Online Precise Motion Measurement of 3-DOF Nanopositioners Based on Image Correlation

Fast and accurate measuring motion with multi-degrees-of-freedom (multi-DOFs) and high resolution has been highly demanded in the development of nanopositioning systems in recent years. This paper develops an efficient and practical image correlation method capable of measuring micromotions of the planar 3-DOF (<inline-formula> <tex-math notation="LaTeX">$x,y,\theta _{z}$ </tex-math></inline-formula>) nanopositioners. In this method, the measurement of 3-DOF micromotion is first transformed into a problem of three-variable optimization by utilizing the correlation function of sum of squared difference. Subsequently, an optimal algorithm based on the inverse compositional Gaussian–Newton searching is developed to instantaneously solve these three variables. Simulation results show that in the image space, accuracy of translational components (<inline-formula> <tex-math notation="LaTeX">$x$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$y$ </tex-math></inline-formula>) and rotation component (<inline-formula> <tex-math notation="LaTeX">$\theta _{Z}$ </tex-math></inline-formula>) of the proposed algorithm can reach to 0.02 pixels and 0.01°, respectively. Experimental results demonstrate that the proposed method can realize real-time motion tracking of a 3-DOF nanopositioner with the performance similar to commonly used multicapacitive sensor scheme.