Optical measurement system based on a fractional orbital angular momentum beam interferometer and simple image processing

Orbital angular momentum (OAM) beams are extensively utilized in optical measurement systems. However, current OAM-based interferometers require the calculation of the rotation angle of the interferogram, which may increase computational complexity and introduce additional errors. In this study, we propose an optical measurement system based on a fractional OAM (FOAM) beam interferometer. We theoretically derive the sinusoidal dependence of FOAM-Gaussian beam interference intensity on phase difference and utilize this relationship to experimentally measure the target’s micromotion. For a uniformly moving target, the average relative error is below 1% for displacements exceeding 100 nm, while a relative error of 1.42% is achieved for targets undergoing non-uniform motion. We also measure the velocity of the target and investigate the impact of the number of sampling points on the measurement accuracy. The experimental resolution estimate is 0.26 nm. Due to the wavelength-scale period of the interferogram, our measurement system is suitable for detecting phase changes corresponding to displacements at the nanometer scale. Our work will contribute to the advancement of OAM-based interferometer design and broaden the potential applications of OAM beams, particularly FOAM beams, in precision metrology and optical sensing.