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Applied Optics

Applied Optics


  • Vol. 44, Iss. 9 — Mar. 21, 2005
  • pp: 1572–1576

Measurement of focal length with phase-shifting Talbot interferometry

Priti Singh, Mohammad Shoeb Faridi, Chandra Shakher, and Rajpal Singh Sirohi  »View Author Affiliations

Applied Optics, Vol. 44, Issue 9, pp. 1572-1576 (2005)

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Phase-shifting interferometry with a Fourier fringe analysis technique is implemented to analyze Talbot interferometric fringes and to evaluate the focal length of a lens. A four-step algorithm is used to obtain the phase map of the lens. The slope of the phase map is related to the focal length, and it is from this relationship that we evaluate the focal length. Experimental results are presented. Our experimental study suggests that phase-shifting Talbot interferometry combined with a Fourier fringe analysis technique can be advantageously used to improve the accuracy of measurement.

© 2005 Optical Society of America

Original Manuscript: June 23, 2004
Revised Manuscript: October 12, 2004
Manuscript Accepted: October 15, 2004
Published: March 20, 2005

Priti Singh, Mohammad Shoeb Faridi, Chandra Shakher, and Rajpal Singh Sirohi, "Measurement of focal length with phase-shifting Talbot interferometry," Appl. Opt. 44, 1572-1576 (2005)

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  1. R. Kingslake, ed., Applied Optics and Optical Engineering (Academic, New York, 1965), Vol. 1, Chap. IV, p. 208.
  2. I. Geatt, O. Kafri, “Determination of the focal length of nonparaxial lenses by Moiré deflectometry,” Appl. Opt. 26, 2507–2508 (1987). [CrossRef]
  3. E. Keren, M. K. Kreske, O. Kafri, “Universal method for determining the focal length of optical systems by moiré deflectometry,” Appl. Opt. 27, 1383–1385 (1988). [CrossRef] [PubMed]
  4. S. D. Nicola, P. Ferraro, A. Finizio, G. Pierattin, “Reflective grating interferometer for measuring the focal length of lens by digital moiré effect,” Opt. Commun. 132, 432–436 (1996). [CrossRef]
  5. Y. Nakano, K. Murata, “Talbot interferometry for measuring the focal length of a lens,” Appl. Opt. 24, 3162–3166 (1985). [CrossRef] [PubMed]
  6. L. M. Bernardo, O. D. D. Soares, “Evaluation of the focal distance of a lens by Talbot interferometry,” Appl. Opt. 27, 296–301 (1988). [CrossRef] [PubMed]
  7. K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Direct determination of focal length by using Talbot interferometry,” Appl. Opt. 31, 5984–5987 (1992). [CrossRef] [PubMed]
  8. C. Shakher, “Talbot interferometry and its applications, presented at the National Symposium on Perspectives in Engineering Optics,” Chaudhary Charan Singh University, Meerut, India, 4–6 April2003.
  9. S. Mirza, C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng., to be published.
  10. L. Angel, M. Tenaldi, R. Henao, “Phase stepping in Lau interferometry,” Opt. Commun. 164, 247–255 (1999). [CrossRef]
  11. M. Thakur, C. Shakher, “Evaluation of the focal distance of lenses by white-light Lau phase interferometry,” Appl. Opt. 41, 1841–1845 (2002). [CrossRef] [PubMed]
  12. D. Malacara, ed., “Phase shifting interferometers,” in Optical Shop Testing, 2nd ed. (Wiley, New York, 1992), Vol. 2, Chap. 14, p. 23.
  13. H. Canabal, J. A. Quigoga, E. Bernabeu, “Improved phase-shifting method for automatic processing of moiré deflectograms,” Appl. Opt. 37, 6227–6233 (1998). [CrossRef]
  14. I. Yamaguchi, J. Liu, J. Kato, “Active phase-shifting interferometers for shape and deformation measurement,” Opt. Eng. 35, 2930–2937 (1996). [CrossRef]
  15. K. Omura, T. Yatagai, “Phase measuring Ronchi test,” Appl. Opt. 27, 523–528 (1988). [CrossRef] [PubMed]
  16. P. Picart, J. C. Pascal, J. M. Breteau, “Systematic error of phase-shifting speckle interferometry,” Appl. Opt. 40, 2107–2116 (2001). [CrossRef]
  17. L. Mertz, “Real-time fringe pattern analysis,” Appl. Opt. 22, 1535–1539 (1983). [CrossRef]
  18. G. Bonsch, H. Bohme, “Phase determination of Fizeau interference by phase-shifting interferometry,” Optik (Stuttgart) 82, 161 (1989).
  19. G. Molesini, M. V. P. Desouza, F. Quercioli, M. Trivi, “Digital phase-shifting interferometry applied to partially developed speckle fields,” Opt. Commun. 75, 14–17 (1990). [CrossRef]
  20. L. Wansong, S. Xianyu, “Real time calibration algorithm for phase shifting in phase-measuring profilometry,” Opt. Eng. 40, 761–766 (2001). [CrossRef]
  21. T. M. Kreis, “Quantitative evaluation of the interference pattern,” in Industrial Optoelectronic Measurement Systems Using Coherent Light, W. F. Fagan, ed., Proc. SPIE863, 68–77 (1987). [CrossRef]
  22. Y. Nakano, K. Murata, “Measurement of phase objects using the Talbot effect and a moiré technique,” Appl. Opt. 23, 2296–2299 (1984). [CrossRef]

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