Optical vortex interferometer: An overview of interferogram demodulation methods for dynamic phase measurement

Different interferogram demodulation methods of optical vortex interferometer (OVI) have been proposed over the last two decades aiming at dynamic phase measurement. Taking the Laguerre-Gaussian (LG) beam for instance, the OVI usually produces either a petal -like interferogram when two conjugated LG beams are superimposed or a spiral interferogram when a Gaussian beam is superimposed with a LG beam. The phase shift of one interference arm relative to the other causes the petal -like fringes or the spiral fringes to rotate azimuthally. The 2 pi periodicity of the azimuth provides a natural benchmark for highly -accurate retrieval of the phase shift. In this sense, the determination of the azimuthal rotation angle from a vortex interferogram acquires a paramount importance in developing an OVI with an accuracy up to the picometer scale. In this paper, the demodulation methods of vortex interferograms are first reviewed in terms of intensity, phase and rotating frequency for uniform phase measurement. Then, the demodulation method is extended to non -uniform phase measurement. Among them, the recent progress of the demodulation methods of high -order radial vortex interferograms are emphasized and the theoretical models of some methods are given. Finally, the applications of the OVI based on the above demodulation methods for the measurement of various dynamic phase objects are introduced and summarized. This paper provides a comprehensive and in-depth understanding of vortex interferogram demodulation, and pave the way of optical metrology using the OVI.