Enhanced accuracy in surface profile reconstruction in white light interferometry using the BM3D algorithm in conjunction with fast Fourier transform

Abstract

The application of White Light Interferometry (WLI) has become increasingly popular across various fields for high-precision surface profile measurement. This method offers several advantages, including fast measurement, non-contact operation, and the ability to measure a wide range of surfaces. The accuracy of the measurement depends significantly on the quality of the interference fringe signals captured by the camera. In this study, we propose a novel two-step approach for WLI signal processing. The first step focuses on denoising individual interference fringe images to obtain cleaner, more accurate fringes, thereby improving correlogram quality. The second step processes the correlogram to extract surface height information precisely. In the preprocessing stage, the BM3D (Block-Matching and 3D Filtering) algorithm is employed for its effectiveness in image denoising. Then, the Fast Fourier Transform (FFT) is applied to suppress noise in the axial signals, combined with an interpolation algorithm to determine surface heights with high precision. The proposed method shows clear improvements in measurement accuracy. This was validated through simulations of arbitrary surface profiles, showing over 40 % improvement compared to the case without the algorithm and up to five fold error reduction under high-noise conditions. When tested on experimental data, the method achieved a deviation of only 0.169  nm compared to a commercial Zygo system, while the traditional FFT method showed an average deviation of 4.713  nm—about 27 times larger. This approach also provides a foundation for developing more advanced WLI signal processing techniques targeting even higher accuracy in future applications.