Analysis of focal length error in torsion angle measurement system

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.