Application of least-square estimation in white-light scanning interferometry

White-light scanning interferometry (WLSI) is a powerful tool for investigating the profile of a test object that contains sharp steps. Due to the light source used in WLSI system, it is able to overcome phase ambiguity problem, which is often encountered in monochromatic interferometry. In this paper, a new algorithm based on least-square estimation using short-time Fourier transform (STFT) is proposed to measure the profile of a test object. STFT is used to extract the peak position of the coherence envelope of a white-light interference signal and retrieve the corresponding phase values simultaneously at first. A complex phasor (CP) method is introduced to further reduce the phase noise. Then, the phase values at several positions around are utilized to achieve a more accurate peak position based on least-square line fitting. Both simulated and experimental results show that the proposed algorithm is able to accurately measure the profile of a test object.

Research Highlights
► In this paper, we have proposed an algorithm based on least-square estimation using short-time Fourier transform (STFT) and a complex phasor (CP) to achieve profile measurement in white-light scanning interferometry.
► With the proposed method, the center wavelength of a white-light source and a more accurate peak position of the coherence envelop could be retrieved simultaneously. The effect of intensity and phase noises are also analyzed.
► Both simulated and experimental results show that the proposed algorithm has good noise immunity and is able to accurately measure the micro-profile of a specimen.