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In wavelength-tuning interferometry, the surface profile of the optical component is a key evaluation index. However, the systematic errors caused by the coupling error between the higher harmonics and phase shift error are considerable. In this research, a new 10N − 9 phase-shifting algorithm comprising a new polynomial window function and a DFT is developed. A new polynomial window function is developed based on characteristic polynomial theory. The characteristic of the new 10N − 9 algorithm is represented in the frequency domain by Fourier description. The phase error of the new algorithm is also discussed and compared with other phase-shifting algorithms. The surface profile of a silicon wafer was measured by using the 10N − 9 algorithm and a wavelength-tuning interferometer. The repeatability measurement error across 20 experiments was 2.045 nm, which indicates that the new 10N − 9 algorithm outperforms the conventional phase-shifting algorithm.

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