Improved symplectic geometry mode decomposition based correlation method in white light scanning interferometry

•A novel surface recovery approach for white light scanning interferometry, which can offer high-accuracy nano-scale surface profiling.•The ISGMD method is proposed as an extension of the SGMD method, with the introduction of spectrum matching.•The relationship between the height difference and the cross-power spectrum phase is established with a more accurate expression by using the Cor method.•Compared with traditional correlation method, the proposed ISGMDCor method offers superior repeatability of measurements. White light scanning interferometry (WLSI) is a widely applied technique for surface recovery, however, the interference signal is often corrupted by various environmental and system disturbances. In this paper, a novel surface recovery method named ISGMDCor is proposed, in which the improved symplectic geometry mode decomposition (ISGMD) for signal denoising and the correlation (Cor) method based on cross-power spectrum phase for surface recovery are combined for high precision measurement. The proposed method decomposes the noisy signal into the superposition finite symplectic geometric components. Moreover, the components with high matching degree to the spectrum distribution of illuminator are selected to reconstruct the denoised signal. The surface recovery achieved by originally positioning zero optical path difference is replaced by solving the cross-power spectrum phase of denoised signals at different pixels. The simulations are carried out under different levels of signal-to-noise ratio (SNR), which demonstrate that the proposed method could effectively reduce the root mean square error (RMSE) down to 0.78 nm when the SNR is 20 dB. In experiments, a step height standard (VLSI, 45.5 nm ± 1.2 nm) is measured to demonstrate the accuracy and the noise immunity of the proposed method, and the mean height of repeated step measurements 45.21 nm with repeatability 1.22 % is achieved, where measurements obtained by commercial profiler are also conducted as comparisons. At the last part of the experiments, two roughness standards with nominal Sa value 0.4 μm and 1.6 μm are tested to further verify the robustness of the proposed method.