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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 53, Iss. 25 — Sep. 1, 2014
  • pp: 5620–5631

Carrier peak isolation from single interferogram using spectrum shift technique

Satoshi Tomioka, Shusuke Nishiyama, and Samia Heshmat  »View Author Affiliations

Applied Optics, Vol. 53, Issue 25, pp. 5620-5631 (2014)

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This paper presents a new method to obtain a wrapped phase distribution from a single interferogram with a spatial carrier modulation. The Fourier transform of the interferogram has three peaks: one is a dc peak around the origin in the Fourier domain, and the other two are carrier peaks that have information of phase modulation by an object placed in the interferometer. Since the wrapped phase can be evaluated by one of the two carrier peaks, the dc peak and the adjoint peak that is the other peak of two carrier peaks should be removed by filters. The proposed filtering process consists of two stages: dc peak filtering and adjoint peak filtering. A spectrum shift filter based on symmetrical characteristics of the spectrum is applied in both stages as a basic filter that can remove most of the undesired spectrum. An additional two filters are applied to remove the remaining spectrum. The new method can automatically isolate the carrier peak, even when the boundary of peaks is not very clear. Numerical evaluations of simulation data and experimental data demonstrate that the proposed method can successfully isolate the carrier peak.

© 2014 Optical Society of America

OCIS Codes
(070.4790) Fourier optics and signal processing : Spectrum analysis
(100.2650) Image processing : Fringe analysis
(100.5070) Image processing : Phase retrieval
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(070.2615) Fourier optics and signal processing : Frequency filtering
(100.5088) Image processing : Phase unwrapping

ToC Category:
Image Processing

Original Manuscript: April 7, 2014
Revised Manuscript: July 23, 2014
Manuscript Accepted: July 24, 2014
Published: August 22, 2014

Satoshi Tomioka, Shusuke Nishiyama, and Samia Heshmat, "Carrier peak isolation from single interferogram using spectrum shift technique," Appl. Opt. 53, 5620-5631 (2014)

