Differential readings of capacitance-based controls of attitude and displacements at the micro/nano scale

Abstract

Four-quadrant plane capacitive sensors with electrodes made by thick metal plates were used in a novel configuration of a bridge-based circuit for measurement of both displacement and small angles over two axes. Their design, fabrication and testing by means of a specifically designed differential set-up is presented and discussed in terms of the measurement model, considerations of signal recovery, linearity, resolution, and noise. Numerical calculations of the capacitors, including corrective terms for fringe effects and tilt between electrodes in a differential configuration, are developed to simulate the overall measuring system. Tests of the model were then performed and validated by means of a comparison with the results of displacement and small angle rotation runs traced by an interferometer and an autocollimator. Sensitivities of approximately 0.11 V µm−1 with a 1 × 10−3 relative standard deviation, and of 0.13 V mrad−1 with a 3 × 10−3 relative standard deviation, were determined, with displacements of up to ±50 µm and yaw rotations of up to ±10 mrad.