OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 11 — May. 24, 2010
  • pp: 11396–11405

Motion detection using extended fractional Fourier transform and digital speckle photography

Basanta Bhaduri, C. J. Tay, C. Quan, and Colin J. R. Sheppard  »View Author Affiliations

Optics Express, Vol. 18, Issue 11, pp. 11396-11405 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (945 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Digital speckle photography is a useful tool for measuring the motion of optically rough surfaces from the speckle shift that takes place at the recording plane. A simple correlation based digital speckle photographic system has been proposed that implements two simultaneous optical extended fractional Fourier transforms (EFRTs) of different orders using only a single lens and detector to simultaneously detect both the magnitude and direction of translation and tilt by capturing only two frames: one before and another after the object motion. The dynamic range and sensitivity of the measurement can be varied readily by altering the position of the mirror/s used in the optical setup. Theoretical analysis and experiment results are presented.

© 2010 OSA

OCIS Codes
(030.6140) Coherence and statistical optics : Speckle
(120.3940) Instrumentation, measurement, and metrology : Metrology
(330.4150) Vision, color, and visual optics : Motion detection
(070.2575) Fourier optics and signal processing : Fractional Fourier transforms

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: March 12, 2010
Revised Manuscript: May 2, 2010
Manuscript Accepted: May 4, 2010
Published: May 14, 2010

Basanta Bhaduri, C. J. Tay, C. Quan, and Colin J. R. Sheppard, "Motion detection using extended fractional Fourier transform and digital speckle photography," Opt. Express 18, 11396-11405 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. H. Tiziani, “A study of the use of laser speckle to measure small tilts of optically rough surfaces accurately,” Opt. Commun. 5(4), 271–276 (1972). [CrossRef]
  2. P. K. Rastogi, “Techniques of displacement and deformation measurements in speckle metrology,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, 1993).
  3. M. Sjödahl, “Electronic speckle photography: measurement of in-plane strain fields through the use of defocused laser speckle,” Appl. Opt. 34(25), 5799–5808 (1995). [CrossRef] [PubMed]
  4. K. J. Gåsvik, Optical Metrology, 3rd ed., (John Wiley & Sons Ltd, Chichester, 2002).
  5. T. Fricke-Begemann, “Three-dimensional deformation field measurement with digital speckle correlation,” Appl. Opt. 42(34), 6783–6796 (2003). [CrossRef] [PubMed]
  6. J. M. Diazdelacruz, “Multiwindowed defocused electronic speckle photographic system for tilt measurement,” Appl. Opt. 44(12), 2250–2257 (2005). [CrossRef] [PubMed]
  7. D. P. Kelly, B. M. Hennelly, and J. T. Sheridan, “Magnitude and direction of motion with speckle correlation and the optical fractional Fourier transform,” Appl. Opt. 44(14), 2720–2727 (2005). [CrossRef] [PubMed]
  8. R. E. Patten, B. M. Hennelly, D. P. Kelly, F. T. O’Neill, Y. Liu, and J. T. Sheridan, “Speckle photography: mixed domain fractional Fourier motion detection,” Opt. Lett. 31(1), 32–34 (2006). [CrossRef] [PubMed]
  9. D. P. Kelly, J. E. Ward, B. M. Hennelly, U. Gopinathan, F. T. O’Neill, and J. T. Sheridan, “Paraxial speckle-based metrology systems with an aperture,” J. Opt. Soc. Am. A 23(11), 2861–2870 (2006). [CrossRef]
  10. E. U. Condon, “Immersion of the Fourier transform in a continuous group of functional transformations,” Proc. Natl. Acad. Sci. U.S.A. 23(3), 158–164 (1937). [CrossRef] [PubMed]
  11. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transformation,” J. Opt. Soc. Am. A 10(10), 2181–2186 (1993). [CrossRef]
  12. J. Hua, L. Liu, and G. Li, “Extended fractional Fourier transforms,” J. Opt. Soc. Am. A 14(12), 3316–3322 (1997). [CrossRef]
  13. M. Sjodahl and L. R. Benckert, “Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy,” Appl. Opt. 32, 2278–2284 (1993). [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