Aiming at the measurement of roll deformation between two devices, we propose a novel scheme and elaborate the structure design in this paper. The scheme can realize the relative measurement of roll angle even if the system does not provide a reference datum, which effectively solves the problems of limited measurement range of moiré fringes and accuracy guarantee only in an extremely small angle range. First, the principle of measuring the roll angle by moiré fringes is introduced, and the effects of various error sources in the system are comprehensively considered. Then, the combined measurement scheme and the entire system composition structure are analyzed in detail. In addition, an experimental setup is designed to verify the accuracy of roll deformation measurement. The measurement results show that the root mean square (RMS) error can reach 6.9" within 3°, and is less than 7.8" in the range of 0°–90°. Hence, our proposed scheme has a good measurement stability in a large roll range.

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.

In the application of using binocular camera to measure the horizontal alignment deviation, due to the limited field of view of the camera, it is difficult for each camera to obtain all the target points to determine the position of the parts. To this end, a binocular position measurement model, where each optical camera corresponds to one cooperative target point, is established to determine the horizontal alignment deviation between the upper and lower parts. To overcome the problem of insufficient information in calculating the horizontal alignment deviation, the measurement data of a biaxial inclinometer and laser rangefinder are added. The Monte Carlo method is used to determine the error level for any position and attitude in the measurement range based on past work experience. The high accuracy of the position measurement method (the overall error does not exceed 2 mm) for a binocular camera without a common target meets the actual application requirements. This conclusion is verified by the experimental results.

Aiming at the torsional deformation scheme of Moiré fringe measurement, the influence of double- grating on the measurement accuracy of torsion angle in the optical system with focal length error was analyzed. Based on the traditional Moiré fringe measurement torsion angle theory formula, the scaling effect of focal length on the grating image was introduced, and the torsion angle measurement model with focal length factor was derived. According to the derived model, as the focal length difference of the optical system increases, the corresponding torsion angle also changes greatly. Especially the change at small angles (1°～3°) is particularly obvious, which ultimately affectes the measurement accuracy of the torsional deformation. In the designed experiment, the theory proposed was verified by using two optical systems with known focal lengths to analyze the torsion angle accuracy by collecting the Moiré fringe image.