Carrier squeezing interferometry with π/4 phase shift: phase extraction in the presence of multi-beam interference

Multi-beam interference exists in testing high-reflectivity surfaces with a Fizeau interferometer. In this paper, the multi-beam interference intensity was estimated as the sum of the first six order harmonics using the Fourier series expansion. Then, by adopting carrier squeezing interferometry with a π/4 phase shift, an algorithm was proposed to extract the phase from multi-beam interferograms. To ensure the separation of the lobes of phase-shift errors and the phase in the frequency domain, conditions of the necessary linear carrier in the proposed algorithm were derived. Simulation results indicated that the phase retrieving precision is better than PV 0.008λ and RMS 0.001λ, even when the reflection coefficient of the test surface is as high as 0.9 and the phase shift varies within π/4±π/20. Compared with the other algorithms, the proposed algorithm for multi-beam interference was validated by its good performance in the experiments, especially when the phase-shift error exists.