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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 46, Iss. 24 — Aug. 20, 2007
  • pp: 6096–6104

Estimation of the phase error in interferometric measurements by evaluation of the speckle field intensity

Ervin Kolenović and Wolfgang Osten  »View Author Affiliations

Applied Optics, Vol. 46, Issue 24, pp. 6096-6104 (2007)

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Intensities recorded with CCD or CMOS sensors represent spatially averaged values of the intensity across the area of a pixel. In this work we investigate the influence of spatial averaging in interferograms on the evaluated phase from an object wave with well resolved, fully developed speckles. Based on an analytical description of the averaging process, a procedure is developed to create a quality map for the evaluated phase, in order to give an estimation of the expected error at each point. The proposed method uses only the local intensity distribution of the object wave for the qualification of the phase values. The theoretical results are tested and verified by means of numerically generated objective and subjective speckle fields.

© 2007 Optical Society of America

OCIS Codes
(030.6140) Coherence and statistical optics : Speckle
(100.5070) Image processing : Phase retrieval
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(120.6160) Instrumentation, measurement, and metrology : Speckle interferometry

ToC Category:

Original Manuscript: March 26, 2007
Revised Manuscript: June 4, 2007
Manuscript Accepted: June 15, 2007
Published: August 14, 2007

Ervin Kolenović and Wolfgang Osten, "Estimation of the phase error in interferometric measurements by evaluation of the speckle field intensity," Appl. Opt. 46, 6096-6104 (2007)

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  1. T. Kreis, Handbook of Holographic Interferometry, 1st ed. (Wiley-VCH, 2004). [CrossRef]
  2. N. Shvartsman and I. Freund, "Speckle spots ride phase saddles sidesaddle," Opt. Commun. 117, 228-234 (1995). [CrossRef]
  3. T. Yoshimura, M. Zhou, K. Yamahai, and Z. Liyan, "Optimum determination of speckle size to be used in electronic speckle pattern interferometry," Appl. Opt. 34, 87-91 (1995). [CrossRef] [PubMed]
  4. M. Lehmann, "Phase-shifting speckle interferometry with unresolved speckles: A theoretical investigation," Opt. Commun. 128, 325-340 (1996). [CrossRef]
  5. M. Lehmann, "Measurement optimization in speckle interferometry: the influence of the imaging lens aperture," Opt. Eng. 36, 1162-1168 (1997). [CrossRef]
  6. T. Maack, R. Kowarschik, and G. Notni, "Optimum lens aperture in phase-shifting speckle interferometric setups for maximum accuracy of phase measurement," Appl. Opt. 36, 6217-6224 (1997). [CrossRef]
  7. V. Eichhorn and H. Helmers, "Phase-shifting electronic speckle pattern interferometry (ESPI) with unresolved speckle," in DGaO-Proceedings, DGaO (DGaO, 2005).
  8. E. Kolenović, W. Osten, and W. Jüptner, "Influence of unresolved speckles in interferometric phase measurements," Proc. SPIE 4101, 104-112 (2000).
  9. E. Kolenović, W. Osten, and W. Jüptner, "Improvement of interferometric phase measurements by consideration of the speckle field topology," Proc. SPIE 4933, 206-211 (2003). [CrossRef]
  10. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  11. Y. Zhu, Z. Luan, Q. Yang, W. Lu, and L. Liu, "Novel method to construct a quality map for phase unwrapping based on modulation and the phase gradient," Opt. Eng. 45(10), 1056.011-1056.015 (2006). [CrossRef]
  12. E. Kolenović, "Correlation between intensity and phase in monochromatic light," J. Opt. Soc. Am. A 22, 899-906 (2005). [CrossRef]
  13. G. Weigelt and B. Stoffregen, "The longitudinal correlation of a three-dimensional speckle intensity distribution," Optik (Jena) 48, 399-407 (1977).
  14. L. Leushacke and M. Kirchner, "Three-dimensional correlation coefficient of speckle intensity for rectangular and circular apertures," J. Opt. Soc. Am. A 7, 827-832 (1990). [CrossRef]
  15. J. W. Goodman, "Statistical properties of laser speckle patterns," in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer Verlag, 1975). [CrossRef]
  16. E. Kolenović, W. Osten, and W. Jüptner, "Non-linear speckle phase changes in the image plane caused by out of plane displacement," Opt. Commun. 171, 333-344 (1999). [CrossRef]
  17. K. Fliegel, "Modeling and measurement of image sensor characteristics," Telecommun. Radio Eng. 13, 27-34 (2004).
  18. O. Hadar and G. D. Boreman, "Oversampling requirements for pixelated-imager systems," Opt. Eng. 38, 782-785 (1999). [CrossRef]
  19. J. W. Goodman, Introduction to Fourier optics, 2nd ed. (McGraw-Hill, 1996).

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