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In this study, a robust orbital angular momentum (OAM) beams-based Fizeau interferometer is proposed and experimentally demonstrated. It takes full advantages of the Fizeau interferometer and OAM beams, where two conjugated OAM beams propagate in a common optical path. Compared with the conventional dual-path interferometers, Fizeau interferometer has a simpler structure and higher stability, for its common optical path structure is less sensitive to the effects of the external perturbations. As a result, petal-like interference patterns can be stably observed on a CCD. By measuring the rotation angle of the petal-like pattern, tiny displacements ranging from 50 to 800 nm were stably and precisely measured with resolution of 40 pm in simulation and 750 pm in experiment. The proposed system may develop a more compact and stable scheme for the precision measurement in the future.

In this study, a simple and reliable method enabling to well synthesize the complex orbit-angular-momentum (OAM) spectrum of hybrid mode in a few-mode fiber is proposed and numerically demonstrated, which is realized by using the so-called inverse scattering method based on the genetic algorithm (GA), where the main Fourier components of a specially-selected ring in intensity distribution of the hybrid mode is used as the optimization objective. As a proof-of-concept example, power spectrum of a hybrid mode consisted of the first- and second-order OAM modes was successfully reconstructed with an accuracy higher than 0.99. This is the first time, to the best of our knowledge, that the complex OAM spectrum of a fiber hybrid mode consisted of more than two kinds of OAM modes is synthesized directly from the intensity distribution of the hybrid mode itself.

A stably acquiring and accurately demodulating interferogram is crucial for the interferometer to achieve ultra-high precision and sensitivity measurements. In this study, a robust orbital angular momentum (OAM) beams-based Fizeau interferometer is proposed and experimentally demonstrated, which is more compact and stable than the OAM interferometers with other structures due to the common optical path characteristic. In accordance with such an interferometric scheme, a phase-demodulation method operated in the domain of the OAM complex spectrum is also proposed and demonstrated in this study. In contrast to other phase-demodulation techniques, the proposed phase-demodulation technique neither requires phase shifters or phase modulators nor brings spectral leakage, which provides a robust alternative enabling to accurately and quickly extract the phase from the OAM interferogram. As a proof-of-concept of the proposed scheme, tiny displacements ranging from 0 to 800 nm were measured. The proposed OAM beams-based Fizeau interferometer and the corresponding azimuthal phase demodulation method may provide a feasible way for exploring further applications of the OAM-based interferometer in metrology.