Self-calibration of a dual-actuated single-axis nanopositioner using measurement transitivity with extensions to calibration of two-axis systems

In this paper we discuss a self-calibration technique for a dual-actuated, single-axis nanopositioner and extend ideas from this method to develop a calibration technique for a two-axis system. The proposed methods exploit concepts of measurement transitivity and redundancy that are will established in self-calibration theory. The developed method has been applied to a dual-actuated single-axis nanopositioner equipped with capacitive displacement sensors with a calibration error in the sub-nanometer range. For the two-axis system, the technique uses a right angle prism as an artifact to calibrate two orthogonal axes. Transitivity between the axes is obtained through the use of a redundant or 'dummy' uncalibrated sensor that maintains the hypotenuse of the right angle prism invariant during sets of measurements. Because, the approach relies on the accuracy of the prism, it cannot be considered to be a self-calibration technique. Nevertheless, experiments indicate that it calibrates a two-axis stage to within 1 nm of the prism.