A compact laser collimation system is presented for the simultaneous measurement of five-degree-of-freedom motion errors. The optical configuration of the proposed system is designed, and the principle of the measurement of five-degree-of-freedom errors is described in detail. The resolution of the roll and the horizontal straightness is doubled compared with other laser collimation methods. A common optical path compensation method is provided to detect light drift in real time and compensate for straightness and angle errors. An experimental setup is constructed, and a series of experiments are performed to verify the feasibility and stability of the system. Compared with commercial instruments, the pitch and yaw residuals are ${\pm 2.5}^{″}$ and ${\pm 3.5}^{″}$ without correction, and the residuals are ${\pm 1.9}^{″}$ and ${\pm 2.8}^{″}$ after correction, respectively. The comparison deviations of the horizontal straightness and vertical straightness changed from $\pm 4.8 \mathsf{\mu }$ m to $\pm 2.8$ μm and $\pm 5.9$ μm to $\pm 3.6$ μm, respectively. The comparison deviation of the roll is ${\pm 4.3}^{″}$ . The experimental results show that the data of the five-degree-of-freedom measurement system obtained are largely the same as the measurement data of commercial instruments. The common optical path compensation can effectively improve the measurement accuracy of the system.

In this paper, we propose a scheme for measuring the focal length of a collimating optical instrument. First, a mathematical model for measuring the focal length of a collimator with double gratings is derived based on the moiré fringe formula and the principles of geometric optics. Mathematical simulation shows that a slight difference in the focal length of two collimators has an important influence on the imaging law of moiré fringes. Our solution has a good resolution ability for focal length differences within 5‰, especially in the small angle range below 4°. Thus, the focal length of collimators can be measured by the amplification of the slight difference. Further, owing to the relative reference measurement, the measurement resolution at the symmetrical position of focal length is poor. Then, in the designed experiment, a corresponding moiré image at different angles is acquired using collimators with known focal length. The experimental results indicate that the root mean square error (RMSE) of the collimator corresponding to grating angles of 2°–4° is better than 4.7‰, indicating an ideal measurement accuracy of the proposed scheme. This work demonstrates that our proposed scheme can achieve an ideal accuracy in the measurement of a symmetrical optical path.