This study investigates how random intensity variations affect phase-shifting methods for high-precision three-dimensional surface-topography reconstruction in precision interferometric measurement, with potential relevance to fibrous materials. To address this issue, a 9N-8 scheme was constructed based on characteristic polynomial theory by combining a newly designed polynomial-shaped window and a discrete Fourier transform component. The sensitivity of the proposed approach to stochastic intensity fluctuations was evaluated, and the corresponding root-sum-square (RSS) error was calculated and compared with those of standard phase-shifting methods. The proposed method was then applied in a wavelength-tuned Fizeau interferometer for surface-topography measurements of optical samples. Experimental results indicate that the 9N-8 approach achieves the lowest RMS and random-intensity errors among the compared techniques, demonstrating strong robustness against both coupling effects and stochastic intensity perturbations. Although the present validation was conducted on standard optical components, the proposed framework may provide methodological support for future interferometric measurement of fibrous materials, where scattering, reflectivity variation, and curved surface geometry introduce additional challenges.

interferometry, tunable-wavelength interferometry, surface shape, random intensity error, fibrous-material measurement