An algorithm based on carrier squeezing interferometry for multi-beam phase extraction in Fizeau interferometer

Abstract

Multi-beam interference will exist in the cavity of Fizeau interferometer due to the high reflectivity of test optics. The random phase shift error will be generated by some factors such as the environmental vibration, air turbulence, etc. Both these will cause phase retrieving error. We proposed a non-iterative approach called Carrier Squeezing Multi-beam Interferometry (CSMI) algorithm, which is based on the Carrier squeezing interferometry (CSI) technique to retrieve the phase distribution from multiple-beam interferograms with random phase shift errors. The intensity of multiple-beam interference was decomposed into fundamental wave and high-order harmonics, by using the Fourier series expansion. Multi-beam phase shifting interferograms with linear carrier were rearranged by row or column, to fuse one frame of spatial-temporal fringes. The lobe of the fundamental component related to the phase and the lobes of high-order harmonics and phase shift errors were separated in the frequency domain, so the correct phase was extracted by filtering out the fundamental component. Suppression of the influence from high-order harmonic components, as well as random phase shift error is validated by numerical simulations. Experiments were also executed by using the proposed CSMI algorithm for mirror with high reflection coefficient, showing its advantage comparing with normal phase retrieving algorithms.