High-precision micro-displacement measurement in a modified reversal shearing interferometer using vortex beams

We propose a novel micro-displacement measurement system that employs a modified reversal shearing interference structure based on vortex beam interference. The micro-displacement in the measurement path caused a change in the light path and resulted in an optical path difference (OPD) between the reference and measurement paths. This OPD led to the rotation of the petal-like pattern obtained by the interference between two paths. The rotation angle of the petal-like pattern was proportional to the OPD caused by micro -displacement. We used the virtual phase-shifting method to extract the helical phase front, and the Radon transform to measure the angle of the helical phase front. We achieved a high-accuracy micro-displacement measurement with a measurement error of less than 0.067 nm when using a vortex beam with a topological charge of six. This system has an extremely simple structure and is easy to adjust. It is of great significance to the miniaturized design of high-precision displacement sensors.