Improved angle measurement model for folded optical paths in multi-degree-of-freedom measurement systems

Multi-degree-of-freedom (MDOF) measurement systems are crucial in the domain of precision manufacturing, where miniaturization represents a significant developmental trend. Folded optical paths are commonly employed in the angle measurement modules of these systems as a means to reduce equipment size. However, these paths introduce angle coupling, which renders traditional angle measurement models inadequate. In this study, angle coupling in the folded optical path and its influence on the angle measurement are investigated in detail, based on which an improved measurement model free of angle coupling is proposed. The effectiveness of the model is verified by simulations and experiments, and the results show a high consistency, moreover, the experimental findings indicate that, by adopting the model, the measurement error of yaw and pitch is reduced by an order of magnitude.