Fractional Orbital Angular Momentum Sensor for Dynamic Micro-Displacement

The optical micro-displacement sensor is one of the cornerstones of quality control in modern nanotechnological devices, lithography, and high-accuracy localization. However, it is a technical challenge to directly achieve the object's displacement, velocity, and direction simultaneously. Here, we propose a fractional orbital angular momentum (FOAM) sensor to simultaneously measure the dynamic displacement, the instantaneous velocity, and the direction. The single petal-like speckle can be generated by the coaxial interference between the measurement FOAM beam and the reference beam with the absolute topological charge less than or equal to 0.5 ($| \ell | \leq 0.5$). The displacement of the moving object is dependent on the rotation angle of the single petal around the dark core, the velocity is related to the angular velocity of the single petal, and the direction is determined by the clockwise or anticlockwise of the single rotating petal, which is monitored in real-time by using a designed algorithm. The experimental results demonstrate that the proposed method can achieve micro-displacement precision ($\pm \text{11.78} \, \rm{nm}$), displacement measurement range (0–250 cm), instantaneous velocity measurement range (0–5 μm/s), velocity precision ($\pm 0.25\mu \rm{m/s}$) and has advantages for the measuring object with dynamic micromotion. In addition, the sensor can perform a non-contact measurement, so it is significant to apply it in future precision measurement technology.