Roughness dependence of the measurement accuracy for precision optical encoders

The degradation of measurement accuracy caused by the edge blurriness of the optical imaging due to the grating roughness poses a significant challenge in the development of precision optical encoders. In this study, a mathematical model based on Fresnel diffraction is established to address the roughness dependence of the optical spatial resolution after grating reflection, which reveals the limit on measurement accuracy of optical encoders. The edge blurriness of the optical imaging after grating reflection is quantified by the edge spread function, and the blurred edge induced by the grating roughness is further obtained, which bridges the final measurement accuracy by optical encoders and the grating profiles (determined by the manufacturing process). The accuracy of the roughness mathematical model was experimentally validated by comparing the width of the blurred interval, with the discrepancy between the experimental and calculated values remaining below 0.014 µm. Compared with previous methods, a unified model was established that incorporates multiple roughness and provides a standard framework for evaluating grating measurement accuracy. Additionally, accuracy compensation was performed based on the mathematical model, resulting in a reduction of the period subdivision error to 11.23 % of its original value. The model provides a promising method to improve the measurement accuracy by compensating for the optical error induced by the grating roughness.