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

Abstract 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.

[1]  Jim Kramer,et al.  Determination of fringe order in white-light interference microscopy. , 2002, Applied optics.

[2]  L. Deck,et al.  Three-dimensional imaging by sub-Nyquist sampling of white-light interferograms. , 1993, Optics letters.

[3]  Peter de Groot,et al.  Optical interferometry for measurement of the geometric dimensions of industrial parts. , 2002, Applied optics.

[4]  Patrick Sandoz,et al.  Profilometry by Zero-order Interference Fringe Identification , 1993 .

[5]  Leslie L. Deck,et al.  Surface Profiling by Analysis of White-light Interferograms in the Spatial Frequency Domain , 1995 .

[6]  Qian Kemao,et al.  Windowed Fourier transform for fringe pattern analysis: theoretical analyses. , 2008, Applied optics.

[7]  O. Sasaki,et al.  Sinusoidal phase modulating interferometry for surface profile measurement. , 1986, Applied optics.

[8]  Cho Jui Tay,et al.  An improved windowed Fourier transform for fringe demodulation , 2010 .

[9]  C. Quan,et al.  Continuous wavelet transform for micro-component profile measurement using vertical scanning interferometry , 2008 .

[10]  Kieran G. Larkin,et al.  Efficient nonlinear algorithm for envelope detection in white light interferometry , 1996 .

[11]  B. Bhushan,et al.  Measurement of surface topography of magnetic tapes by Mirau interferometry. , 1985, Applied optics.

[12]  P. J. Caber.  Interferometric profiler for rough surfaces. , 1993, Applied optics.

[13]  Gunther Notni,et al.  Analysis of white light interferograms using wavelet methods , 1998 .

[14]  J. Wyant,et al.  Improved vertical-scanning interferometry. , 2000, Applied optics.

[15]  Zehra Saraç,et al.  Analysis of white-light interferograms by using Stockwell transform , 2008 .

[16]  Qian Kemao,et al.  Windowed Fourier transform for fringe pattern analysis. , 2004, Applied optics.

[17]  Cho Jui Tay,et al.  Retrieval of instantaneous frequency from digital holograms based on adaptive windows , 2008 .

[18]  Min-Cheol Park,et al.  Direct quadratic polynomial fitting for fringe peak detection of white light scanning interferograms , 2000 .

[19]  James C. Wyant,et al.  ADVANCES IN INTERFEROMETRIC OPTICAL PROFILING , 1992 .

[20]  Patrick Sandoz,et al.  An algorithm for profilometry by white-light phase-shifting interferometry , 1996 .

[21]  Hao Chen,et al.  Temporal phase retrieval from a complex field in digital holographic interferometry. , 2007, Optics letters.

[22]  G S Kino,et al.  Mirau correlation microscope. , 1990, Applied optics.

[23]  Emil Wolf,et al.  Principles of Optics: Contents , 1999 .

[24]  Jingang Zhong,et al.  Multiscale windowed Fourier transform for phase extraction of fringe patterns. , 2007, Applied optics.

[25]  S S Chim,et al.  Three-dimensional image realization in interference microscopy. , 1992, Applied optics.

[26]  Rihong Zhu,et al.  Micro-profile measurement based on windowed Fourier transform in white-light scanning interferometry , 2011 .

[27]  B. T. Meggitt,et al.  Digital signal-processing techniques for electronically scanned optical-fiber white-light interferometry. , 1992, Applied optics.