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  1. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982). [CrossRef]
  2. W. W. Macy, “Two-dimensional fringe-pattern analysis,” Appl. Opt. 22, 3898–3901 (1983). [CrossRef]
  3. D. J. Bone, H.-A. Bachor, and R. J. Sandeman, “Fringe-pattern analysis using a 2-D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986). [CrossRef]
  4. M. Takeda, “Spatial-carrier fringe-pattern analysis and its applications to precision interferometry and profilometry: an overview,” Ind. Metrol. 1, 79–99 (1990).
  5. M. Takeda, “Fourier fringe analysis and its application to metrology of extreme physical phenomena: a review,” Appl. Opt. 52, 20–29 (2013). [CrossRef]
  6. Y. Arai, S. Yokozeki, K. Shiraki, and T. Yamada, “High precision two-dimensional spatial fringe analysis method,” J. Mod. Opt. 44, 739–751 (1997). [CrossRef]
  7. J. A. Ferrari and E. M. Frins, “Multiple phase-shifted interferograms obtained from a single interferogram with linear carrier,” Opt. Commun. 271, 59–64 (2007). [CrossRef]
  8. K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson and G. T. Reid, eds. (IOP, 1993), pp. 94–140.
  9. J. C. Wyant, “Computerized interferometric surface measurements,” Appl. Opt. 52, 1–8 (2013). [CrossRef]
  10. J.-M. Desse, P. Picart, and P. Tankam, “Digital three-color holographic interferometry for flow analysis,” Opt. Express 16, 5471–5480 (2008). [CrossRef]
  11. K. Creath and G. Goldstein, “Dynamic quantitative phase imaging for biological objects using a pixelated phase mask,” Biomed. Opt. Express 3, 2866–2880 (2012). [CrossRef]
  12. D. I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, and G. R. Zurita, “Radial slope measurement of dynamic transparent samples,” J. Opt. 14, 045706 (2012). [CrossRef]
  13. J. Heil, T. Bauer, T. Sure, and J. Wesner, “Iterative full-bandwidth wavefront reconstruction from a set of low-tilt Fizeau interferograms for high-numerical-aperture surface characterization,” Appl. Opt. 45, 4270–4283 (2006). [CrossRef]
  14. M. Kujawinska and J. Wójciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325–339 (1991). [CrossRef]
  15. C. Roddier and F. Roddier, “Interferogram analysis using Fourier transform techniques,” Appl. Opt. 26, 1668–1673 (1987). [CrossRef]
  16. R. W. Gerchberg, “Super-resolution through error energy reduction,” Opt. Acta 21, 709–720 (1974). [CrossRef]
  17. J. Yañez-Mendiola, M. Servín, and D. Malacara-Hernández, “Iterative method to obtain the wrapped phase in an interferogram with a linear carrier,” Opt. Commun. 178, 291–296 (2000). [CrossRef]
  18. S. Tomioka and S. Nishiyama, “Nondestructive three-dimensional measurement of gas temperature distribution by phase tomography,” Proc. SPIE 8296, 829617 (2011). [CrossRef]
  19. D. Malacara, ed., “Interferometric optical profilers,” in Optical Shop Testing, 3rd ed. (Wiley, 2007), Chap. 15.4, pp. 695–702.
  20. S. Kostianovski, S. G. Lipson, and E. N. Ribak, “Interference microscopy and Fourier fringe analysis applied to measuring the spatial refractive-index distribution,” Appl. Opt. 32, 4744–4750 (1993). [CrossRef]
  21. J.-F. Lin and X. Su, “Two-dimensional Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 34, 3297–3302 (1995). [CrossRef]
  22. J. H. Massig and J. Heppner, “Fringe-pattern analysis with high accuracy by use of the Fourier-transform method: theory and experimental tests,” Appl. Opt. 40, 2081–2088 (2001). [CrossRef]
  23. L.-C. Chen, H.-W. Ho, and X.-L. Nguyen, “Fourier transform profilometry (FTP) using an innovative band-pass filter for accurate 3-D surface reconstruction,” Opt. Lasers Eng. 48, 182–190 (2010). [CrossRef]
  24. M. A. Herráez, D. Burton, and M. Lalor, “Accelerating fast Fourier transform and filtering operations in Fourier fringe analysis for accurate measurement of three-dimensional surfaces,” Opt. Lasers Eng. 31, 135–145 (1999). [CrossRef]
  25. Z. Ge, F. Kobayashi, S. Matsuda, and M. Takeda, “Coordinate-transform technique for closed-fringe analysis by the Fourier-transform method,” Appl. Opt. 40, 1649–1657 (2001). [CrossRef]
  26. T. Kreis, “Digital holographic interference-phase measurement using the Fourier-transform method,” J. Opt. Soc. Am. A 3, 847–855 (1986). [CrossRef]
  27. Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007). [CrossRef]
  28. M. Servin, J. L. Marroquin, and F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt. 36, 4540–4548 (1997). [CrossRef]
  29. M. Servin, J. L. Marroquin, and J. A. Quiroga, “Regularized quadrature and phase tracking from a single closed-fringe interferogram,” J. Opt. Soc. Am. A 21, 411–419 (2004). [CrossRef]
  30. J. C. Estrada, M. Servín, J. A. Quiroga, and J. L. Marroquín, “Path independent demodulation method for single image interferograms with closed fringes within the function space c2,” Opt. Express 14, 9687–9698 (2006). [CrossRef]
  31. C. Tian, Y. Yang, T. Wei, T. Ling, and Y. Zhuo, “Demodulation of a single-image interferogram using a Zernike-polynomial-based phase-fitting technique with a differential evolution algorithm,” Opt. Lett. 36, 2318–2320 (2011). [CrossRef]
  32. G. Rajshekhar and P. Rastogi, “Fringe demodulation using the two-dimensional phase differencing operator,” Opt. Lett. 37, 4278–4280 (2012). [CrossRef]
  33. G. Rajshekhar and P. Rastogi, “Multiple signal classification technique for phase estimation from a fringe pattern,” Appl. Opt. 51, 5869–5875 (2012). [CrossRef]
  34. I. Gurov and M. Volynsky, “Interference fringe analysis based on recurrence computational algorithms,” Opt. Lasers Eng. 50, 514–521 (2012). [CrossRef]
  35. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, “Optimal (Wiener) filtering with the FFT,” in Numerical Recipes: the Art of Scientific Computing, 3rd ed. (Cambridge University, 2007), Chap. 13.3, pp. 649–652.
  36. S. Tomioka and S. Nishiyama, “Phase unwrapping for noisy phase map using localized compensator,” Appl. Opt. 51, 4984–4994 (2012). [CrossRef]

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