Micro-displacement measurement of optical interference with two-ring conjugated vortices

In this paper, we propose a two-ring conjugated vortex beam interferometer. The inner ring and outer ring of the vortex beams has different signs and topological charges. When combined, they produce an intricate pattern of interference fringes that resemble a flower petal, featuring both concentric inner and outer rings which rotates with different directions. We use the scale-invariant feature transformation algorithm to find the feature points. Then we use these points to measure the rotation angle of the outer ring relative to the inner ring and calculate the displacement based on it. We realize the measurement of sub-nanometer displacement. The displacement resolution is 0.38° nm⁻¹. It is improved by about 12.55% compared with only the inner ring. The displacement corresponding to the minimum detectable angle of CCD is reduced from 0.080 nm to 0.060 nm. It will be a promising method in precision machining micro-vibration sensing, surface unevenness sensing, and microbial movement sensing and high-precision measurement of micro-displacement.