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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 16, Iss. 3 — Mar. 1, 1999
  • pp: 475–480

Phase-shifted interferometry without phase unwrapping: reconstruction of a decentered wave front

Gonzalo Páez and Marija Strojnik  »View Author Affiliations

JOSA A, Vol. 16, Issue 3, pp. 475-480 (1999)

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We apply the method of the line integration of the phase gradient to determine unambiguously the phase from several phase-shifted interferograms (intensity fringe patterns) without phase unwrapping. The ambiguities introduced owing to the multiple values of the arctangent function and to the necessity to invoke a priori knowledge in the regions of high-intensity gradients are avoided. A decentered wave front with circular boundaries is reconstructed from high-fringe-density interferograms with an error of less than 0.1 percent, thus demonstrating the feasibility of testing the off-axis optical elements with approximate reference components.

© 1999 Optical Society of America

OCIS Codes
(100.2650) Image processing : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.4610) Instrumentation, measurement, and metrology : Optical fabrication
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure

Original Manuscript: October 12, 1998
Manuscript Accepted: November 9, 1998
Published: March 1, 1999

Gonzalo Páez and Marija Strojnik, "Phase-shifted interferometry without phase unwrapping: reconstruction of a decentered wave front," J. Opt. Soc. Am. A 16, 475-480 (1999)

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  1. J. D. Gallagher, D. R. Herriott, “Wavefront measurement,” U.S. Patent3,694,088 (1972).
  2. J. H. Bruning, D. R. Herriott, J. D. Gallaghar, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974). [CrossRef] [PubMed]
  3. P. Hariharan, B. F. Oreb, T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987). [CrossRef] [PubMed]
  4. C. Joenathan, “Phase-measuring interferometry: new methods and error analysis,” Appl. Opt. 33, 4147–4155 (1994). [CrossRef] [PubMed]
  5. O. Y. Kwon, D. Shough, R. A. Williams, “Stroboscopic phase-shifting interferometry,” Opt. Lett. 12, 855–857 (1987). [CrossRef] [PubMed]
  6. Y.-Y. Cheng, J. C. Wyant, “Phase shifter calibration in phase-shifting interferometry,” Appl. Opt. 24, 3049–3052 (1985). [CrossRef] [PubMed]
  7. K. Hibino, B. F. Oreb, D. I. Farrant, “Phase shifting for nonsinusoidal waveforms with phase-shift errors,” J. Opt. Soc. Am. A 12, 761–768 (1995). [CrossRef]
  8. C. P. Brophy, “Effect of intensity error correlation on the computed phase of phase-shifting interferometry,” J. Opt. Soc. Am. A 7, 537–541 (1990). [CrossRef]
  9. R. Onodera, Y. Ishii, “Phase-extraction analysis of laser-diode phase-shifting interferometry that is insensitive to changes in laser power,” J. Opt. Soc. Am. A 13, 139–146 (1996). [CrossRef]
  10. D. W. Robinson, “Phase unwrapping methods,” in Interferogram Analysis, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 195–229.
  11. J. E. Greivenkamp, “Sub-Nyquist interferometry,” Appl. Opt. 26, 5245–5258 (1987). [CrossRef] [PubMed]
  12. G. Páez, M. Strojnik, “Fringe analysis and phase reconstruction from modulated intensity patterns,” Opt. Lett. 22, 1669–1971 (1997). [CrossRef]
  13. G. Páez, M. Strojnik, “Convergent, recursive phase reconstruction from noisy, modulated intensity patterns by use of synthetic interferograms,” Opt. Lett. 23, 406–408 (1998). [CrossRef]
  14. G. A. Korn, T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1968), p. 155.
  15. M. S. Scholl, “Recursive exact ray trace equations through the foci of the tilted off-axis confocal prolate spheroids,” J. Mod. Opt. 43, 1583–1588 (1996). [CrossRef]
  16. M. S. Scholl, G. Páez Padilla, “Using the y, y-bar diagram to control stray light noise in IR systems,” Infr. Phys. Technol. 38, 25–30 (1997). [CrossRef]
  17. M. S. Scholl, G. Páez Padilla, “Image-plane incidence for a baffled infrared telescope,” Infr. Phys. Technol. 38, 87–92 (1997). [CrossRef]

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