OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 20 — Oct. 4, 2004
  • pp: 4681–4697

An integral approach to phase shifting interferometry using a super-resolution frequency estimation method

Abhijit Patil, Rajesh Langoju, and Pramod Rastogi  »View Author Affiliations


Optics Express, Vol. 12, Issue 20, pp. 4681-4697 (2004)
http://dx.doi.org/10.1364/OPEX.12.004681


View Full Text Article

Enhanced HTML    Acrobat PDF (1247 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The objective of this paper is to describe an integral approach -based on the use of a super-resolution frequency estimation method - to phase shifting interferometry, starting from phase step estimation to phase evaluation at each point on the object surface. Denoising is also taken into consideration for the case of a signal contaminated with white Gaussian noise. The other significant features of the proposal are that it caters to the presence of multiple PZTs in an optical configuration, is capable of determining the harmonic content in the signal and effectively eliminating their influence on measurement, is insensitive to errors arising from PZT miscalibration, is applicable to spherical beams, and is a robust performer even in the presence of white Gaussian intensity noise.

© 2004 Optical Society of America

OCIS Codes
(090.2880) Holography : Holographic interferometry
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.4120) Instrumentation, measurement, and metrology : Moire' techniques
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Research Papers

History
Original Manuscript: August 17, 2004
Revised Manuscript: September 15, 2004
Published: October 4, 2004

Citation
Abhijit Patil, Rajesh Langoju, and Pramod Rastogi, "An integral approach to phase shifting interferometry using a super-resolution frequency estimation method," Opt. Express 12, 4681-4697 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-20-4681


