A rapid measurement method for structured surface in white light interferometry.

White light interferometry (WLI) is an effective and widely-used technique for structured surface measurement. However, it requires multiframe interferograms with vertical scanning to realise large-scale measurement, which is time consuming and computationally intensive. This paper proposes a rapid surface measurement method to realise surface recovery with a single interferogram by white light interferometry. First, the feasibility to solve the wrapped phase of a single white-light interferogram by Hilbert transform is certified. Then, unwrapped phases against zero optical path difference position (OPD) are achieved by a zero optical path difference detection algorithm applied to unwrapping process, which provides efficient surface recovery. To ensure the accuracy of phase solution in the proposed method, the necessary number and width of the interference fringes in the interferogram are analysed and determined based on Hilbert transform and sampling analysis. Finally, measurement results of a standard step sample and a standard reticle template are presented, which prove the accuracy and efficiency of the proposed method. LAY DESCRIPTION: As an effective and widely-used technique for structured surface measurement, white light interferometry (WLI) has the major advantage to measure noncontinuous surfaces using the short coherence length of a wide bandwidth source. However, frequently vertical scanning is required to get series of white light interferograms at different axial positions for surface recovery by recovered algorithms. The vertical scanning process is complicated and time consuming. This paper proposes a fast and efficient method to realise rapid surface measurement using only a single-frame interferogram based on WLI. First, the feasibility of using only one single white light interferogram to solve wrapped phases by Hilbert transform (HT) is discussed. Next, unwrapping process and zero optical path difference（OPD） detection algorithms are combined to unwrap phases against zero OPD position, which makes the structured surface recovery much easier. After that, the feasible number and width of interference fringes are determined based on sampling analysis and HT to guarantee the reliability and accuracy of phase solution in the proposed method. Finally, the accuracy and efficiency of this method is verified by measurement experiments of a standard step sample and a standard reticle template.