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               22. K. B. Wolf, Geometric Optics in Phase Space, Springer, New York, 2004.
               23. T. Alieva and M. J. Bastiaans, “Alternative representation of the linear canonical
                  integral transform,” Opt. Lett. 30: 3302–3304 (2005).
               24. R. Simon, K. Sundar, and N. Mukunda, “Twisted Gaussian Schell-model beams.
                  I. Symmetry structure and normal-mode spectrum,” J. Opt. Soc. Am. A 10: 2008–
                  2016 (1993).
               25. R. Simon and G. S. Agarwal, “Wigner representation of Laguerre-Gaussian
                  beams,” Opt. Lett. 25: 1313–1315 (2000).
               26. R. Simon and N. Mukunda, “Optical phase space, Wigner representation, and
                  invariant quality parameters,” J. Opt. Soc. Am. A 17: 2440–2463 (2000).
               27. T. Alieva and M. J. Bastiaans, “Dynamic and geometric phase accumulation by
                  Gaussian-type modes in first-order optical systems,” Opt. Lett. 33: 1659–1661
                  (2008).
               28. A. Lohmann, “Image rotation, Wigner rotation, and the fractional order Fourier
                  transform,” J. Opt. Soc. Am. A 10: 2181–2186 (1993).
               29. T. Alieva, V. Lopez, F. Agullo-Lopez, and L. B. Almeida, “The fractional Fourier
                  transform in optical propagation problems,” J. Mod. Opt. 41: 1037–1044 (1994).
               30. J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Gyrator transform: Properties and
                  applications,” Opt. Express 15: 2190–2203 (2007).
               31. J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Experimental implementation of the
                  gyrator transform,” J. Opt. Soc. Am. A 24: 3135–3139 (2007).
               32. J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Applications of gyrator transform
                  for image processing,” Opt. Comm. 278: 279–284 (2007).
               33. J. A. Rodrigo, “First-Order Optical Systems in Information Processing and Op-
                  tronic Devices,” Ph.D. thesis, Universidad Complutense de Madrid, Spain,
                  2008.
               34. H.-Y. Fan and H.-L. Lu, “Eigenmodes of fractional Hankel transform derived
                  by the entangled-state method,” Opt. Lett. 28: 680–683 (2003).
               35. E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,”
                  J. Opt. A.: Pure Appl. Opt. 6: S157–S161 (2004).
               36. M. J. Bastiaans and T. Alieva, “First-order optical systems with unimodular
                  eigenvalues,” J. Opt. Soc. Am. A 23: 1875–1883 (2006).
               37. M. J. Bastiaans and T. Alieva, “Classification of lossless first-order optical sys-
                  tems and the linear canonical transformation,” J. Opt. Soc. Am. A 24: 1053–1062
                  (2007).
               38. T. Alieva, “Fractional Fourier transform as a tool for investigation of fractal
                  objects,” J. Opt. Soc. Am. A 13: 1189–1192 (1996).
               39. T. Alieva and M. J. Bastiaans, “Mode mapping in paraxial lossless optics,” Opt.
                  Lett. 30: 1461–1463 (2005).
               40. A. W¨unsche, “General Hermite and Laguerre two-dimensional polynomials,”
                  J. Phys. A: Math. Gen. 33: 1603–1629 (2000).
               41. T. Alieva M. J. Bastiaans, “Orthonormal mode sets for the two-dimensional
                  fractional Fourier transformation,” Opt. Lett. 32: 1226–1228 (2007).
               42. M. J. Bastiaans and T. Alieva, “Propagation law for the generating function of
                  Hermite-Gaussian-type modes in first-order optical systems,” Opt. Express 13:
                  1107–1112 (2005).
               43. M. J. Padgett and J. Courtial, “Poincar´e-sphere equivalent for light beams con-
                  taining orbital angular momentum,” Opt. Lett. 24: 430–432 (1999).
               44. G. F. Calvo, “Wigner representation and geometric transformations of optical
                  orbital angular momentum spatial modes,” Opt. Lett. 30: 1207–1209 (2005).
               45. G. S. Agarwal, “SU(2) structure of the Poincar´e sphere for light beams with
                  orbital angular momentum,” Opt. Lett. 16: 2914–2916 (1999).
               46. D. Mendlovic, Y. Bitran, R. G. Dorsh, C. Ferreira, J. Garc´ıa, and H. M. Oza-
                  ktaz, “Anamorphic fractional Fourier transform: Optical implementation and
                  applications,” Appl. Opt. 34: 7451–7456 (1995).
               47. J. Garc´ıa, R. G. Dorsch, A. W. Lohmann, C. Ferreira, and Z. Zalevsky, “Flexible
                  optical implementation of fractional Fourier transform processors, applications
                  to correlation and filtering,” Opt. Comm. 133: 393–400 (1997).
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