Sort:  Journal  |  Reset  

References

  1. P. Carré, �??Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures,�?? Metrologia 2, 13-23 (1966). [CrossRef]
  2. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, �??Digital wavefront measuring interferometer for testing optical surfaces and lenses, App. Opt. 13, 2693-2703 (1974). [CrossRef]
  3. K. Creath, �??Phase-shifting holographic interferometry,�?? Holographic Interferometry, P. K. Rastogi, ed. (Springer Series in Optical Sciences, Berlin 1994), Vol.68, pp. 109-150.
  4. T. Kreis, �??Holographic interferometry Principles and Methods,�?? Akademie Verlag, 1996, pp. 101-170.
  5. J. E. Greivenkamp and J. H. Bruning, Phase shifting interferometry Optical Shop Testing ed D. Malacara (New York: Wiley ) 501-598 (1992).
  6. 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]
  7. Y. Zhu and T. Gemma, �??Method for designing error-compensating phase-calculation algorithms for phase-shifting interferometry,�?? App. Opt. 40, 4540-4546 (2001). [CrossRef]
  8. P. Hariharan, B. F. Oreb, and T. Eiju, �??Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,�?? App. Opt. 26, 2504-2506 (1987). [CrossRef]
  9. J. Schwider, O. Falkenstorfer, H. Schreiber, and A. Zoller, �??New compensating four-phase algorithm for phase-shift interferometry,�?? Opt. Eng. 32, 1883-1885 (1993). [CrossRef]
  10. Y. Surrel, �??Phase stepping: a new self-calibrating algorithm,�?? Appl. Opt. 32, 3598-3600 (1993). [CrossRef] [PubMed]
  11. Y. Surrel, �??Design of algorithms for phase measurements by the use of phase stepping,�?? Appl. Opt. 35, 51-60 (1996). [CrossRef] [PubMed]
  12. J. van Wingerden, H. J. Frankena, and C. Smorenburg, �??Linear approximation for measurement errors in phase shifting interferometry,�?? Appl. Opt. 30, 2718-2729 (1991). [CrossRef] [PubMed]
  13. 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]
  14. 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]
  15. Y. �??Y. Cheng and J. C. Wyant, �??Phase-shifter calibration in phase-shifting interferometry,�?? App. Opt. 24, 3049-3052 (1985). [CrossRef]
  16. B. Zhao, �??A statistical method for fringe intensity-correlated error in phase-shifting measurement: the effect of quantization error on the N-bucket algorithm,�?? Meas. Sci. Technol. 8, 147-153 (1997). [CrossRef]
  17. B. Zhao and Y. Surrel, �??Effect of quantization error on the computed phase of phase-shifting measurements,�?? Appl. Opt. 36, 2070-2075 (1997). [CrossRef] [PubMed]
  18. R. Józwicki, M. Kujawinska, and M. Salbut, �??New contra old wavefront measurement concepts for interferometric optical testing, Opt. Eng. 31, 422-433 (1992). [CrossRef]
  19. P. de Groot, �??Vibration in phase-shifting interferometry,�?? J. Opt. Soc. Am. A 12, 354-365 (1995). [CrossRef]
  20. P. de Groot and L. L. deck, �??Numerical simulations of vibration in phase-shifting interferometry,�?? App. Opt. 35, 2172-2178 (1996). [CrossRef]
  21. C. Rathjen, �??Statistical properties of phase-shift algorithms,�?? J. Opt. Soc. Am. A 12, 1997-2008 (1995). [CrossRef]
  22. P. L. Wizinowich, �??Phase-shifting interferometry in the presence of vibration: a new algorithm and system,�?? Appl. Opt. 29, 3271-3279 (1990). [CrossRef] [PubMed]
  23. C. Joenathan and B. M. Khorana, �??Phase measurement by differentiating interferometric fringes, �??J. Mod. Opt. 39, 2075-2087 (1992). [CrossRef]
  24. K. Kinnnstaetter, A. W. Lohmann, J Schwider, and N. Streibl, �??Accuracy of phase shifting interferometry,�?? Appl. Opt. 27, 5082-5089 (1988). [CrossRef]
  25. C. J. Morgan, �??Least squares estimation in phase-measurement interferometry,�?? Opt. Lett. 7, 368-370 (1982). [CrossRef] [PubMed]
  26. J. E. Grievenkamp, �??Generalized data reduction for heterodyne interferometry,�?? Opt. Eng. 23, 350-352 (1984).
  27. Y. Ishii and R. Onodera, �??Phase-extraction algorithm in laser diode phase-shifting interferometry,�?? Opt. Lett. 20, 1883-1885 (1995). [CrossRef] [PubMed]
  28. Ch. Ai and J. C. Wyant, �??Effect of spurious reflection on phase shift interferometry,�?? Appl. Opt. 27, 3039-3045 (1988). [CrossRef] [PubMed]
  29. J. Schmit and K. Creath, �??Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry,�?? Appl. Opt. 34, 3610-3619 (1995). [CrossRef] [PubMed]
  30. B. V. Dorrío and J. L. Fernández, �??Phase-evaluation methods in whole-field optical measurement techniques,�?? Meas. Sci. Technol. 10, R33-R55 (1999). [CrossRef]
  31. 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]
  32. S. Ellingsrud and G. O. Rosvold, �??Analysis of data-based TV-holography system used to measure small vibration amplitudes,�?? J. Opt. Soc. Am. A 9, 237-251 (1992). [CrossRef]
