28 August 2016 A non-linear piezoelectric actuator calibration using N-dimensional Lissajous figure
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Abstract
Piezoelectric translators (PZTs) are very often used as phase shifters in interferometry. However, they typically present a non-linear behavior and strong hysteresis. The use of an additional resistive or capacitive sensor make possible to linearize the response of the PZT by feedback control. This approach works well, but makes the device more complex and expensive. A less expensive approach uses a non-linear calibration. In this paper, the authors used data from at least five interferograms to form N-dimensional Lissajous figures to establish the actual relationship between the applied voltages and the resulting phase shifts [1]. N-dimensional Lissajous figures are formed when N sinusoidal signals are combined in an N-dimensional space, where one signal is assigned to each axis. It can be verified that the resulting Ndimensional ellipsis lays in a 2D plane. By fitting an ellipsis equation to the resulting 2D ellipsis it is possible to accurately compute the resulting phase value for each interferogram. In this paper, the relationship between the resulting phase shift and the applied voltage is simultaneously established for a set of 12 increments by a fourth degree polynomial. The results in speckle interferometry show that, after two or three interactions, the calibration error is usually smaller than 1°.
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A. Albertazzi, A. Albertazzi, M. R. Viotti, M. R. Viotti, C. L. N. Veiga, C. L. N. Veiga, A. V. Fantin, A. V. Fantin, } "A non-linear piezoelectric actuator calibration using N-dimensional Lissajous figure", Proc. SPIE 9960, Interferometry XVIII, 99600L (28 August 2016); doi: 10.1117/12.2237367; https://doi.org/10.1117/12.2237367
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