Dynamic surface displacement measurement using carrier optical vortex interferometer: A numerical study

The measurement of dynamic surface displacement is crucial in understanding mechanical and thermophysical dynamics at nanometre to micrometer-scale. Interferometers using optical vortices are gaining attention due to their ability to demodulate fringe patterns with helical phase profiles. In this paper, we propose a novel carrier optical vortex interferometer (COVI) that overcomes the limitations of conventional pixelated morphological operations for demodulating fringe patterns. The COVI introduces a carrier frequency by placing a rotating chopper, a collecting lens and a point photodetector at the exit of the interferometer when there is no surface displacement. When the surface moves, the time-dependent total intensity of the chopped fringe pattern produces a Doppler frequency shift with respect to the carrier frequency. Moreover, a high-order Laguerre-Gaussian (LG) beam exhibiting multiple concentric rings is employed to extend the COVI to the dynamic measurement of non-uniform surface displacement with an axisymmetric profile. In this case, the Doppler frequency shift splits into multiple peaks corresponding to the radii of the rings of the LG beam. Locating the Doppler frequency peaks gives an immediate indication of the surface displacement velocities at those radii. Accordingly, the dynamic surface displacement can be retrieved by integrating the velocities over time. The basic principle and the performance of the COVI are theoretically analysed and numerically demonstrated. In addition, the effect of surface misalignment on the displacement measurement is studied thoroughly and the limitations of the measurable velocity are discussed. Although the proposed approach requires further development to make it more applicable in practice, our study provides a first insight into how to measure a dynamic surface displacement using the COVI.