Improved accuracy of capacitive sensor-based micro-angle measurement with angular-to-linear displacement conversion

This paper presents a capacitive sensor-based micro-angle measurement (CSMAM) method that uses an angular-to-linear displacement conversion to achieve high accuracy. The principal and secondary error components of CSMAMs are modeled and analyzed to reveal their impacts on the measurement accuracy. The theoretical accuracies of six types of commonly used CSMAMs are analyzed to determine the optimum configuration of capacitive sensors for 1D and 2D micro-angle measurements. An angular-to-linear displacement conversion method with a linear motional stage and a hemisphere decoupler is used to eliminate the principal error of CSMAM. Experimental results indicate that the optimized CSMAM can achieve accuracies of 0.157 arc sec and 0.052 arc sec in the ranges of ±900 arc sec and ±300 arc sec, respectively, in the case that the effective length of the rotation arm is 100 mm and the linear displacement measurement accuracy of the capacitive sensor is 2 nm. These results can be used as a reference to further improve CSMAM designs and achieve high accuracy in a large measurement range, for use in a wide range of precision engineering applications including angle metrology, micro- and nano-radian angle generators, beam steering mechanisms, and high-performance precision stages.