OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 27, Iss. 2 — Feb. 1, 2010
  • pp: 276–285

Fourier analysis of two-stage phase-shifting algorithms

Marta Miranda and Benito V. Dorrío  »View Author Affiliations

JOSA A, Vol. 27, Issue 2, pp. 276-285 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (678 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Differential phase-shifting algorithms (DPSAs) and sum phase-shifting algorithms (SPSAs) recover directly the phase difference and the phase sum, respectively, encoded in two patterns. These algorithms can be obtained, for instance, by an appropriate combination of phase-shifting algorithms (PSAs), which makes unnecessary the previous calculation and subtraction or addition of each individual optical phase by means of conventional PSAs. A filtering process in the frequency domain is presented that allows us to obtain in a simple and elegant manner a qualitative characterization with a Fourier description of the two-stage phase-shifting evaluation that reveals possible phase shifter miscalibration errors and unexpected harmonics in the signal.

© 2010 Optical Society of America

OCIS Codes
(050.5080) Diffraction and gratings : Phase shift
(100.2650) Image processing : Fringe analysis
(100.5070) Image processing : Phase retrieval
(120.5060) Instrumentation, measurement, and metrology : Phase modulation
(070.2615) Fourier optics and signal processing : Frequency filtering

ToC Category:
Image Processing

Original Manuscript: August 6, 2009
Revised Manuscript: November 24, 2009
Manuscript Accepted: December 1, 2009
Published: January 25, 2010

Marta Miranda and Benito V. Dorrío, "Fourier analysis of two-stage phase-shifting algorithms," J. Opt. Soc. Am. A 27, 276-285 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. B. V. Dorrío and J. L. Fernández, “Phase-evaluation methods in whole-field optical measurement techniques,” Meas. Sci. Technol. 10, 33-35 (1999). [CrossRef]
  2. J. E. Greivenkamp, “Generalized data reduction for heterodyne interferometry,” Opt. Eng. 23, 350-352 (1984).
  3. K. Freischlad and C. L. Koliopoulos, “Fourier description of digital phase-measuring interferometry,” J. Opt. Soc. Am. A 7, 542-551 (1990). [CrossRef]
  4. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley, 1998).
  5. Q. Kemao, H. S. Seah, and A. K. Asundi, “Algorithm for directly retrieving the phase difference: a generalization,” Opt. Eng. 42, 1721-1724 (2003). [CrossRef]
  6. M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Appl. Opt. 44, 6861-6868 (2005). [CrossRef] [PubMed]
  7. M. R. Viotti, A. E. Dolinko, G. E. Galizzi, and G. H. Kaufmann, “A portable digital speckle pattern interferometry device to measure residual stresses using the hole drilling technique,” Opt. Lasers Eng. 44, 1052-1066 (2006). [CrossRef]
  8. B. Bhaduri, M. P. Kothiyal, and N. K. Mohan, “A comparative study of phase-shifting algorithms in digital speckle pattern interferometry,” Optik 119, 147-152 (2008). [CrossRef]
  9. N.-I. Toto-Arellano, G. Rodriguez-Zurita, C. Meneses-Fabian, and J. F. Vazquez-Castillo, “Phase shifts in the Fourier spectra of phase gratings and phase grids: an application for one-shot phase-shifting interferometry,” Opt. Express 16, 19330-19341 (2008). [CrossRef]
  10. K. A. Stetson and W. R. Brohinsky, “Electro-optic holography and its application to hologram interferometry,” Appl. Opt. 24, 3631-3637 (1985). [CrossRef] [PubMed]
  11. H. O. Saldner, N.-E. Molin, and K. A. Stetson, “Fourier transform evaluation of phase data in spatially phase-biased TV holograms,” Appl. Opt. 35, 332-336 (1996). [CrossRef] [PubMed]
  12. J. Burke and H. Helmers, “Complex division as a common basis for calculating phase differences in electronic speckle pattern interferometry in one step,” Appl. Opt. 37, 2589-2590 (1998). [CrossRef]
  13. J. M. Huntley, “Random phase measurement errors in digital speckle pattern interferometry,” Opt. Lasers Eng. 26, 131-150 (1997). [CrossRef]
  14. M. Miranda and B. V. Dorrío, “Error-phase compensation properties of differential phase-shifting algorithms for Fizeau fringe patterns,” in RIAO/OPTILAS 2007, Proceedings of the 2007 Iberoamerican Conference on Optics/Latinoamerican Meeting on Optics, Lasers and Applications (AIP, 2007), Vol. 992, pp. 993-998. http://riao-optilas.ifi.unicamp.br.
  15. M. Miranda and B. V. Dorrío, “Error behavior in differential phase-shifting algorithms,” Proc. SPIE 7102, 71021B-1-71021B-9 (2008).
  16. K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, “Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts,” J. Opt. Soc. Am. A 14, 918-930 (1997). [CrossRef]
  17. Y. Surrel, “Phase-shifting algorithms for nonlinear and spatially nonuniform phase-shifts: comment,” J. Opt. Soc. Am. A 15, 1227-1233 (1998). [CrossRef]
  18. K. Hibino, “Error-compensating phase measuring algorithms in a Fizeau interferometer,” Opt. Rev. 6, 529-538 (1999). [CrossRef]
  19. J. Burke and H. Helmers, “Spatial versus temporal phase shifting in electronic speckle-pattern interferometry: noise comparison in phase maps,” Appl. Opt. 39, 4598-4606 (2000). [CrossRef]
  20. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, 2000).
  21. R. Hanayama, K. Hibino, S. Warisawa, and M. Mitsuishi, “Phase measurement algorithm in wavelength scanned Fizeau interferometer,” Opt. Rev. 11, 337-343 (2004). [CrossRef]
  22. K. Hibino, R. Hanayama, J. Burke, and B. F. Oreb, “Tunable phase-extraction formulae for simultaneous shape measurement of multiple surfaces with wavelength-shifting interferometry,” Opt. Express 12, 5579-5594 (2004). [CrossRef] [PubMed]
  23. K. G. Larkin and B. F. Oreb, “Design and assessment of symmetrical phase-shifting algorithms,” J. Opt. Soc. Am. A 9, 1740-1748 (1992). [CrossRef]
  24. K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, “Phase shifting for nonsinusoidal waveforms with phase-shift errors,” J. Opt. Soc. Am. A 12, 761-768 (1995). [CrossRef]
  25. D. Malacara-Doblado and B. V. Dorrío, “Family of detuning-insensitive phase-shifting algorithms,” J. Opt. Soc. Am. A 17, 1857-1863 (2000). [CrossRef]
  26. D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Taylor & Francis, 2005). [CrossRef]
  27. J. Schwider, R. Burow, K. E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, “Digital wave-front measuring interferometry: some systematic error sources,” Appl. Opt. 22, 3421-3432 (1983). [CrossRef] [PubMed]
  28. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504-2506 (1987). [CrossRef] [PubMed]
  29. D. C. Williams, N. S. Nassar, J. E. Banyard, and M. S. Virdee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147-150 (1991). [CrossRef]
  30. M. Kuechel, “Method and apparatus for phase evaluation of pattern images used in optical measurement,” US Patent 5361312, 1 November 1994.
  31. J. Burke, “2-D spectral error analysis for phase-shifting formulas,” in Proceedings of FRINGE '01 (4th International Workshop on Automatic Processing of Fringe Patterns) (Elsevier, 2001), pp. 199-207.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited