This study presents an analysis of the cyclic nonlinearity in the homodyne interferometer starting from the interference principle. We present the design for an enhanced homodyne interferometer without DC offset, for which the nonlinearity model will not be influenced by the intensity of the measurement beam. Our experimental results show that the enhanced interferometer can suppress the nonlinearity to less than 0.5 nm with a system calibration involving gain adjustment and phase-correction methods.

An investigation of a segmented annular coplanar capacitor is presented. We focus on its theoretical model, and a mathematical expression of the capacitance value is derived by solving a Laplace equation with Hankel transform. The finite element method is employed to verify the analytical result. Different control parameters are discussed, and each contribution to the capacitance value of the capacitor is obtained. On this basis, we analyze and optimize the structure parameters of a segmented coplanar capacitive tilt sensor, and three models with different positions of the electrode gap are fabricated and tested. The experimental result shows that the model (whose electrode-gap position is 10 mm from the electrode center) realizes a high sensitivity: 0.129 pF/° with a non-linearity of <0.4% FS (full scale of ±40°). This finding offers plenty of opportunities for various measurement requirements in addition to achieving an optimized structure in practical design.

A measurement system with three degrees of freedom (3 DOF) that compensates for errors caused by incident beam drift is proposed. The system’s measurement model (i.e. its mathematical foundation) is analyzed, and a measurement module (i.e. the designed orientation measurement unit) is developed and adopted to measure simultaneously straightness errors and the incident beam direction; thus, the errors due to incident beam drift can be compensated. The experimental results show that the proposed system has a deviation of 1 μm in the range of 200 mm for distance measurements, and a deviation of 1.3 μm in the range of 2 mm for straightness error measurements.