메뉴 건너뛰기




Volumn , Issue , 2005, Pages

Linear Ray and Wave Optics in Phase Space

(1)  Torre, Amalia a  

a NONE

Author keywords

[No Author keywords available]

Indexed keywords


EID: 85013778509     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-0-444-51799-9.X5000-6     Document Type: Book
Times cited : (115)

References (655)
  • 2
    • 77956709047 scopus 로고
    • The light ray (contribution to the theory of the light field)
    • Rozenberg G.V. The light ray (contribution to the theory of the light field). Sov. Phys. Usp. 1977, 20:55-79.
    • (1977) Sov. Phys. Usp. , vol.20 , pp. 55-79
    • Rozenberg, G.V.1
  • 3
    • 0002564471 scopus 로고
    • General Principles of Geometric Optics
    • Mc-Graw Hill, New York, ch. 1; and references therein, M. Bass, E.W. Van Stryland, D.R. Williams, W.L. Wolfe (Eds.)
    • Goodman D.S. General Principles of Geometric Optics. Handbook of Optics 1995, Mc-Graw Hill, New York, ch. 1; and references therein. 2nd ed. M. Bass, E.W. Van Stryland, D.R. Williams, W.L. Wolfe (Eds.).
    • (1995) Handbook of Optics
    • Goodman, D.S.1
  • 9
    • 0001017624 scopus 로고
    • Sur la théorie de la variation des constantes arbitraires
    • Liouville J. Sur la théorie de la variation des constantes arbitraires. Journ. de Math. Pures et Appl. 1838, 3:342-349.
    • (1838) Journ. de Math. Pures et Appl. , vol.3 , pp. 342-349
    • Liouville, J.1
  • 10
    • 0042301473 scopus 로고
    • Cambridge Univ. Press, Redwood City
    • Synge J.L. Geometrical Optics 1937, Cambridge Univ. Press, Redwood City.
    • (1937) Geometrical Optics
    • Synge, J.L.1
  • 21
    • 84882114157 scopus 로고
    • The modern development of Hamiltonian Optics
    • ch. 1, North-Holland, Berlin, E. Wolf (Ed.)
    • Pegis R.J. The modern development of Hamiltonian Optics. Progress in Optics 1963, 1-29. ch. 1, North-Holland, Berlin. E. Wolf (Ed.).
    • (1963) Progress in Optics , pp. 1-29
    • Pegis, R.J.1
  • 22
    • 77956980133 scopus 로고
    • Hamiltonian theory of beam propagation
    • ch. 6, North-Holland, Amsterdam, E. Wolf (Ed.)
    • Arnand J.A. Hamiltonian theory of beam propagation. Progress in Optics 1973, 247-304. ch. 6, North-Holland, Amsterdam. E. Wolf (Ed.).
    • (1973) Progress in Optics , pp. 247-304
    • Arnand, J.A.1
  • 23
    • 0042977563 scopus 로고
    • The Hamiltonian formulation of optics
    • Sekiguchi T., Wolf K.B. The Hamiltonian formulation of optics. Am. J. Phys. 1987, 55:830-835.
    • (1987) Am. J. Phys. , vol.55 , pp. 830-835
    • Sekiguchi, T.1    Wolf, K.B.2
  • 24
    • 0012684770 scopus 로고
    • Generalization of Hamilton's formalism for geometrical optics
    • Alonso M.A., Forbes G.W. Generalization of Hamilton's formalism for geometrical optics. J. Opt. Soc. Am. A 1995, 12:2744-2752.
    • (1995) J. Opt. Soc. Am. A , vol.12 , pp. 2744-2752
    • Alonso, M.A.1    Forbes, G.W.2
  • 25
    • 84882149983 scopus 로고
    • Gauthier-Villars, Amsterdam
    • de Fermat P. Œvreus 1891, 354. Gauthier-Villars, Amsterdam.
    • (1891) Œvreus , pp. 354
    • de Fermat, P.1
  • 26
    • 84882083352 scopus 로고
    • An extension of Fermat's theorem
    • Hopkins H.H. An extension of Fermat's theorem. Opt. Acta 1970, 17:223-225.
    • (1970) Opt. Acta , vol.17 , pp. 223-225
    • Hopkins, H.H.1
  • 27
    • 27144556240 scopus 로고
    • Generalized Fermat principle
    • Newcomb W.A. Generalized Fermat principle. Am. J. Phys. 1983, 51:338-340.
