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Noise-robust Phase Gradient Retrieval Formulation for Phase-shifting Interferometry

  • Park, Dae-Seo (SEM Co. - Inha University, Precision Inspection and Measurement Center (PIMC)) ;
  • O, Beom-Hoan (SEM Co. - Inha University, Precision Inspection and Measurement Center (PIMC)) ;
  • Park, Se-Geun (Optics and Photonics Elite Research Academy (OPERA), Inha University) ;
  • Lee, El-Hang (Optics and Photonics Elite Research Academy (OPERA), Inha University) ;
  • Park, Jae-Hyun (SEM Co. - Inha University, Precision Inspection and Measurement Center (PIMC)) ;
  • Lee, Seung-Gol (SEM Co. - Inha University, Precision Inspection and Measurement Center (PIMC))
  • Received : 2010.01.04
  • Accepted : 2010.04.05
  • Published : 2010.06.25

Abstract

Modification of the phase gradient formulation is proposed in order to make phase retrieval less susceptible to noise. The modified formulation is derived from separation of the phase terms and the intensity modulation terms of interferograms, and subsequent differentiation to reduce the noise-induced error of the phase gradient vector. Its performance is evaluated and compared to that of the conventional formulation, and noise-robust nature is confirmed.

Keywords

References

  1. D. Malacara, Optical Shop Testing (John Wiley & Sons Inc., New Jersey, USA, 1992).
  2. D. Malacara, M. Servin, and A. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker Inc., New York, USA, 1996).
  3. W. S. Ji, D. C. Kim, H. J. Kim, B. H. O, S. G. Park, E. H. Lee, and S. G. Lee, “NSOM-based characterization method applicable to optical channel waveguide with a solid-state cladding,” IEEE Photon. Technol. Lett. 17, 846-848(2005). https://doi.org/10.1109/LPT.2005.844004
  4. D. Kim and Y. J. Cho, “3-D surface profile measurement using an acousto-optic tunable filter based spectral phase shifting technique,” J. Opt. Soc. Korea 12, 281-287 (2008). https://doi.org/10.3807/JOSK.2008.12.4.281
  5. T. M. Jeong, C. M. Kim, D. K. Ko, and J. Lee, “Reconstruction of wavefront aberration of 100-TW Ti:sapphire laser pulse using phase retrieval method,” J. Opt. Soc. Korea 12, 186-191 (2008). https://doi.org/10.3807/JOSK.2008.12.3.186
  6. Y.-Y. Cheng and J. C. Wyant, “Multiple-wavelength phaseshifting interferometry,” Appl. Opt. 24, 804-807 (1985). https://doi.org/10.1364/AO.24.000804
  7. R. M. Neal and J. C. Wyant, “Polarization phase-shifting point-diffraction interferometer,” Appl. Opt. 45, 3463-3476 (2006). https://doi.org/10.1364/AO.45.003463
  8. S. H. Jeon and S. K. Gil, “Measurement of a mirror surface topography using 2-frame phase-shifting digital interferometry,” J. Opt. Soc. Korea 13, 245-250 (2009). https://doi.org/10.3807/JOSK.2009.13.2.245
  9. G. Paez and M. Strojnik, “Fringe analysis and phase reconstruction from modulated intensity patterns,” Opt. Lett. 22, 1669-1671 (1997). https://doi.org/10.1364/OL.22.001669
  10. G. Paez and M. Strojnik, “Phase-shifted interferometry without phase unwrapping: reconstruction of a decentered wave front,” J. Opt. Soc. Am. A 16, 475-480 (1999). https://doi.org/10.1364/JOSAA.16.000475
  11. D. S. Park, Y. S. Lee, D. C. Kim, B. H. O, S. G. Park, E. H. Lee, and S. G. Lee, “Modified formulation of phase gradient for noise-immune phase retrieval in phase-shifting interferometry,” in Proc. Optical Fabrication and Testing (Rochester, NY, USA, Oct. 2008), CD, paper JWD4.
  12. Y. Surrel, “Additive noise effect in digital phase detection,” Appl. Opt. 36, 271-276 (1997). https://doi.org/10.1364/AO.36.000271
  13. G. Paez and M. Strojnik, “Analysis and minimization of noise effects in phase shifting interferometry,” Proc. SPIE 3744, 295-305 (1999). https://doi.org/10.1117/12.357727
  14. G. Paez and M. Strojnik, “Phase reconstruction from undersampled intensity patterns,” J. Opt. Soc. Am. A 17, 46-52 (2000). https://doi.org/10.1364/JOSAA.17.000046
  15. M. Servin, J. C. Estrada, J. A. Quiroga, J. F. Mosino, and M. Cywiak, “Noise in phase shifting interferometry,” Opt. Exp. 17, 8789-8794 (2009). https://doi.org/10.1364/OE.17.008789
  16. P. Gao, B. Yao, N. Lindlein, K. Mantel, I. Harder, and E. Geist, “Phase-shift extraction for generalized phase-shifting interferometry,” Opt. Lett. 34, 3553-3555 (2009). https://doi.org/10.1364/OL.34.003553
  17. L. L. Deck, “Suppressing phase errors from vibration in phase-shifting interferometry,” Appl. Opt. 48, 3948-3960 (2009). https://doi.org/10.1364/AO.48.003948
  18. F. Bai and C. Rao, “Phase-shifts n$\pi$/2 calibration method for phase-stepping interferometry,” Opt. Exp. 17, 16861-16868 (2009). https://doi.org/10.1364/OE.17.016861
  19. R. L. Burden and J. D. Faires, Numerical Analysis (Thomson Books/Cole Publishing Company, Australia, 2005), Chapter 4.

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