Error motions of a linear stage directly influence the performance of the precision positioning system in which the stage is used. Therefore, it is a critical task to measure the error motions. A measurement method for the determination of three-degree-of-freedom (3-DOF) error motions based on non-diffracting Moiré fringes is proposed.

A semi-transparent mirror (STM), a beam splitter and a mirror are adopted as the measurement head, which is fixed on the moving stage in order to sense 3-DOF angular errors. Two CCDs are used to capture the non-diffracting beams patterns that are carrying the errors. Computer generated holograms (CGHs) are loaded into a liquid crystal spatial light modulator (SLM) to produce non-diffracting beams. A beam splitter prism (BS1), placed after the SLM, splits the non-diffracting beam into two beams, the transmitted beam and the reflection beam. The reflected non-diffracting beam, after reflection by mirror 2, traveling through BS3, is reflected by the STM, and reaches CCD1. The image of the non-diffracting beams is captured by CCD1. The other beam transmits from BS3 to CCD2 after travelling through STM and BS2. The transmitted non-diffracting beam exiting BS1 passes through an attenuator, and then is reflected by mirror 1, from where it meets the beam from the moving unit. These two non-diffracting beams generate non-diffracting Moiré fringes, which are captured by CCD2.

When the stage moves, the position of the central points of the non-diffracting beams (as received by CCD 1) and the forms of Moiré fringes (obtained by CCD 2) will change in relation to different errors. It can measure the 3-DOF errors, which are yaw, pitch, and roll. By analyzing the geometric position of these center points, mathematical models for 3-DOF motion errors are established. Obviously, one of central points in CCD2 will be unchanged while the other one will changes according to different motion errors of stage.

A rotary table is used to simulate the 3-DOF motion errors and demonstrate the theoretical analysis. The measurement head is fixed on the table, which rotates different small angles (0°, 0.125°, 0.25°, 0.375°, 0.5°). The on-diffracting beam and non-diffracting Moiré fringe patterns are obtained by CCD1 and CCD2, respectively. The actual angular displacement is calculated by the offset of the center of the spot with the mathematical models. Compared with the theoretical value, the angular displacement error is less than 0.0104°, which verifies the feasibility and correctness of the 3-DOF measurement system for non-diffracting Moiré fringes.