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

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.

Dynamic non-uniform phase shift measurement via Doppler frequency shift in vortex interferometer.

A vortex beam interferometer based on Doppler frequency shift is proposed to retrieve the dynamic non-uniform phase shift from the petal-like fringes produced by the coaxial superposition of high-order conjugated Laguerre-Gaussian modes. Unlike the uniform phase shift measurement in which the petal-like fringes rotate as a whole, the fringes due to the dynamic non-uniform phase shift rotate at different angles at different radii, resulting in highly twisted and stretched petals; this hinders rotation angle identification and phase retrieval via image morphological operation. To address the problem, a rotating chopper combined with a collecting lens and a point photodetector are placed at the exit of the vortex interferometer to introduce a carrier frequency in the absence of the phase shift. Once the phase starts to shift non-uniformly, the petals at different radii generate different Doppler frequency shifts, owing to their different rotation velocities. Thus, identification of spectral peaks near the carrier frequency immediately indicates the rotation velocities of the petals and the phase shifts at those radii. The results verified a relative error of phase shift measurement to be within 2.2% at the surface deformation velocities of 1, 0.5, and 0.2 µm/s. The method manifests itself to have potential in exploiting mechanical and thermophysical dynamics from the nanometer to micrometer scale.