Parallel plates are commonly used as optical transmission elements. Their main optical parameters include the optical homogeneity, optical thickness, and surface shape. If the optical parameters are not consistent, the transmissive wavefront will be changed, and the performance of the optical system will be reduced. Herein, a weighted multi-step phase-shifting algorithm is developed. The algorithm can measure the optical parameters with high accuracy based on wavelength tuning interferometry, and extracts the phase at the target frequency by weighting the sampling values. Both the simulated and experimental results show that the algorithm can suppress high-order harmonics and is insensitive to the phase-shifting errors caused by nonlinear wavelength tuning and coupling errors between phase-shifting and harmonic errors. Moreover, the algorithm requires fewer interferograms, improves the fringe contrast, and has a high detection efficiency. It is suitable for high-precision parallel plate optical parameter measurements.
When the optical homogeneity of parallel plates is measured using wavelength phase shifting interferometers, the nonlinearity of phase shifts caused by nonlinear wavelength tuning results in spectrum aliasing, and thus the optical homogeneity cannot be obtained accurately. We propose a nonuniform fast Fourier transform algorithm based on low-rank approximation and Taylor expansion (LRTE-NUFFT) to solve the problem. The principle of the LRTE-NUFFT method is introduced and compared with the FFT method and the nonuniform fast Fourier transform algorithm based on fast Gauss gridding (FGG-NUFFT) method proposed earlier through simulations and experiments. The results show that LRTE-NUFFT can improve the accuracy of the optical homogeneity measurement of parallel plates compared with the FFT method, and it can also improve the computational efficiency compared with the FGG-NUFFT method.
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