When white light interferometry (WLI) is applied to measure fine circuit boards, it is affected by the sample’s extremely narrow linewidths, high aspect ratio trenches, and high surface roughness, which induce multiple superimposed interference signals, such as sidewall scattered light, diffuse reflection from rough surfaces, and environmental micro-vibrations. Therefore, the positioning accuracy of the zero optical path difference (ZOPD) location is adversely affected by both linear and nonlinear baseline drift and random intensity noise, which further causes distortion in the reconstructed surface topography. Most existing time-domain processing methods can only suppress either linear baseline drift or intensity noise individually. Although frequency-domain analysis methods can mitigate both to a certain extent, they heavily depend on the appropriate selection of the spectral extraction window and suffer from low computational efficiency. For this reason, a time-domain preprocessing algorithm based on the moving sine average (MSA) algorithm is proposed to suppress the effects of both baseline drift and intensity noise.

The proposed method first constructed and analyzed the theoretical model of light intensity of white light interference signals. Leveraging the sinusoidal modulation characteristic of WLI signals and the distribution features of random noise, it selected multiple sets of intensity signals with a phase difference of π within a sliding window of the interference image sequence for differential averaging. This differential operation simultaneously suppressed both linear and nonlinear baseline drift and reduced random noise. Then, the envelope peak was coarsely positioned using a hill-climbing algorithm. Subsequently, the phase of the envelope peak was compensated by combining a five-step phase-shifting algorithm to improve the positioning accuracy of the ZOPD position. This method required no additional hardware and avoided computationally costly steps such as frequency-domain transformation, featuring simple implementation, and high computational efficiency.

Experiments were conducted on a fine circuit board with a nominal etching depth of 26.05 μm ± 0.050 μm. The proposed method was compared with the fast Fourier transform combined with white light phase shifting interferometry and the Hilbert transform. As shown in Fig.4, the 3-D surface topography reconstructed by the proposed method had a continuous, smooth surface without significant spikes, whereas the surfaces reconstructed by the fast Fourier transform combined with white light phase shifting interferometry (FFT-WLPSI) method and the Hilbert transform (HT) method both exhibited numerous spikes. As shown in Table 1, using the nominal value as a reference, the proposed method achieved a mean relative error of 1.19% and a standard deviation of 0.020 μm based on 30 sets of repeatability measurements. This performance was significantly superior to the FFT-WLPSI method (3.31% and 0.085 μm) and the HT method (2.57% and 0.047 μm). These results verified that the proposed method could effectively suppress the adverse effects of mechanical vibration, environmental disturbances, sidewall reflection, and surface diffuse reflection on the measurement accuracy of WLI for fine circuit boards.

The proposed time-domain preprocessing method based on the moving sine average effectively suppresses background drift and random noise without requiring additional hardware. Combined with an optimized ZOPD localization method, it enhances the accuracy of the WLI topography reconstruction algorithm for fine circuit boards. This provides a reference solution for high-precision surface measurement of fine circuit boards using white light interferometry.