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This paper presents a novel method for measuring two-degree-of-freedom (DOF) motion of flexure-based nanopositioning systems based on optical knife-edge sensing (OKES) technology, which utilizes the interference of two superimposed waves: a geometrical wave from the primary source of light and a boundary diffraction wave from the secondary source. This technique allows for two-DOF motion measurement of the linear and pitch motions of nanopositioning systems. Two capacitive sensors (CSs) are used for a baseline comparison with the proposed sensor by simultaneously measuring the motions of the nanopositioning system. The experimental results show that the proposed sensor closely agrees with the fundamental linear motion of the CS. However, the two-DOF OKES technology was shown to be approximately three times more sensitive to the pitch motion than the CS. The discrepancy in the two sensor outputs is discussed in terms of measuring principle, linearity, bandwidth, control effectiveness, and resolution.

We analyzed the parameter effects of an optical knife-edge sensor (OKES) and the measurement uncertainty to achieve high linearity, long range, and high accuracy for nanopositioning stage applications. The OKES utilizes interference fringes produced from diffraction across the knife-edge. The total field at the detector was calculated from superposition of the incident field and the diffracted field at the knifeedge, and the edge diffraction effects on the sensor design parameters (distance between the knife-edge and detector, wavelength and beam diameter) were investigated by using a design of experiment (DOE), 3-Level L 9 matrix from the Taguchi Method. Multi-factor experiments were designed to determine the relationship between factors affecting the interferogram and the sensor linearity. It was found that a shorter knife edge-detector distance, shorter wavelength, and larger beam diameter show high signal-tonoise ratio for sensing linearity. The OKES was modeled by using the electromagnetic wave propagation principle, and it was experimentally verified by controlling the positioning of an XY nanopositioning stage by the OKES. The sensor noise level showed X 20.1 nm and Y 19.4 nm, and the fundamental sensing limits of the OKES were estimated to be X 0.19 nm/ and Y 0.23 nm/ for a ±1.0 mm working range. These results indicate that the OKES can be a good alternative to other precision metrology tools because of its large working range, positioning accuracy, resolution, linearity, and bandwidth, as well as its compact size and low cost.