A Compact and High-Precision Three-Degree-of-Freedom Grating Encoder Based on a Quadrangular Frustum Pyramid Prism

A compact and high-precision three-degrees-of-freedom (DOF; X, Y, and Z directions) grating encoder based on the quadrangular frustum pyramid (QFP) prisms is proposed in this paper to solve the insufficient installation space problem of the reading head of the multi-DOF in high-precision displacement measurement applications. The encoder is based on the grating diffraction and interference principle, and a three-DOF measurement platform is built through the self-collimation function of the miniaturized QFP prism. The overall size of the reading head is 12.3 × 7.7 × 3 cm³ and has the potential for further miniaturization. The test results show that three-DOF measurements can be realized simultaneously in the range of X-250, Y-200, and Z-100 μm due to the limitations of the measurement grating size. The measurement accuracy of the main displacement is below 500 nm on average; the minimum and maximum errors are 0.0708% and 2.8422%, respectively. This design will help further popularize the research and applications of multi-DOF grating encoders in high-precision measurements.