A linearization method with improved robustness for determining the displacement from sine and cosine signals generated by optical encoders is presented. The proposed scheme is based on a ratiometric technique and a dedicated compensation method. The scheme converts the sinusoidal signals into a nearly perfectly linear output signal, from which the displacement is determined precisely using a simple linear equation. Under the condition of ideal input signals, the theoretical analysis shows that the converter enables a determination of the displacement with a non-linearity error below 0.0029 µm for a linear optical encoder with a period of 20 µm. The performance of the converter with non-ideal input signals is also evaluated by establishing the relationship between the positioning errors and the parameter deviations of the input signals. Due to the robustness of the converter against the signal amplitude imbalance, a signal processing circuit is developed to convert the signal phase-shift error into the signal amplitude imbalance error. A displacement measurement experiment was carried out by applying the converter to a linear optical encoder with a period of 20 µm. A positioning accuracy of 0.2 µm over a travel length of 80 mm was achieved under laboratory conditions. The feasibility of the proposed converter has been confirmed from the experimental results.
Transverse sensitivity that is mainly resulted from parasitic error motions can introduce undesired motion components and remarkably lower the manipulation qualities of most inertial sensors. This problem becomes even more apparent for multi-axial sensors as additional demands for multi-degree-of-freedom detection become higher. In this letter, a method to minify the transverse sensitivity of an inertial sensor by multi-degree-of-freedom optical sensing and measurement has been reported and tested. A multi-axis-surface-encoder-based biaxial optical accelerometer is fabricated for scheme validation. The surface encoder adopts multi-reading-unit arrangement, and it can not only detect small changes in displacement to calculate the applied acceleration along X- and Y-axes but also quantify the parasitic error motion caused by Z-twist. A suitable compensation strategy is also developed to reveal the concerned outputs without parasitic errors. Experimental results show that the configuration combined with the parasitic error compensation algorithm remarkably diminishes the sensor's transverse sensitivity and measurement error to 1.76% and 2.24%, respectively. Compared with the simple structure optimizations, the technique we proposed is more straightforward and effective. It is also applicable for transverse sensitivity suppression of other inertial sensors, allowing for a similar configuration, such as vibration sensors and inclinometers.
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