    • (1983) Am. J. Phys. , vol.51 , pp. 338-340
    • Newcomb, W.A.1
  • 28
    • 84975624451 scopus 로고
    • Hamiltonian formulation of geometrical anisotropic optics
    • Rivera A.L., Chumakov S.M., Wolf K.B. Hamiltonian formulation of geometrical anisotropic optics. J. Opt. Soc. Am. 1995, A12:1380-1389.
    • (1995) J. Opt. Soc. Am. , vol.A12 , pp. 1380-1389
    • Rivera, A.L.1    Chumakov, S.M.2    Wolf, K.B.3
  • 29
    • 3943057500 scopus 로고    scopus 로고
    • Fermat's principle, the general eikonal equation, and space geometry in a static anisotropic medium
    • Shen W., Zhang J., Wang S., Zhu S. Fermat's principle, the general eikonal equation, and space geometry in a static anisotropic medium. J. Opt. Soc. Am. 1997, A14:2850-2854.
    • (1997) J. Opt. Soc. Am. , vol.A14 , pp. 2850-2854
    • Shen, W.1    Zhang, J.2    Wang, S.3    Zhu, S.4
  • 33
    • 0345055629 scopus 로고
    • Analogy between optical rays and nonrelativistic particle trajectories: a comment
    • Arnaud J.A. Analogy between optical rays and nonrelativistic particle trajectories: a comment. Am. J. Phys. 1976, 44:1067-1069.
    • (1976) Am. J. Phys. , vol.44 , pp. 1067-1069
    • Arnaud, J.A.1
  • 34
    • 0020750352 scopus 로고
    • Hamiltonian analysis of beams in an optical slab guide
    • Kahn W.K., Yang S. Hamiltonian analysis of beams in an optical slab guide. J. Opt. Soc. Am. 1983, 73:684-690.
    • (1983) J. Opt. Soc. Am. , vol.73 , pp. 684-690
    • Kahn, W.K.1    Yang, S.2
  • 36
    • 0037785501 scopus 로고
    • Fiber-optic analogies with mechanics
    • Black R.J., Ankiewicz A. Fiber-optic analogies with mechanics. Am. J. Phys. 1985, 53:554-563.
    • (1985) Am. J. Phys. , vol.53 , pp. 554-563
    • Black, R.J.1    Ankiewicz, A.2
  • 37
    • 84882203001 scopus 로고
    • Electron Optics
    • Suppl. Note # 1, California Univ. Press, London
    • Chako N., Blank B.B. Electron Optics. Mathematical Theory of Optics 1964, 373-410. Suppl. Note # 1, California Univ. Press, London.
    • (1964) Mathematical Theory of Optics , pp. 373-410
    • Chako, N.1    Blank, B.B.2
  • 39
    • 0004109271 scopus 로고
    • Princeton Univ. Press, Turnbridge Wells
    • Weyl H. The Classical Groups 1946, Princeton Univ. Press, Turnbridge Wells.
    • (1946) The Classical Groups
    • Weyl, H.1
  • 45
    • 33645820068 scopus 로고
    • Illustrative examples of the symplectic group
    • Kim Y.S., Noz M.E. Illustrative examples of the symplectic group. Am. J. Phys. 1983, 51:368-375.
    • (1983) Am. J. Phys. , vol.51 , pp. 368-375
    • Kim, Y.S.1    Noz, M.E.2
  • 47
    • 0007378611 scopus 로고
    • Lie series, Lie transformations, and their applications
    • Springer-Verlag, New York, ch. 3, J. Sánchcz Mondragón, K.B. Wolf (Eds.)
    • Steinberg S. Lie series, Lie transformations, and their applications. Lie Methods in Optics 1986, 45-104. Springer-Verlag, New York, ch. 3. J. Sánchcz Mondragón, K.B. Wolf (Eds.).
    • (1986) Lie Methods in Optics , pp. 45-104
    • Steinberg, S.1
  • 48
    • 36749113095 scopus 로고
    • Lie series and invariant functions for analytic symplectic maps
    • Dragt A.J., Finn J.M. Lie series and invariant functions for analytic symplectic maps. J. Math. Phys. 1976, 17:2215-2227.
