White light scanning interferometry (WLSI) is a powerful technique for surface profilometry and has been widely applied in semiconductor inspection, additive manufacturing, film thickness characterization, and other precision measurements. However, in actual measurements, the hysteresis effect of piezoelectric ceramics and unpredictable environmental disturbances can distort the interference signal by increasing phase noise, leading to inaccurate localization of the zero optical path difference. Therefore, effectively suppressing phase noise without altering the structure of the white light interferometry system is significantly important in practice. In recent years, various approaches have been proposed to mitigate phase noise. Some scholars have developed advanced iterative algorithms to compensate for phase noise. However, these algorithms exhibit slow convergence and require additional computation for envelope and phase extraction, significantly increasing computational complexity, particularly for large-field interferometry. Other methods incorporate preprocessing techniques, such as short-time spectrum threshold denoising or improved complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), to filter out phase noise before integrating phase analysis for height extraction. However, these methods are constrained by pixel-by-pixel processing, limiting their efficiency. To address these challenges, we propose a multi-period moving difference phase noise preprocessing method. A multi-period difference equation is derived from the white light interference signal using a non-iterative least squares sinusoidal fitting approach. Compared to other preprocessing techniques, this method does not require additional hardware assistance or complex iterative optimization, ensuring an effective noise suppression rate while significantly reducing computational complexity. In addition, fast Fourier transform (FFT) and an improved seven-step phase shift method are combined to calculate the phase, minimizing scenarios where the phase step error is not π/2 and further improving phase calculation accuracy.

In this paper, we propose a fast multi-period differential signal preprocessing method, which is computationally efficient and can be processed using a forward recurrence operation. First, mathematical analysis is employed to separate key parameter information including step phase and phase noise from the white light interference signal. Using least squares sinusoidal fitting, a multi-period difference equation is derived. Then, leveraging the normal distribution characteristics of phase noise, the noise term in the equation is compensated, and moving differential filtering is applied to significantly suppress phase noise. Finally, FFT is utilized to extract the envelope of the interference signal after noise suppression, and the improved seven-step phase shift method is applied to enhance phase calculation, effectively minimizing the influence of residual phase noise.

Simulations and experiments are conducted to verify the computational efficiency and performance. The proposed method requires only 0.01 s to process a interference signal matrice with sampling length of 100 frame and size of 100 pixel×100 pixel, demonstrating an operational efficiency about ten times higher than that of Savitzky-Golay (S-G) filtering, continuous wavelet transform (CWT), and CEEMDAN, thus confirming its high computational efficiency. Table 1 shows the residual scanning errors of four different preprocessing methods under different noise levels. Compared to other methods, the proposed method yields the lowest residual scanning error (Δs), demonstrating superior performance in noise suppression. In addition, when the error amplitude increases to 50 nm, the residual scanning errors of the other three methods approach the Gaussian scanning error added by simulation, while the proposed method achieves a residual error that is only 30% of the simulated error value. To validate the feasibility and effectiveness of the proposed method, a standard step sample and an inner etching groove step sample are measured. The interference signal and carrier phase distribution with phase noise are illustrated in Fig. 3, while the denoised signals after preprocessing are shown in Figs. 4 and 6. The phase noise suppression rates for the two step samples after preprocessing are 92.8% and 94.6%, respectively. Repetitive measurements of 10 sets of data reveal that the average depth of the standard step height is (11.963±0.006) μm, with a relative error of 0.005% compared to the nominal value of (11.970±0.05) μm. In addition, to assess the model’s effectiveness for complex surface structures, the morphology and curvature radius of a microlens array are measured. The measurement results are shown in Fig. 9, while Table 6 demonstrates the 10-set statistical results of the curvature radius. The microlens array’s curvature radius is determined to be (1.082±0.016) mm, with a relative error of about 0.53% compared to the nominal value of (1.076±0.033) mm, further confirming the method’s effectiveness in surpassing phase noise and its applicability to complex structures.

In this paper, we propose a multi-period moving difference signal preprocessing method for white light interferometry, effectively mitigating unavoidable phase noise caused by mechanical vibrations and environmental disturbances. The multi-period differential filtering method, based on least squares fitting, applies a moving smoothing process to suppress phase noise efficiently. In addition, FFT-based coherence peak detection is integrated with an enhanced seven-step phase shift algorithm to accurately determine the zero optical path difference position, thus reducing the influence of residual phase noise on measurement accuracy. Comparative measurements of a standard step sample and an inner etching groove step sample demonstrate that the proposed method achieves a relative error of less than 0.7%, outperforming the frequency domain analysis (FDA) algorithm and the white light demodulation algorithm based on FFT and white light shift. The phase noise suppression rates for the interference signals of the two test samples are 92.8% and 94.6%, while the phase noise processing times are only 4.2764 s and 2.1235 s, respectively. In addition, microlens array measurements confirm that the proposed algorithm maintains high accuracy and repeatability even for complex structures. These results validate the effectiveness of the proposed phase noise suppression method and offer a new approach to anti-vibration measurement technology in low-vibration environments.