Pseudo Wigner-Ville distribution for 3D white light scanning interferometric measurement

Abstract

White light scanning interferometry is a commonly used optical measurement method for three-dimensional (3D) surface profiles. In the case of large phase errors, accurate height values can generally be obtained indirectly from the interferometric signal envelope information derived using various envelope extraction methods. However, the current envelope extraction algorithms have the disadvantages of low robustness, increasing the half-width of the envelope information, and requiring correct parameter settings in advance. In this study, the pseudo Wigner–Ville distribution is modified and applied to white light scanning interferometric 3D measurement to avoid the above-mentioned drawbacks. Simulations and experiments are performed in a single-frequency mode (only the approximate central wave-number is used to guide both the proposed and wavelet transform methods). The simulation results prove that the proposed method has a 31.7% higher reconstruction accuracy than the wavelet transform method under a 25 dB signal to noise ratio condition. Concurrently, the proposed method is insensitive to the change in the central wavelength with a constant central wave-number parameter and has a good extraction effect for a long coherent length. The experiments measure standard step objects (VLSI standard, 1.761 ± 0.01 µm), and the reconstruction height error of the proposed method is 0.0035 µm. Simulations and experiments show that the proposed method can adaptively provide accurate envelope information after half-width reduction under the condition that only the approximate central wave-number a priori knowledge is used. Simultaneously, the proposed method is shown to be robust and effective.