    • (1976) J. Math. Phys. , vol.17 , pp. 2215-2227
    • Dragt, A.J.1    Finn, J.M.2
  • 49
    • 0003264910 scopus 로고
    • Lectures on nonlinear orbit dynamics
    • AIP, Berlin, R.A. Carrigan, F.R. Huson, M. Month (Eds.) Physics of High Energy Particle Accelerators
    • Dragt A.J. Lectures on nonlinear orbit dynamics. AIP Conf. Proc. 1982, 87:147-313. AIP, Berlin. R.A. Carrigan, F.R. Huson, M. Month (Eds.).
    • (1982) AIP Conf. Proc. , vol.87 , pp. 147-313
    • Dragt, A.J.1
  • 50
    • 84882156488 scopus 로고    scopus 로고
    • Lie Methods for Nonlinear Dynamics with Applications to Accelerator Physics
    • Lie Methods for Nonlinear Dynamics with Applications to Accelerator Physics. Univ. Maryland Phys. Dept. Rep. 1998.
    • (1998) Univ. Maryland Phys. Dept. Rep.
  • 51
    • 0020102825 scopus 로고
    • Lie algebraic theory of geometrical optics and optical aberrations
    • Dragt A.J. Lie algebraic theory of geometrical optics and optical aberrations. J. Opt. Soc. Am. 1982, 72:372-378.
    • (1982) J. Opt. Soc. Am. , vol.72 , pp. 372-378
    • Dragt, A.J.1
  • 52
    • 84882137501 scopus 로고    scopus 로고
    • Lie Algebraic Methods for Ray and Wave Optics
    • Lie Algebraic Methods for Ray and Wave Optics. Univ. Maryland Phys. Dept. Rep. 1998.
    • (1998) Univ. Maryland Phys. Dept. Rep.
  • 53
    • 0039615415 scopus 로고
    • Foundations of a Lie algebraic theory of geometrical optics
    • ch. 4, Springer-Verlag, New York, J. Sánchez Mondragon, K.B. Wolf (Eds.)
    • Dragt A.J., Forrest E., Wolf K.B. Foundations of a Lie algebraic theory of geometrical optics. Lie Methods in Optics 1986, 105-157. ch. 4, Springer-Verlag, New York. J. Sánchez Mondragon, K.B. Wolf (Eds.).
    • (1986) Lie Methods in Optics , pp. 105-157
    • Dragt, A.J.1    Forrest, E.2    Wolf, K.B.3
  • 54
    • 0011523537 scopus 로고
    • Symmetry in Lie optics
    • Wolf K.B. Symmetry in Lie optics. Ann. Phys. 1986, 172:1-25.
    • (1986) Ann. Phys. , vol.172 , pp. 1-25
    • Wolf, K.B.1
  • 55
    • 0009172051 scopus 로고
    • The group-theoretical treament of aberrating systems. I. Aligned lens systems in third aberration order
    • Navarro Saad M., Wolf K.B. The group-theoretical treament of aberrating systems. I. Aligned lens systems in third aberration order. J. Math. Phys. 1986, 27:1449-1457.
    • (1986) J. Math. Phys. , vol.27 , pp. 1449-1457
    • Navarro Saad, M.1    Wolf, K.B.2
  • 56
    • 33645167450 scopus 로고
    • The group-theoretical treament of aberrating systems. II. Axissymmetric inhomogeneous systems and fiber optics in third aberration order
    • Wolf K.B. The group-theoretical treament of aberrating systems. II. Axissymmetric inhomogeneous systems and fiber optics in third aberration order. J. Math. Phys. 1986, 27:1458-1465.
    • (1986) J. Math. Phys. , vol.27 , pp. 1458-1465
    • Wolf, K.B.1
  • 57
    • 0043108034 scopus 로고
    • The group-theoretical treament of aberrating systems. III. The classification of asymmetric aberrations
    • Wolf K.B. The group-theoretical treament of aberrating systems. III. The classification of asymmetric aberrations. J. Math. Phys. 1987, 28:2498-2507.
    • (1987) J. Math. Phys. , vol.28 , pp. 2498-2507
    • Wolf, K.B.1
  • 58
    • 0039023163 scopus 로고
    • Symmetry-adapted classification of aberrations
    • Wolf K.B. Symmetry-adapted classification of aberrations. J. Opt. Soc. Am. A 1988, 5:1226-1232.
    • (1988) J. Opt. Soc. Am. A , vol.5 , pp. 1226-1232
    • Wolf, K.B.1
  • 59
    • 0040708456 scopus 로고
    • Computation of maps for particle and light optics by scaling, splitting, and squaring
    • Dragt A.J. Computation of maps for particle and light optics by scaling, splitting, and squaring. Phys. Rev. Lett. 1995, 75:1946-1948.
