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.
Keywords: double grating; focal length measurement; mathematical model; moiré fringe; self-collimating optical system.