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. •Avoid complex optical path and adjustments to achieve accurate displacement measurements.•Radon transform was used to solve the rotation angle of the dislocation line in the phase front.•Slight swing of the retroreflector will not change the direction of the measurement beam, this structure is more stable for displacement measurement based on conjugated vortex beam interference.