    • (1995) Phys. Rev. Lett. , vol.75 , pp. 1946-1948
    • Dragt, A.J.1
  • 60
    • 0007347727 scopus 로고
    • Lie algebraic solution of linear differential equations
    • Wei J., Norman E. Lie algebraic solution of linear differential equations. J. Math Phys. 1963, 4:575-581.
    • (1963) J. Math Phys. , vol.4 , pp. 575-581
    • Wei, J.1    Norman, E.2
  • 61
    • 0042638530 scopus 로고
    • Exponential operators and parameter differentiation in quantum physics
    • Wilcox R.M. Exponential operators and parameter differentiation in quantum physics. J. Math. Phys. 1967, 8:962-982.
    • (1967) J. Math. Phys. , vol.8 , pp. 962-982
    • Wilcox, R.M.1
  • 62
    • 51249176676 scopus 로고
    • An algebraic view to the operatorial ordering and its applications to optics
    • Dattoli G., Gallardo J.C., Torre A. An algebraic view to the operatorial ordering and its applications to optics. Riv. Nuovo Cim. 1988, 11(11):1-79.
    • (1988) Riv. Nuovo Cim. , vol.11 , Issue.11 , pp. 1-79
    • Dattoli, G.1    Gallardo, J.C.2    Torre, A.3
  • 63
    • 0040158328 scopus 로고
    • A general view to Lie algebraic methods in applied mathematics, optics and transport systems for charged beam accelerators
    • World Sc., Berlin, G. Maino, L. Fronzoni, M. Pettini (Eds.)
    • Dattoli G., Torre A. A general view to Lie algebraic methods in applied mathematics, optics and transport systems for charged beam accelerators. Dynamical Symmetrics and Chaotic Behaviour in Physical Systems 1991, 21-89. World Sc., Berlin. G. Maino, L. Fronzoni, M. Pettini (Eds.).
    • (1991) Dynamical Symmetrics and Chaotic Behaviour in Physical Systems , pp. 21-89
    • Dattoli, G.1    Torre, A.2
  • 64
    • 0039862091 scopus 로고    scopus 로고
    • Evolution operator equations: integration with algebraic and finite-difference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory
    • Dattoli G., Ottaviani P.L., Torre A., Vázquez L. Evolution operator equations: integration with algebraic and finite-difference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory. Riv. Nuovo Cim. 1997, 20(2):1-133.
    • (1997) Riv. Nuovo Cim. , vol.20 , Issue.2 , pp. 1-133
    • Dattoli, G.1    Ottaviani, P.L.2    Torre, A.3    Vázquez, L.4
  • 69
    • 84967948419 scopus 로고
    • A group-theoretic treatment of Gaussian optics and 3rd-order aberrations
    • Wolf K.B. A group-theoretic treatment of Gaussian optics and 3rd-order aberrations. Lecture Note Phys. 1984, 201:133-136.
    • (1984) Lecture Note Phys. , vol.201 , pp. 133-136
    • Wolf, K.B.1
  • 70
    • 0022078298 scopus 로고
    • Applications of a factorization theorem for 9th-order aberration optics
    • Saad M.Navarro, Wolf K.B. Applications of a factorization theorem for 9th-order aberration optics. J. Symb. Comput. 1985, 1:235-239.
    • (1985) J. Symb. Comput. , vol.1 , pp. 235-239
    • Saad, M.N.1    Wolf, K.B.2
  • 71
    • 0039615416 scopus 로고
    • Group-classified polynomials of phase-space in higher-order aberration expansions
    • Wolf K.B., Krotzsch G. Group-classified polynomials of phase-space in higher-order aberration expansions. J. Symb. Comput. 1991, 12:673-693.
    • (1991) J. Symb. Comput. , vol.12 , pp. 673-693
    • Wolf, K.B.1    Krotzsch, G.2
  • 76
    • 0001017624 scopus 로고
    • Sur la théorie de la variation des constantes arbitraires
    • Liouville J. Sur la théorie de la variation des constantes arbitraires. Journ. de Math. Pure et Appl. 1838, 3:342-349.
    • (1838) Journ. de Math. Pure et Appl. , vol.3 , pp. 342-349
    • Liouville, J.1
  • 77
    • 0003437218 scopus 로고
    • ch. 9, Addison Wesley, New York
    • Goldstein H. Classical Mechanics 1980, 426-428. ch. 9, Addison Wesley, New York. 2nd ed.
