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102   Chapter Three



          Acknowledgments
               I am pleased to express my gratitude to M. J. Bastiaans, J. A. Rodrigo,
               and M. L. Calvo for fruitful collaboration in many of the discussed
               topics and to E. G. Abramochkin for careful reading of the manuscript
               and valuable comments. I also thank J. A. Rodrigo and A. Camara
               Iglesias for the help in figure preparation.




          References
                1. Jr. S. A. Collins, “Lens-system diffraction integral written in terms of matrix
                  optics,” J. Opt. Soc. Am. 60: 1168–1177 (1970).
                2. M. Moshinsky and C. Quesne, “Linear canonical transformations and their
                  unitary representations,” J. Math. Phys. 12: 1772–1780 (1971).
                3. K. B. Wolf, “Integral Transforms in Sience and Engineering,” Plenum Publishing
                  Corp., New York, 1979.
                4. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform
                  with Applications in Optics and Signal Processing, Wiley, New York, 2001.
                5. A. Torre, Linear Ray and Wave Optics in Phase Space, Elsevier, Amsterdam, 2005.
                6. T. Alieva, M. J. Bastiaans, and M. L. Calvo, “Fractional transforms in optical in-
                  formation processing,” EURASIP J. Appl. Signal Process. 2005: 1498–1519 (2005).
                7. T. Alieva and M. J. Bastiaans, “Properties of the linear canonical integral trans-
                  formation,” J. Opt. Soc. Am. A 24: 3658–3665 (2007).
                8. T. Alieva, “First-order optical systems for information processing,” in A. Friberg
                  and R. Dandliker (eds.), Advances in Information Optics and Photonics, SPIE,
                  Bellingham, Wash., 2008, pp. 1–26.
                9. A. Van der Lugt (ed.), Optical Signal Processing, Wiley, New York, 1992.
               10. J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill, New York, 1996.
                11. V. Namias, “The fractional order Fourier transform and its applications to quan-
                  tum mechanics,” J. Inst. Math. and Appl. 25: 241–265 (1980).
               12. L. B. Almeida, “The fractional Fourier transform and time-frequency represen-
                  tations,” IEEE Trans. Sign. Proc. 42: 3084–3091 (1994).
               13. D. Mendlovic and H. M. Ozaktas, “Fractional Fourier transforms and their
                  optical implementation: I,” J. Opt. Soc. Am. A 10: 1875–1881 (1993).
               14. H. M. Ozaktas and D. Mendlovic, “Fractional Fourier transforms and their
                  optical implementation: II,” J. Opt. Soc. Am. A 10: 2522–2531 (1993).
               15. J. Garc´ıa, D. Mendlovic, Z. Zalevsky, and A. W. Lohmann, “Space-variant si-
                  multaneous detection of several objects by the use of multiple anamorphic
                  fractional-Fourier transform filters,” Appl. Opt. 35: 3945–3952 (1996).
               16. G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-
                  random phase encoding in the fractional Fourier domain,” Opt. Lett. 25: 887–889
                  (2000).
               17. N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption
                  using a localized fractional Fourier transform,” Opt. Engin. 42: 3566–3571 (2003).
               18. B. Hennelly and J. T. Sheridan, “Fractional Fourier transform-based image en-
                  cryption: Phase retrieval algorithm,” Opt. Comm. 226: 61–80 (2003).
               19. S. Q. Zhang and M. A. Karim, “Fractional correlation filter for fuzzy associative
                  memories,” Opt. Eng. 41: 126–129 (2002).
               20. K. Sundar, N. Mukunda, and R. Simon, “Coherent mode decomposition of
                  general anisotropic Gaussian Schell-model beams,” J. Opt. Soc. Am. A 12: 560-
                  569 (1995).
               21. R. Simon and K. B. Wolf, “Structure of the set of paraxial optical systems,”
                  J. Opt. Soc. Am. A 17: 342–355 (2000).
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