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Multi-axis measurement of motion is indispensable for characterization of dynamic systems and control of motion stages. This paper presents an optical beam deflection-based measurement system to simultaneously measure three-axis out-of-plane motion of both micro- and macro-scale targets. Novel strategies are proposed to calibrate the sensitivities of the measurement system. Subsequently the measurement system is experimentally realized and calibrated. The system is employed to characterize coupled linear and angular motion of a piezo-actuated stage. The measured motion is shown to be in agreement with theoretical expectation. Next, the high bandwidth of the measurement system has been showcased by utilizing it to measure coupled two-axis transient motion of a Radio Frequency Micro-Electro-Mechanical System switch with a rise time of about 60 μs. Finally, the ability of the system to measure out-of-plane angular motion about the second axis has been demonstrated by measuring the deformation of a micro-cantilever beam. [ABSTRACT FROM AUTHOR]

Aiming at reducing the estimation error of the sensor frequency response function (FRF) estimated by the commonly used window-based spectral estimation method, the error models of interpolation and transient errors are derived in the form of non-parameter models. Accordingly, window effects on the errors are analyzed and reveal that the commonly used hanning window leads to smaller interpolation error which can also be significantly eliminated by the cubic spline interpolation method when estimating the FRF from the step response data, and window with smaller front-end value can restrain more transient error. Thus, a new dual-cosine window with its non-zero discrete Fourier transform bins at −3, −1, 0, 1, and 3 is constructed for FRF estimation. Compared with the hanning window, the new dual-cosine window has the equivalent interpolation error suppression capability and better transient error suppression capability when estimating the FRF from the step response; specifically, it reduces the asymptotic property of the transient error from O(N−2) of the hanning window method to O(N−4) while only increases the uncertainty slightly (about 0.4 dB). Then, one direction of a wind tunnel strain gauge balance which is a high order, small damping, and non-minimum phase system is employed as the example for verifying the new dual-cosine window-based spectral estimation method. The model simulation result shows that the new dual-cosine window method is better than the hanning window method for FRF estimation, and compared with the Gans method and LPM method, it has the advantages of simple computation, less time consumption, and short data requirement; the actual data calculation result of the balance FRF is consistent to the simulation result. Thus, the new dual-cosine window is effective and practical for FRF estimation. [ABSTRACT FROM AUTHOR]