    • (1980) Classical Mechanics , pp. 426-428
    • Goldstein, H.1
  • 79
    • 0003890009 scopus 로고
    • ch. 3, Van Nostrand-Reinhold, Princeton, New York
    • Marcuse D. Light Transmission Optics 1972, 112-124. ch. 3, Van Nostrand-Reinhold, Princeton, New York.
    • (1972) Light Transmission Optics , pp. 112-124
    • Marcuse, D.1
  • 80
    • 0015022785 scopus 로고
    • Compression of a bundle of light rays
    • Marcuse D. Compression of a bundle of light rays. Appl. Opt. 1971, 10:494-497.
    • (1971) Appl. Opt. , vol.10 , pp. 494-497
    • Marcuse, D.1
  • 81
    • 0016058502 scopus 로고
    • Calculation of the maximum optical coupling efficiency into multimode optical waveguides
    • Hudson M.C. Calculation of the maximum optical coupling efficiency into multimode optical waveguides. Appl. Opt. 1974, 13:1029-1033.
    • (1974) Appl. Opt. , vol.13 , pp. 1029-1033
    • Hudson, M.C.1
  • 83
    • 0037903165 scopus 로고
    • Laser beam analysis by geometrical optics
    • Adam Hilger, Bucharest, D.R. Hall, P.E. Jackson (Eds.)
    • Geothals W.A.E. Laser beam analysis by geometrical optics. The Physics and Technology of Laser Resonators 1989, 143-153. Adam Hilger, Bucharest. D.R. Hall, P.E. Jackson (Eds.).
    • (1989) The Physics and Technology of Laser Resonators , pp. 143-153
    • Geothals, W.A.E.1
  • 86
    • 0019282807 scopus 로고
    • Emittance and Brightness: Definitions and Measurements
    • Academic Press, New York, A. Septier (Ed.) Applied Charged Particle Optics
    • Lejeune C., Aubert J. Emittance and Brightness: Definitions and Measurements. Adv. Electron. & Electr. Physics, Suppl. 1980, 13A:159-259. Academic Press, New York. A. Septier (Ed.).
    • (1980) Adv. Electron. & Electr. Physics, Suppl. , vol.13 A , pp. 159-259
    • Lejeune, C.1    Aubert, J.2
  • 88
    • 0003739233 scopus 로고
    • 3 vols, Vol. 3, 1994, Academic Press, Orlando, Florida
    • Hawkes P.W., Kasper E. Principles of Electron Optics 1989, Vol. 1-2. 3 vols, Vol. 3, 1994, Academic Press, Orlando, Florida.
    • (1989) Principles of Electron Optics , vol.1-2
    • Hawkes, P.W.1    Kasper, E.2
  • 92
    • 0003589745 scopus 로고
    • Here, Lie operators and Lie transformations are introduced and exploited; also, both the classical and the quantum phase-space pictures are presented, the latter being conveyed through the Wigner distribution function., John Wiley & Sons, Oxford
    • Balesen R. Equilibrium and Nonequilibrium Statistical Mechanics 1975, Here, Lie operators and Lie transformations are introduced and exploited; also, both the classical and the quantum phase-space pictures are presented, the latter being conveyed through the Wigner distribution function., John Wiley & Sons, Oxford.
    • (1975) Equilibrium and Nonequilibrium Statistical Mechanics
    • Balesen, R.1
  • 93
    • 0003589741 scopus 로고
    • Liouville's theorem of classical statistical mechanics is discussed, whose correspondence to quantum statistical mechanics is as well elucidated through the Wigner distribution function., Springer-Verlag, New York
    • Toda M., Kubo R., Saitô N. Statistical Physics I. Equilibrium Statistical Mechanics 1983, Liouville's theorem of classical statistical mechanics is discussed, whose correspondence to quantum statistical mechanics is as well elucidated through the Wigner distribution function., Springer-Verlag, New York.
    • (1983) Statistical Physics I. Equilibrium Statistical Mechanics
    • Toda, M.1    Kubo, R.2    Saitô, N.3
  • 95
    • 0007378611 scopus 로고
    • Lie serie, Lie transformations, and their applications
    • Springer-Verlag, New York, ch. 3, J. Sánchez Mondragón, K.B. Wolf (Eds.)
