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.