Carrier optical vortex interferometer using segmentation demodulation method for dynamic measurement of axisymmetric surface deformation

Abstract

The dynamic measurement of surface deformation with an axisymmetric profile at nanometer- to micrometer-scale is of great interest in understanding micromechanical and thermophysical dynamics. We propose a carrier optical vortex interferometer (COVI) to measure such surface deformation dynamically by segmentation demodulation of the petal-like interferogram that is produced by the coaxial superposition of conjugated p-radial order Laguerre–Gaussian beams. Specifically, a rotating chopper placed at the exit of the interferometer introduces a carrier frequency in the absence of surface deformation. A camera placed behind the chopper uses a multi-ring segmentation detection scheme to produce a Doppler shift relative to the carrier frequency at the radius of each ring in the presence of axisymmetric surface deformation. Locating the Doppler shifts gives the surface deformation velocities at those radii. Thus, the dynamic surface deformation profile can be obtained by integrating the velocities over time. We reveal the basic principles of the carrier frequency and the Doppler shifts in the COVI theoretically. As a proof-of-concept, an external force-induced axisymmetric mechanical surface deformation is measured dynamically to demonstrate the validity of the COVI. The results show that the measurement error of the surface deformation velocity is within (−2.1, 1.1 nm/s) for the velocity ranging from 20 to 86 nm/s. The lower limit of the measurable velocity can reach 20 nm/s. The measurement error of the surface deformation profile is less than 2.5 nm for the amplitude of the surface deformation of 500 nm.