    • Steinberg S. Lie serie, Lie transformations, and their applications. Lie Methods in Optics 1986, 45-104. Springer-Verlag, New York, ch. 3. J. Sánchez Mondragón, K.B. Wolf (Eds.).
    • (1986) Lie Methods in Optics , pp. 45-104
    • Steinberg, S.1
  • 97
    • 84960605603 scopus 로고
    • On a law of combination of operators
    • Campbell J.E. On a law of combination of operators. Proc. London Math. Soc. 1897, 29:14-32.
    • (1897) Proc. London Math. Soc. , vol.29 , pp. 14-32
    • Campbell, J.E.1
  • 98
    • 84960602359 scopus 로고
    • On the exponential theorem for a simply transitive continuous group, and the calculation of the finite equations from constants of structure
    • Baker H.F. On the exponential theorem for a simply transitive continuous group, and the calculation of the finite equations from constants of structure. Proc. London Math. Soc. 1901, 3:91-129.
    • (1901) Proc. London Math. Soc. , vol.3 , pp. 91-129
    • Baker, H.F.1
  • 100
    • 84940252991 scopus 로고
    • On the exponential solution of differential equations for a linear opcrator
    • Magnus W. On the exponential solution of differential equations for a linear opcrator. Comm. Pure Appl. Math. 1954, 7:649-673.
    • (1954) Comm. Pure Appl. Math. , vol.7 , pp. 649-673
    • Magnus, W.1
  • 101
    • 84980076829 scopus 로고
    • Espansions of the Campbell-Baker-Hausdorff formula by computer
    • Richtmeyer R.D., Greenspan S. Espansions of the Campbell-Baker-Hausdorff formula by computer. Comm. Pure Appl. Math. 1965, 18:107-108.
    • (1965) Comm. Pure Appl. Math. , vol.18 , pp. 107-108
    • Richtmeyer, R.D.1    Greenspan, S.2
  • 102
    • 0042638530 scopus 로고
    • Exponential operators and parameter differentiation in quantum physics
    • Wilcox R.M. Exponential operators and parameter differentiation in quantum physics. J. Math. Phys. 1967, 8:962-982.
    • (1967) J. Math. Phys. , vol.8 , pp. 962-982
    • Wilcox, R.M.1
  • 108
    • 0004020655 scopus 로고
    • ch. 5, and references therein, Cambridge University Press, Boston
    • Mandel L., Wolf E. Optical Coherence and Quantum Optics 1995, 287-307. ch. 5, and references therein, Cambridge University Press, Boston.
    • (1995) Optical Coherence and Quantum Optics , pp. 287-307
    • Mandel, L.1    Wolf, E.2
  • 109
  • 110
    • 0000572780 scopus 로고
    • Radiometry and Coherence
    • Walther A. Radiometry and Coherence. J. Opt. Soc. Am. 1968, 58:1256-1259.
    • (1968) J. Opt. Soc. Am. , vol.58 , pp. 1256-1259
    • Walther, A.1
  • 111
    • 0000273864 scopus 로고
    • Radiometry and Coherence
    • Walther A. Radiometry and Coherence. J. Opt. Soc. Am. 1973, 63:1622-1623.
    • (1973) J. Opt. Soc. Am. , vol.63 , pp. 1622-1623
    • Walther, A.1
  • 112
    • 0017926394 scopus 로고
    • Coherence and Radiometry
    • Wolf E. Coherence and Radiometry. J. Opt. Soc. Am. 1978, 68:6-17.
    • (1978) J. Opt. Soc. Am. , vol.68 , pp. 6-17
    • Wolf, E.1
  • 113
    • 0018309158 scopus 로고
    • On the existence of a radiance function for finite planar sources of arbitrary states of coherence
    • Friberg A.T. On the existence of a radiance function for finite planar sources of arbitrary states of coherence. J. Opt. Soc. Am. 1979, 69:192-197.
    • (1979) J. Opt. Soc. Am. , vol.69 , pp. 192-197
    • Friberg, A.T.1
  • 114
    • 84975650921 scopus 로고
    • Phase-space methods for partially coherent wavefields
    • Amer. Inst. Phys., Cambridge, M.A. Machado, L.M. Narducci (Eds.)
    • Friberg A.T. Phase-space methods for partially coherent wavefields. Optics in four dimensions 1981, 313-330. Amer. Inst. Phys., Cambridge. M.A. Machado, L.M. Narducci (Eds.).
