Moiré-Based Phase Imaging for Sensing and Adjustment of In-Plane Twist Angle

We explore the feasibility of a controllable and easy-to-implement moiré-based phase-sensitive imaging scheme for in-plane twist angle sensing and adjustment between two parallel planes, e.g., the optical alignment in nanoimprint lithography, photolithography, and X-ray lithography. The fundamental derivation of in-plane twist angle detection is given. Any angle variations can be readily sensed and monitored by the phase shift of optical field that occurs at the surface of two overlapped gratings. The performances of a circular grating and a specially designed composite linear grating were tested. Computational and experimental results show that the in-plane twist angle can be readily sensed and remedied within the magnitude of
$10^{-4}~{\rm rad}$
even in a manual operation mode by this method.