Three-dimensional Fourier transform evaluation of sequences of spatially and temporally modulated speckle interferograms |
Optics Express, Vol. 18, Issue 14, pp. 15017-15027 (2010)
http://dx.doi.org/10.1364/OE.18.015017
Acrobat PDF (1468 KB)
Abstract
Phase evaluation methods based on the 2D spatial Fourier transform of a speckle interferogram with spatial carrier usually assume that the Fourier spectrum of the interferogram has a trimodal distribution, i. e. that the side lobes corresponding to the interferential terms do not overlap the other two spectral terms, which are related to the intensity of the object and reference beams, respectively. Otherwise, part of the spectrum of the object beam is inside the inverse-transform window of the selected interference lobe and induces an error in the resultant phase map. We present a technique for the acquisition and processing of speckle interferogram sequences that separates the interference lobes from the other spectral terms when the aforementioned assumption does not apply and regardless of the temporal bandwidth of the phase signal. It requires the recording of a sequence of interferograms with spatial and temporal carriers, and their processing with a 3D Fourier transform. In the resultant 3D spectrum, the spatial and temporal carriers separate the conjugate interferential terms from each other and from the term related to the object beam. Experimental corroboration is provided through the measurement of the amplitude of surface acoustic waves in plates with a double-pulsed TV holography setup. The results obtained with the proposed method are compared to those obtained with the processing of individual interferograms with the regular spatial-carrier 2D Fourier transform method.
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1. Introduction
2. Theory
5. K. Qian, H. S. Seah, and A. K. Asundi, “Algorithm for directly retrieving the phase difference: a generalization,” Opt. Eng. 42(6), 1721–1724 (2003). [CrossRef]
3. Experimental
3.1. Set-up
3.2. 3D Fourier transform processing
3.3. Optical phase-change maps ΔΦ_{n}
3.4. Maps of mechanical complex amplitude
7. C. Trillo, A. F. Doval, D. Cernadas, O. López, J. C. López, B. V. Dorrío, J. L. Fernández, and M. Pérez-Amor, “Measurement of the complex amplitude of transient surface acoustic waves using double-pulsed TV holography and a two-stage spatial Fourier transform method,” Meas. Sci. Technol. 14(12), 2127–2134 (2003). [CrossRef]
4. Results
5. Discussion
9. Y. Morimoto and M. Fujisawa, “Fringe pattern analysis by a phase-shifting method using Fourier transform,” Opt. Eng. 33(11), 3709–3714 (1994). [CrossRef]
6. Conclusions
Acknowledgments
References:
1. | D. J. Bone, H.-A. Bachor, and R. J. Sandeman, “Fringe-pattern analysis using a 2-D Fourier transform,” Appl. Opt. 25(10), 1653–1660 (1986). [CrossRef] [PubMed] |
2. | 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(2), 332–336 (1996). [CrossRef] [PubMed] |
3. | C. Trillo, and A. F. Doval, “Spatiotemporal Fourier transform method for the measurement of narrowband ultrasonic surface acoustic waves with TV holography,” Proc. SPIE 6341, 63410M–1-6 (2006). |
4. | H. S. Abdul-Rahman, M. A. Gdeisat, D. R. Burton, M. J. Lalor, F. Lilley, and A. Abid, “Three-dimensional Fourier Fringe Analysis,” Opt. Lasers Eng. 46(6), 446–455 (2008). [CrossRef] |
5. | K. Qian, H. S. Seah, and A. K. Asundi, “Algorithm for directly retrieving the phase difference: a generalization,” Opt. Eng. 42(6), 1721–1724 (2003). [CrossRef] |
6. | W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C, (Cambridge University Press, 1988), Chap.12. |
7. | C. Trillo, A. F. Doval, D. Cernadas, O. López, J. C. López, B. V. Dorrío, J. L. Fernández, and M. Pérez-Amor, “Measurement of the complex amplitude of transient surface acoustic waves using double-pulsed TV holography and a two-stage spatial Fourier transform method,” Meas. Sci. Technol. 14(12), 2127–2134 (2003). [CrossRef] |
8. | J. E. Greivenkamp, and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (John Wiley & Sons, New York, 1992). |
9. | Y. Morimoto and M. Fujisawa, “Fringe pattern analysis by a phase-shifting method using Fourier transform,” Opt. Eng. 33(11), 3709–3714 (1994). [CrossRef] |
OCIS Codes
(070.4790) Fourier optics and signal processing : Spectrum analysis
(100.6890) Image processing : Three-dimensional image processing
(090.1995) Holography : Digital holography
ToC Category:
Holography
History
Original Manuscript: May 7, 2010
Revised Manuscript: June 11, 2010
Manuscript Accepted: June 14, 2010
Published: June 29, 2010
Citation
C. Trillo, A. F. Doval, and J. C. López-Vázquez, "Three-dimensional Fourier transform evaluation of sequences of spatially and temporally modulated speckle interferograms," Opt. Express 18, 15017-15027 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-14-15017
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References
- D. J. Bone, H.-A. Bachor, and R. J. Sandeman, “Fringe-pattern analysis using a 2-D Fourier transform,” Appl. Opt. 25(10), 1653–1660 (1986). [CrossRef] [PubMed]
- 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(2), 332–336 (1996). [CrossRef] [PubMed]
- C. Trillo, and A. F. Doval, “Spatiotemporal Fourier transform method for the measurement of narrowband ultrasonic surface acoustic waves with TV holography,” Proc. SPIE 6341, 63410M–1-6 (2006).
- H. S. Abdul-Rahman, M. A. Gdeisat, D. R. Burton, M. J. Lalor, F. Lilley, and A. Abid, “Three-dimensional Fourier Fringe Analysis,” Opt. Lasers Eng. 46(6), 446–455 (2008). [CrossRef]
- K. Qian, H. S. Seah, and A. K. Asundi, “Algorithm for directly retrieving the phase difference: a generalization,” Opt. Eng. 42(6), 1721–1724 (2003). [CrossRef]
- W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C, (Cambridge University Press, 1988), Chap.12.
- C. Trillo, A. F. Doval, D. Cernadas, O. López, J. C. López, B. V. Dorrío, J. L. Fernández, and M. Pérez-Amor, “Measurement of the complex amplitude of transient surface acoustic waves using double-pulsed TV holography and a two-stage spatial Fourier transform method,” Meas. Sci. Technol. 14(12), 2127–2134 (2003). [CrossRef]
- J. E. Greivenkamp and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (John Wiley & Sons, New York, 1992).
- Y. Morimoto and M. Fujisawa, “Fringe pattern analysis by a phase-shifting method using Fourier transform,” Opt. Eng. 33(11), 3709–3714 (1994). [CrossRef]
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