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.