Linear canonical transforms, and speckle based metrology

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 5879, Issue , 2005, Pages 1-12

  Kelly, Damien P ^a   Patten, Robert F ^a   Hennelly, Bryan M ^a   Liu, Ying ^a   Ward, Jennifer E ^a   Sheridan, John T ^a  

^a UNIVERSITY COLLEGE DUBLIN   (Ireland)

Author keywords

Correlation; Fractional Fourier Transform; Linear Canonical Transforms; Optical Metrology; Speckle Photography

Indexed keywords

FOURIER TRANSFORMS; LENSES; OPTICAL CORRELATION; PHOTOGRAMMETRY;

FRACTIONAL FOURIER TRANSFORM; LINEAR CANONICAL TRANSFORMS; OPTICAL METROLOGY; SPECKLE PHOTOGRAPHY;

OPTICAL SYSTEMS;

EID: 29244467433     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.617465     Document Type: Conference Paper

References (24)

1. J. W. Goodman, Statistical properties of laser speckle patterns, in Laser Speckle and Related Phenomena, J. C. Dainty, ed. Springer-Verlag, Berlin, 1975.
2. R. Jones and C. Wykes, Holographic and Speckle Interferometry, Cambridge U. Press, Cambridge, 1989.
3. H. Tiziani, "A study of the use of laser speckle to measure small tilts of optically rough surfaces accurately," Opt. Commun. 5, 271-274 (1972).
4. H. Tiziani, "Vibration analysis and deformation measurement," in Speckle Metrology, R. K. Erf, ed. (Academic, New York, 1978), pp. 73-110.
5. P. K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques, Wiley, Chichester U.K., 2001.
6. P. K. Rastogi, Techniques of displacement and deformation measurement in speckle metrology, Speckle Metrology, R. S. Sirohi (Ed.) Marcel Dekker Inc., New York, 1993.
7. M. Sjodahl, "Electronic speckle photography: measurement of in-plane strain fields through the use of defocused laser speckle," Appl. Opt. 34, 5799-5808 (1995).
8. J. M. Diazdelacruz, "Multiwindowed defocused electronic speckle photographic system for tilt measurement", Appl. Opt., 44, 2250-57, (2005).
9. D. Mendlovic, M. Ozaktas, Zeev Zalevsky, The fractional Fourier transform with applications in optics and signal processing, Wiley, Chichester U.K., 2001.
10. D. Mendlovic, M. Ozaktas, and A. W. Lohmann, "Graded-index media, Wigner-distribution functions, and the fractional Fourier transform", Appl. Opt. 33, 6188-93, 1994.
11. D. Mendlovic, H. M. Ozatkas, "Fractional Fourier transformations and their optical implementations", J. Opt. Soc. Am., 10, Part I. 1875-81, Part II. 2522-31, 1993.
12. A. W. Lohmann, "Image rotation, Wigner rotation and the fractional Fourier transformation", J. Opt. Soc. Am., 10, 2181-86, 1993.
13. R. G. Dorsch, "Fractional Fourier transform of variable order based on a modular lens system", Appl. Opt., 34, 6016-20, 1995.
14. S. Abe, J.T. Sheridan, "Generalization of the fractional Fourier transformation to an arbitrary linear lossless transformation: an operator approach," J. Phys. A, 27, 4179-4187 1994.
15. S. Abe, J.T. Sheridan, "Optical operations on wave functions as the Abelian subgroups of the special affine Fourier transformation," Opt. Lett. 19, 1801-1803 1994.
16. A. W. Lohmann, "A fake zoom lens for fractional Fourier experiments", Opt. Comm., 115, 427-443, 1995.
17. L. Z. Cai, Y. Q. Wang, "Optical Implementation of scale invariant fractional Fourier transform of continuously variable orders with a two-lens system", Opt. Comm., 34, 249-252, 2002.
18. J. T. Sheridan, R. Patten, "Fractional Fourier Speckle Photography: Motion Detection and the Optical Fractional Fourier Transformation", Optik, 111, No. 7, 329-331, 2000.
19. J. T. Sheridan, R. Patten, Holographic Interferometry and the Fractional Fourier Transformation, Opt. Lett., 25, 448-450, (2000).
20. J. T. Sheridan, B.M. Hennelly, D. Kelly, "Motion dectection, the Wigner Distribution Function and the optical fractional Fourier transform", Opt. Lett., Vol 28, No. 11, 884-886, 2003.
21. D. P. Kelly, B. M. Hennelly, J. T. Sheridan, "Magnitude and direction of motion with speckle correlation and the optical fractional Fourier transform," Appl Opt, 44, 2720-2727, 2005.
22. D. P. Kelly, B. M. Hennelly, J. T. Sheridan, "Speckle correlation and the Fractional Fourier Transform" in Optical Information Systems II, Bahram Javidi, ed., Proc. SPIE, 5557, 2004.
23. Collins, S.A., Lens system diffraction integral written in terms of matrix optics, J. Opt. Soc. Am., 60, 1168-77, (1970).
24. Y. Liu, D. P. Kelly, B. M. Hennelly, J. E. Ward, R. F. Patten, J. T. Sheridan, "Linear Canonical Transforms, and Speckle Based Metrology" in Optical Sensing, Gerald O'Sullivan, Hugh Byrne, Enda McGlynn, eds, Proc SPIE, 5826, 2005