DOI QR코드

DOI QR Code

Fringe-Order Determination Method in White-Light Phase-Shifting Interferometry for the Compensation of the Phase Delay and the Suppression of Excessive Phase Unwrapping

  • Kim, SeongRyong (School of Mechanical and Aerospace Engineering, Seoul National University) ;
  • Kim, JungHwan (School of Mechanical and Aerospace Engineering, Seoul National University) ;
  • Pahk, HeuiJae (School of Mechanical and Aerospace Engineering, Seoul National University)
  • Received : 2013.07.16
  • Accepted : 2013.09.24
  • Published : 2013.10.25

Abstract

White-light phase-shifting interferometry (WLPSI) is widely recognized as a standard method to measure shapes with high resolution over a long distance. In practical applications, WLPSI, however, is associated with some degree of ambiguity of its phase, which occurs due to a phase delay, which is the offset between the phase of the fringes and the fringe envelope peak position. In this paper, a new algorithm is proposed for the determination of a fringe order suitable for samples in which the phase delay mainly occurs due to noise, diffraction and a steep angle. The concepts of the decouple factor and the connectivity are introduced and a method for calculating the decouple factor and the connectivity is developed. With the phase-unwrapping procedure which considers these values, it is demonstrated that our algorithm determines the correct fringe order. To verify the performance of the algorithm, a simulation was performed with the virtual step height under noise. Some specimens such as step height standard and a column spacer with a steep angle are also measured with a Mirau interference microscope, after which the algorithm is shown to be effective and robust.

Keywords

References

  1. G. S. Kino and S. S. C. Chim, "Mirau correlation microscope," Appl. Opt. 29, 3775-3783 (1990). https://doi.org/10.1364/AO.29.003775
  2. K. G. Larkin, "Efficient nonlinear algorithm for envelope detection in white light interferometry," J. Opt. Soc. Am. A 13, 832-843 (1996).
  3. P. Sandoz, "An algorithm for profilometry by white-light phase-shifting interferometry," J. Mod. Opt. 43, 1545-1554 (1996).
  4. P. Sandoz, R. Devillers, and A. Plata, "Unambiguous profilometry by fringe-order identification in white-light phaseshifting interferometry," J. Mod. Opt. 44, 519-534 (1997). https://doi.org/10.1080/09500349708232918
  5. A. Harasaki and J. C. Wyant, "Fringe modulation skewing effect in white-light vertical scanning interferometry," Appl. Opt. 39, 2101-2106 (2000). https://doi.org/10.1364/AO.39.002101
  6. A. Harasaki, J. Schmit, and J. C. Wyant, "Improved verticalscanning interferometry," Appl. Opt. 39, 2107-2115 (2000). https://doi.org/10.1364/AO.39.002107
  7. J. Schmit and A. Olszak, "High-precision shape measurement by white-light interferometry with real-time scanner error correction," Appl. Opt. 41, 5943-5950 (2002). https://doi.org/10.1364/AO.41.005943
  8. P. de Groot, X. C. de Lega, J. Kramer, and M. Turzhitsky, "Determination of fringe order in white-light interference microscopy," Appl. Opt. 41, 4571-4578 (2002). https://doi.org/10.1364/AO.41.004571
  9. K. Itoh, "Analysis of the phase unwrapping problem," Appl. Opt. 21, 2470-2470 (1982). https://doi.org/10.1364/AO.21.002470
  10. M. A. Herraez, D. R. Burton, M. J. Lalor, and M. A. Gdeisat, "Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path," Appl. Opt. 41, 7437-7444 (2002). https://doi.org/10.1364/AO.41.007437
  11. J.-H. Kim, S.-W. Yoon, J.-H. Lee, W.-J. Ahn, and H.-J. Pahk, "New algorithm of white-light phase-shifting interferometry pursing higher repeatability by using numerical phase error correction schemes of pre-processor, main processor, and post-processor," Optics and Lasers in Engineering 46, 140-148 (2008). https://doi.org/10.1016/j.optlaseng.2007.08.008

Cited by

  1. Spatial Modulation-Assisted Scanning White-Light Interferometry for Noise Suppression vol.30, pp.4, 2018, https://doi.org/10.1109/LPT.2017.2787100
  2. Quadrature wavelength scanning interferometry vol.55, pp.20, 2016, https://doi.org/10.1364/AO.55.005332
  3. Thickness and Surface Measurement of Transparent Thin-Film Layers using White Light Scanning Interferometry Combined with Reflectometry vol.18, pp.3, 2014, https://doi.org/10.3807/JOSK.2014.18.3.236
  4. Unambiguous 3D Surface Measurement Method for a Micro-Fresnel Lens-Shaped Lenticular Lens Based on a Transmissive Interferometer vol.18, pp.1, 2014, https://doi.org/10.3807/JOSK.2014.18.1.037
  5. Methods to Measure the Critical Dimension of the Bottoms of Through-Silicon Vias Using White-Light Scanning Interferometry vol.18, pp.5, 2014, https://doi.org/10.3807/JOSK.2014.18.5.531