  33. G. T. Reid, �??Automatic fringe pattern analysis: a review,�?? Opt. and Lasers Eng. 7, 37-68 (1986). [CrossRef]
  34. Q. Kemao, S. Fangjun, and W. Xiaoping, �??Determination of the best phase step of the Carré algorithm in phase shifting interferometry,�?? Meas. Sci. Technol. 11, 1220-1223 (2000). [CrossRef]
  35. G. Lai and T. Yatagai, �??Generalized phase-shifting interferometry,�?? J. Opt. Soc. Am. A 8, 822-827 (1991). [CrossRef]
  36. K. G. Larkin, �??A self-calibrating phase-shifting algorithm based on the natural demodulation of twodimensional fringe patterns,�?? Opt. Exp. 9, 236-253 (2001). [CrossRef]
  37. C. T. Farrell and M. A. Player, �??Phase step measurement and variable step algorithms in phase-shifting interferometry,�?? Meas. Sci. Technol. 3, 953-958 (1992). [CrossRef]
  38. C. T. Farrell and M. A. Player, �??Phase-step insensitive algorithms for phase-shifting interferometry,�?? Meas. Sci. Technol. 5, 648-652 (1994). [CrossRef]
  39. F. L. Bookstein, �??Fitting conic sections to scattered data,�?? Com. Graphics and Image Process. 9, 56-71 (1979). [CrossRef]
  40. A. Fitzgibbon, M. Pilu, and R. B. Fisher, �??Direct least square fitting of ellipses,�?? Pattern Anal. and Machine Intelligence. 21, 474-480 (1999).
  41. L. Z. Cai, Q. Liu, and X. L. Yang, �??Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps,�?? Opt. Let. 28, 1808-1810 (2003). [CrossRef]
  42. X Chen, M. Gramaglia, and J. A. Yeazell, �??Phase-shifting interferometry with uncalibrated phase shifts,�?? Appl. Opt. 39, 585-591 (2000). [CrossRef]
  43. G. �??S. Han and S. �??W. Kim, �??Numerical correction of reference phases in phase-shifting interferometry by iterative least-squares fitting,�?? Appl. Opt. 33, 7321-7325 (1994). [CrossRef] [PubMed]
  44. W. Jüptner, T. Kreis, and H. Kreitlow, �??Automatic evaluation of holographic interferograms by reference beam phase shifting,�?? In W. F. Fagan, ed., Industrial Applications of Laser Technology, Proc. Of Soc. Photo- Opt. Instr. Eng., 1553, 569-582 (1991).
  45. G. Stoilov and T. Dragostinov, �??Phase-stepping interferometry: five-frame algorithm with an arbitrary step,�?? Opt. and Lasers in Eng. 28, 61-69 (1997). [CrossRef]
  46. B. Raphael and I. F. C. Smith, �??A direct stochastic algorithm for global search,�?? App. Mathematics & Computation 146/2-3, 729-758 (2003). [CrossRef]
  47. A. Patil, B. Raphael, and P. Rastogi, �??Generalized phase-shifting interferometry by use of a direct stochastic algorithm for global search,�?? Opt. Lett. 29, 1381-1383 (2004). [CrossRef] [PubMed]
  48. P. K. Rastogi, �??Phase shifting applied to four-wave holographic interferometers,�?? App. Opt. 31, 1680-1681 (1992). [CrossRef]
  49. P. K. Rastogi, �??Phase-shifting holographic moiré: phase-shifter error-insensitive algorithms for the extraction of the difference and sum of phases in holographic moiré,�?? App. Opt. 32, 3669-3675 (1993). [CrossRef]
  50. P. Stoica and R. Moses, Introduction to Spectral Analysis (Prentice Hall, New Jersey, 1997).
  51. J. J. Fuchs, �??Estimating the number of sinusoids in additive white noise,�?? IEEE Transactions on Acoustics, Speech, and Signal Processing 36, 1846-1853 (1988). [CrossRef]
  52. M. Dendrinos, S. Bakamidis, and G. Carayannis, �??Speech enhancement from noise: A regenerative approach,�?? Speech Communication 10, 45-57 (1991). [CrossRef]
  53. P. C. Hansen and S. H. Jensen, �??FIR filter representations of reduced-rank noise reduction,�?? IEEE Transactions on Signal Processing 46, 1737-1741 (1998). [CrossRef]
  54. P. K. Rastogi and E. Denarié, �??Visualization of in-plane displacement fields using phase shifting holographic moiré: application to crack detection and propagation,�?? Appl. Opt. 31, 2402-2404 (1992). [CrossRef] [PubMed]
  55. P. K. Rastogi, M. Barillot, and G. Kaufmann, �??Comparative phase shifting holographic interferometry,�?? Appl. Opt. 30, 722-728 (1991). [CrossRef] [PubMed]
  56. P. K. Rastogi, �??Visualization and measurement of slope and curvature fields using holographic interferometry: an application to flaw detection,�?? J. Mod. Opt. 38, 1251-1263 (1991). [CrossRef]
  57. R. Kumaresan and D. W. Tufts, �??Estimating the angles of arrival of multiple plane waves,�?? IEEE Transactions on Aerospace and Electronic Systems AES-19, 134-139 (1983). [CrossRef]
  58. K. B. Hill, S. A. Basinger, R. A. Stack, and D. J. Brady, �??Noise and information in interferometric cross correlators,�?? Appl. Opt. 36, 3948-3958 (1997). [CrossRef] [PubMed]

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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited