메뉴 건너뛰기




Volumn 17, Issue 12, 2000, Pages 2368-2381

Fractional Fourier transforms in two dimensions

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; HAMILTONIANS; MATRIX ALGEBRA; OPTICAL SYSTEMS;

EID: 0008639393     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.17.002368     Document Type: Article
Times cited : (50)

References (52)
  • 1
    • 0027652515 scopus 로고
    • Fractional Fourier transforms and their implementations. I
    • D. Mendlovic and H. M. Ozaktas, “Fractional Fourier transforms and their implementations. I,” J. Opt. Soc. Am. A 10 1875–1881 (1993)
    • (1993) J. Opt. Soc. Am. A , vol.10 , pp. 1875-1881
    • Mendlovic, D.1    Ozaktas, H.M.2
  • 2
    • 0027740848 scopus 로고
    • Mendlovic, “Fractional Fourier transforms and their implementations. 11,”J
    • H. M. Ozaktas and D. Mendlovic, “Fractional Fourier transforms and their implementations. 11,”J. Opt. Soc. Am. A 10, 2522–2531 (1993)
    • (1993) Opt. Soc. Am. A , vol.10 , pp. 2522-2531
    • Ozaktas, H.M.1
  • 3
    • 0027641018 scopus 로고
    • Fractional Fourier transforms of fractional order and their optical interpretation
    • H. M. Ozaktas and D. Mendlovic, “Fractional Fourier transforms of fractional order and their optical interpretation,” Opt. Commun. 101, 163–169 (1993)
    • (1993) Opt. Commun. , vol.101 , pp. 163-169
    • Ozaktas, H.M.1    Mendlovic, D.2
  • 4
    • 21344493264 scopus 로고
    • Generalization of the fractional Fourier transformation to an arbitrary linear lossless transformation: An operator approach
    • S. Abe and 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)
    • (1994) J. Phys. A , vol.27 , pp. 4179-4187
    • Abe, S.1    Sheridan, J.T.2
  • 7
    • 0006053360 scopus 로고    scopus 로고
    • Significance of phase and amplitude in the Fourier domain
    • A. W. Lohmann, D. Mendlovic, and G. Shabtay, “Significance of phase and amplitude in the Fourier domain,” J. Opt. Soc. Am. A 14, 2901–2904 (1997)
    • (1997) J. Opt. Soc. Am. A , vol.14 , pp. 2901-2904
    • Lohmann, A.W.1    Mendlovic, D.2    Shabtay, G.3
  • 8
    • 77957719167 scopus 로고    scopus 로고
    • Introduction to the fractional Fourier transform and its applications
    • H. M. Ozaktas, M. Alper Kutay, and D. Mendlovic, “Introduction to the fractional Fourier transform and its applications,” Adv. Imaging Electron Phys. 106, 239–291 (1999).
    • (1999) Adv. Imaging Electron Phys. , vol.106 , pp. 239-291
    • Ozaktas, H.M.1    Alper Kutay, M.2    Mendlovic, D.3
  • 9
    • 0029716077 scopus 로고    scopus 로고
    • Discrete fractional Fourier transform
    • Institute of Electrical and Electronics Engineers, Piscataway, N.J
    • S. C. Pei and M. H. Yeh, “Discrete fractional Fourier transform,” in Proceedings of IEEE International Symposium on Circuits Systems (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1996), pp. 536–539
    • (1996) Proceedings of IEEE International Symposium on Circuits Systems , pp. 536-539
    • Pei, S.C.1    Yeh, M.H.2
  • 10
    • 0031190361 scopus 로고    scopus 로고
    • Improved discrete fractional Fourier transform
    • S. C. Pei and M. H. Yeh, “Improved discrete fractional Fourier transform,” Opt. Lett. 22, 1047–1049 (1997)
    • (1997) Opt. Lett. , vol.22 , pp. 1047-1049
    • Pei, S.C.1    Yeh, M.H.2
  • 11
    • 0032072124 scopus 로고    scopus 로고
    • Two dimensional discrete fractional Fourier transform
    • S. C. Pei and M. H. Yeh, “Two dimensional discrete fractional Fourier transform,” Signal Process. 67, 99–108 (1998)
    • (1998) Signal Process , vol.67 , pp. 99-108
    • Pei, S.C.1    Yeh, M.H.2
  • 12
    • 0032669485 scopus 로고    scopus 로고
    • Discrete fractional Fourier transform based on orthogonal projections
    • S.-C. Pei, M.-H. Yeh, and C.-C. Tseng, “Discrete fractional Fourier transform based on orthogonal projections,” IEEE Trans. Signal Process. 47, 1335–1347 (1999).
    • (1999) IEEE Trans. Signal Process. , vol.47 , pp. 1335-1347
    • Pei, S.-C.1    Yeh, M.-H.2    Tseng, C.-C.3
  • 13
    • 0028483920 scopus 로고
    • A simple realization of fractional Fourier transform and relation to harmonic oscillator Greens function
    • G. S. Agarwal and R. Simon, “A simple realization of fractional Fourier transform and relation to harmonic oscillator Green’s function,” Opt. Commun. 110, 23–26 (1994).
    • (1994) Opt. Commun. , vol.110 , pp. 23-26
    • Agarwal, G.S.1    Simon, R.2
  • 15
    • 0034132255 scopus 로고    scopus 로고
    • Structure of the set of paraxial optical systems
    • R. Simon and K. B. Wolf, “Structure of the set of paraxial optical systems,” J. Opt. Soc. Am. A 17, 342–355 (2000).
    • (2000) J. Opt. Soc. Am. A , vol.17 , pp. 342-355
    • Simon, R.1    Wolf, K.B.2
  • 16
    • 0020102107 scopus 로고
    • First-order optics—a canonical operator representation: Lossless systems
    • M. Nazarathy and J. Shamir, “First-order optics—a canonical operator representation: lossless systems,” J. Opt. Soc. Am. 72, 356–364 (1982).
    • (1982) J. Opt. Soc. Am. , vol.72 , pp. 356-364
    • Nazarathy, M.1    Shamir, J.2
  • 17
    • 0001332130 scopus 로고
    • Realisation of first order optical systems using thin lenses
    • E. C. G. Sudarshan, N. Mukunda, and R. Simon, “Realisation of first order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985)
    • (1985) Opt. Acta , vol.32 , pp. 855-872
    • Sudarshan, E.C.G.1    Mukunda, N.2    Simon, R.3
  • 20
    • 25344431927 scopus 로고
    • Gaussian pure states in quantum mechanics and the symplectic group
    • R. Simon, E. C. G. Sudarshan, and N. Mukunda, “Gaussian pure states in quantum mechanics and the symplectic group,” Phys. Rev. A 37, 2028–2038 (1988).
    • (1988) Phys. Rev. A , vol.37 , pp. 2028-2038
    • Simon, R.1    Sudarshan, E.C.G.2    Mukunda, N.3
  • 22
    • 36849112629 scopus 로고
    • Linear canonical transformations and their unitary representation
    • M. Moshinsky and C. Quesne, “Linear canonical transformations and their unitary representation,” J. Math. Phys. 12, 1772–1780 (1971)
    • (1971) J. Math. Phys. , vol.12 , pp. 1772-1780
    • Moshinsky, M.1    Quesne, C.2
  • 23
    • 36849112326 scopus 로고
    • Canonical transformations and matrix elements
    • M. Moshinsky and C. Quesne, “Canonical transformations and matrix elements,” J. Math. Phys. 12, 1780–1783 (1971)
    • (1971) J. Math. Phys. , vol.12 , pp. 1780-1783
    • Moshinsky, M.1    Quesne, C.2
  • 25
    • 27644491636 scopus 로고
    • Root and power transformations in optics
    • J. Shamir and N. Cohen, “Root and power transformations in optics,” J. Opt. Soc. Am. A 12, 2415–2423 (1995).
    • (1995) J. Opt. Soc. Am. A , vol.12 , pp. 2415-2423
    • Shamir, J.1    Cohen, N.2
  • 27
    • 0000750528 scopus 로고
    • Anisotropic Gaussian Schell-model beams: Passage through first order systems and associated invariants
    • R. Simon, E. C. G. Sudarshan, and N. Mukunda, “Anisotropic Gaussian Schell-model beams: passage through first order systems and associated invariants,” Phys. Rev. A 31, 2419–2434 (1985).
    • (1985) Phys. Rev. A , vol.31 , pp. 2419-2434
    • Simon, R.1    Sudarshan, E.C.G.2    Mukunda, N.3
  • 28
    • 0001679261 scopus 로고
    • Quantum noise matrix for multimode systems: U(n) invariance, squeezing, and normal forms
    • R. Simon, N. Mukunda, and B. Dutta, “Quantum noise matrix for multimode systems: U(n) invariance, squeezing, and normal forms,” Phys. Rev. A 49, 1567–1583 (1994).
    • (1994) Phys. Rev. A , vol.49 , pp. 1567-1583
    • Simon, R.1    Mukunda, N.2    Dutta, B.3
  • 29
    • 0037545183 scopus 로고
    • Optical systems for rotating a beam
    • P. M. Mejías, H. Weber, R. Martínez-Herrero, and A. González-Urena, eds. (Sociedad Españila de Optica, Madrid
    • G. Nemes and A. G. Kostenbauder, “Optical systems for rotating a beam,” in Laser Beam Characterization, P. M. Mejías, H. Weber, R. Martínez-Herrero, and A. González-Urena, eds. (Sociedad Españila de Optica, Madrid, 1993), pp. 99–109.
    • (1993) Laser Beam Characterization , pp. 99-109
    • Nemes, G.1    Kostenbauder, A.G.2
  • 30
    • 0001515953 scopus 로고
    • Immersion of the Fourier transform in a continuous group of functional transformations
    • E. U. Condon, “Immersion of the Fourier transform in a continuous group of functional transformations,” Proc. Natl. Acad. Sci. USA 23, 158–164 (1937).
    • (1937) Proc. Natl. Acad. Sci. USA , vol.23 , pp. 158-164
    • Condon, E.U.1
  • 31
    • 0010869715 scopus 로고
    • Hamiltons theory of turns and a new geometrical representation for polarization optics,” Pramana
    • R. Simon, N. Mukunda, and E. C. G. Sudarshan, “Hamilton’s theory of turns and a new geometrical representation for polarization optics,” Pramana J. Phys. 32, 769–792 (1989).
    • (1989) J. Phys. , vol.32 , pp. 769-792
    • Simon, R.1    Mukunda, N.2    Sudarshan, E.C.G.3
  • 32
    • 0001543889 scopus 로고
    • Minimal three component SU(2) gadget for polarization optics
    • R. Simon and N. Mukunda, “Minimal three component SU(2) gadget for polarization optics,” Phys. Lett. A 143, 165–169 (1990)
    • (1990) Phys. Lett. A , vol.143 , pp. 165-169
    • Simon, R.1    Mukunda, N.2
  • 36
    • 0000236590 scopus 로고    scopus 로고
    • Nonseparable two-dimensional fractional Fourier transform
    • A. Sahin, M. Alper Kutay, and H. M. Ozaktas, “Nonseparable two-dimensional fractional Fourier transform,” Appl. Opt. 37, 5444–5453 (1998).
    • (1998) Appl. Opt. , vol.37 , pp. 5444-5453
    • Sahin, A.1    Alper Kutay, M.2    Ozaktas, H.M.3
  • 37
    • 0000881252 scopus 로고    scopus 로고
    • Jones-matrix formalism As a representation of the Lorentz group
    • D. Han, Y. S. Kim, and M. E. Noz, “Jones-matrix formalism As a representation of the Lorentz group,” J. Opt. Soc. Am. A 14, 2290–2298 (1997).
    • (1997) J. Opt. Soc. Am. A , vol.14 , pp. 2290-2298
    • Han, D.1    Kim, Y.S.2    Noz, M.E.3
  • 38
    • 0037570555 scopus 로고
    • The SO(N, 1) Wigner rotation as an SL(2, R) problem
    • R. Simon and N. Mukunda, “The SO(n, 1) Wigner rotation as an SL(2, R) problem,” Found. Phys. Lett. 3, 425–434 (1990).
    • (1990) Found. Phys. Lett. , vol.3 , pp. 425-434
    • Simon, R.1    Mukunda, N.2
  • 39
    • 0029277263 scopus 로고
    • Coherent-mode decomposition of general anisotropic Gaussian Schell-model beams
    • 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).
    • (1995) J. Opt. Soc. Am. A , vol.12 , pp. 560-569
    • Sundar, K.1    Mukunda, N.2    Simon, R.3
  • 40
    • 0027652533 scopus 로고
    • Twisted Gaussian Schell-model beams: I. Symmetry structure and normalmode spectrum
    • R. Simon, K. Sundar, and N. Mukunda, “Twisted Gaussian Schell-model beams: I. Symmetry structure and normalmode spectrum,” J. Opt. Soc. Am. A 10, 2008–2016 (1993).
    • (1993) J. Opt. Soc. Am. A , vol.10 , pp. 2008-2016
    • Simon, R.1    Sundar, K.2    Mukunda, N.3
  • 41
    • 0028444203 scopus 로고
    • Photon distribution in two-mode squeezed coherent states with complex displacement and squeeze parameters
    • M. Selvadoray, M. Sanjay Kumar, and R. Simon, “Photon distribution in two-mode squeezed coherent states with complex displacement and squeeze parameters,” Phys. Rev. A 49, 4957–4967 (1994).
    • (1994) Phys. Rev. A , vol.49 , pp. 4957-4967
    • Selvadoray, M.1    Sanjay Kumar, M.2    Simon, R.3
  • 42
    • 77958407025 scopus 로고
    • The fractional order Fourier transform and its application to quantum mechanics
    • V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” J. Inst. Math. Its Appl. 25, 241–265 (1980)
    • (1980) J. Inst. Math. Its Appl. , vol.25 , pp. 241-265
    • Namias, V.1
  • 43
    • 84894009925 scopus 로고
    • General thin-lens action on spatial intensity distribution behaves as non-integer powers of Fourier transform
    • of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C
    • L. F. Ludwig, “General thin-lens action on spatial intensity distribution behaves as non-integer powers of Fourier transform,” in Spatial Light Modulators and Applications, Vol. 8 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 173–176.
    • (1988) Spatial Light Modulators and Applications , vol.8 , pp. 173-176
    • Ludwig, L.F.1
  • 44
    • 0002839282 scopus 로고
    • On angular momentum
    • L. C. Biedenharn and H. van Dam, eds. (Academic, New York
    • See, e.g., J. Schwinger, “On angular momentum,” in Quantum Theory of Angular Momentum, L. C. Biedenharn and H. van Dam, eds. (Academic, New York, 1965), pp. 229–279.
    • (1965) Quantum Theory of Angular Momentum , pp. 229-279
    • See, E.G.1    Schwinger, J.2
  • 46
    • 0000328798 scopus 로고
    • Analogies between two optical systems (Photon beam splitters and laser beams) and two quantum systems (the two-dimensional oscillator and the two-dimensional hydrogen atom)
    • S. Danakas and P. K. Aravind, “Analogies between two optical systems (photon beam splitters and laser beams) and two quantum systems (the two-dimensional oscillator and the two-dimensional hydrogen atom),” Phys. Rev. A 45, 1973–1977 (1992).
    • (1992) Phys. Rev. A , vol.45 , pp. 1973-1977
    • Danakas, S.1    Aravind, P.K.2
  • 47
    • 0032184596 scopus 로고    scopus 로고
    • Free-space diffraction and the fractional Fourier transform
    • C. J. R. Sheppard, “Free-space diffraction and the fractional Fourier transform,” J. Mod. Opt. 45, 2097–2103 (1998).
    • (1998) J. Mod. Opt. , vol.45 , pp. 2097-2103
    • Sheppard, C.J.R.1
  • 48
    • 0038450087 scopus 로고
    • Canonical transforms for paraxial wave optics
    • J. Sánchez-Mondragón and K. B. Wolf, eds., Vol. 250 of Lecture Notes in Physics (Springer-Verlag, Heidelberg
    • O. Castanos, E. Lopez-Moreno, and K. B. Wolf, “Canonical transforms for paraxial wave optics,” in Lie Methods in Optics, J. Sánchez-Mondragón and K. B. Wolf, eds., Vol. 250 of Lecture Notes in Physics (Springer-Verlag, Heidelberg, 1986), pp. 159–182
    • (1986) Lie Methods in Optics , pp. 159-182
    • Castanos, O.1    Lopez-Moreno, E.2    Wolf, K.B.3
  • 49
    • 0037570557 scopus 로고
    • The symplectic groups, their parameterization and cover
    • J. Sánchez-Mondragón and K. B. Wolf, eds., Vol. 250 of Lecture Notes in Physics, Springer-Verlag, Heidelberg
    • K. B. Wolf, “The symplectic groups, their parameterization and cover,” in Lie Methods in Optics, J. Sánchez-Mondragón and K. B. Wolf, eds., Vol. 250 of Lecture Notes in Physics (Springer-Verlag, Heidelberg, 1986), pp. 227–238.
    • (1986) Lie Methods in Optics , pp. 227-238
    • Wolf, K.B.1
  • 51
    • 0000136245 scopus 로고    scopus 로고
    • Poincaré-sphere equivalent for light beams containing orbital angular momentum
    • M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24, 430–432 (1999).
    • (1999) Opt. Lett. , vol.24 , pp. 430-432
    • Padgett, M.J.1    Courtial, J.2
  • 52
    • 0008913550 scopus 로고    scopus 로고
    • SU(2) structure of the Poincaré sphere for light beams with orbital angular momentum
    • G. S. Agarwal, “SU(2) structure of the Poincaré sphere for light beams with orbital angular momentum,” J. Opt. Soc. Am. A 16, 2914–2916 (1999).
    • (1999) J. Opt. Soc. Am. A , vol.16 , pp. 2914-2916
    • Agarwal, G.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.