transformation method. Secondly, the optical field distribution of the reference surface is propagated to the coupling lens plane through diffraction, and then to the fiber plane through the phase modulation of the coupling lens. Subsequently, the optical field distribution on the fiber plane can be obtained. Finally, the ideal fiber coupling efficiency can be calculated by the mode field matching method combined with the mode field distribution of single-mode fiber. The relationship between different mechanical deformations and the coupling efficiency of optical fiber is obtained by analyzing the change of parameters in the coupling model of off-axis signal caused by different mechanical deformations.

The relationship between mechanical deformation and fiber coupling efficiency is obtained by the coupling model of off-axis signal optical transmission. Firstly, the relationship between the eccentricity of the coupling lens and the coupling efficiency is studied (Fig. 4). When the coupling efficiency is better than 40%, the maximum allowable range of the offset is about ±1.5 μm. When the beam passes through the tilted coupling lens, the wavefront changes caused by the tilt of the lens near the front and rear surfaces cancel each other out. Therefore, the tilt of the coupling lens exerts no effect on the coupling efficiency if the aberration of the coupling lens is ignored. Next, the influence of the fiber misalignment and the fiber misalignment angle on fiber coupling efficiency is studied. The fiber coupling efficiency is more sensitive to the optical fiber misalignment in the x-y direction [Fig. 6(a)] and less sensitive to the optical fiber misalignment in the z direction [Fig. 6(b)], and the change with the optical fiber misalignment angle is less obvious (Fig. 8). In addition, the out-of-plane vibration caused by the object under test will also affect the fiber coupling efficiency of the off-axis optical path (Fig. 10). When the out-of-plane vibration displacement is within the range of ±3 μm, the coupling efficiency slowly decreases from 76.5% to about 60.0%, which is acceptable in the actual utilization of the system.

A coupling model of optical transmission and transmission of off-axis signals in a 3D laser Doppler micro-vibration measurement system is built. The effect of mechanical deformation on the optical coupling efficiency of off-axis signals in the system is further studied. The simulation results show that the off-axis optical coupling efficiency is sensitive to the coupling lens offset and the optical fiber misalignment. Under the micron displacement error, the off-axis coupling efficiency decreases sharply. Therefore, the two mechanical errors should be avoided first during the system design. The optical coupling efficiency of the off-axis signal is less sensitive to the defocus of fiber and the fiber misalignment angle. When the actual system is adopted, if the out-of-plane vibration range of the object to be measured is ±3 μm, the coupling efficiency of the off-axis signal light slowly decreases from 76.5% to about 60.0%, which has little influence on the system. When the aberration of the coupling lens is ignored, the coupling efficiency is not affected by the coupling lens tilt. This study is of guiding significance for the design of off-axis detection optical path of 3D laser Doppler micro-vibration measurement system. The diffraction propagation calculation and the construction and analysis of the coupling model can be further extended to other single-mode fiber imaging systems.