    • (1981) Optics in four dimensions , pp. 313-330
    • Friberg, A.T.1
  • 115
    • 2942726818 scopus 로고
    • Photometry and coherence: wave aspects of the theory of radiation transport
    • Apresyan L.A., Kravtsov Yu.A. Photometry and coherence: wave aspects of the theory of radiation transport. Sov. Phys. Usp. 1984, 27:301-313.
    • (1984) Sov. Phys. Usp. , vol.27 , pp. 301-313
    • Apresyan, L.A.1    Kravtsov, Y.2
  • 116
    • 0022131204 scopus 로고
    • Radiometry as a short-wavelength limit of statistical wave theory with globally incoherent sources
    • Foley J.T., Wolf E. Radiometry as a short-wavelength limit of statistical wave theory with globally incoherent sources. Opt. Comm. 1985, 55:236-241.
    • (1985) Opt. Comm. , vol.55 , pp. 236-241
    • Foley, J.T.1    Wolf, E.2
  • 117
    • 0023327893 scopus 로고
    • The radiance and phase-space representations of the cross-spectral density operator
    • Agarwal G.S., Foley J.T., Wolf E. The radiance and phase-space representations of the cross-spectral density operator. Opt. Comm. 1987, 62:67-72.
    • (1987) Opt. Comm. , vol.62 , pp. 67-72
    • Agarwal, G.S.1    Foley, J.T.2    Wolf, E.3
  • 118
  • 120
    • 0038246169 scopus 로고
    • The two-dimensional symplectic and metaplectic groups and their universal cover
    • Plenum Press, New York, B. Gruber (Ed.)
    • Simon R., Mukunda N. The two-dimensional symplectic and metaplectic groups and their universal cover. Symmetries in Science VI 1993, 659-689. Plenum Press, New York. B. Gruber (Ed.).
    • (1993) Symmetries in Science VI , pp. 659-689
    • Simon, R.1    Mukunda, N.2
  • 121
    • 51249166312 scopus 로고
    • The Real symplectic groups in quantum mechanics and optics
    • also in arXiv:quantph/9509002 v3
    • Arvind, Dutta B., Mukunda N., Simon R. The Real symplectic groups in quantum mechanics and optics. Pramana 1995, 45:471-513. also in arXiv:quantph/9509002 v3.
    • (1995) Pramana , vol.45 , pp. 471-513
    • Arvind1    Dutta, B.2    Mukunda, N.3    Simon, R.4
  • 122
    • 0030527751 scopus 로고    scopus 로고
    • On the symplectic structures arising in geometric optics
    • Cariñena J.F., Nasarre J. On the symplectic structures arising in geometric optics. Fortschr. Phys. 1996, 44:181-198.
    • (1996) Fortschr. Phys. , vol.44 , pp. 181-198
    • Cariñena, J.F.1    Nasarre, J.2
  • 123
    • 0034132255 scopus 로고    scopus 로고
    • Structure of the set of paraxial optical systems
    • Simon R., Wolf K.B. Structure of the set of paraxial optical systems. J. Opt. Soc. Am. 2000, 17:342-355.
    • (2000) J. Opt. Soc. Am. , vol.17 , pp. 342-355
    • Simon, R.1    Wolf, K.B.2
  • 127
    • 0004084482 scopus 로고
    • John Wiley & Sons, Englewood Cliffs
    • Klein M.V., Furtak T. Optics 1986, John Wiley & Sons, Englewood Cliffs. 2nd ed.
    • (1986) Optics
    • Klein, M.V.1    Furtak, T.2
  • 128
    • 0004750517 scopus 로고
    • Matrix representation of Gaussian optics
    • Halbach K. Matrix representation of Gaussian optics. Am. J. Phys. 1964, 32:90-108.
    • (1964) Am. J. Phys. , vol.32 , pp. 90-108
    • Halbach, K.1
  • 129
    • 84893906822 scopus 로고
    • Imaging of optical modes - Resonators with internal lenses
    • Kogelnik H. Imaging of optical modes - Resonators with internal lenses. Bell System Tech. J. 1965, 44:455-494.
    • (1965) Bell System Tech. J. , vol.44 , pp. 455-494
    • Kogelnik, H.1
  • 130
    • 0003391643 scopus 로고
    • ch. 6, John Wiley & Sons, New York
    • Yariv A. Quantum Elctronics 1975, 99-129. ch. 6, John Wiley & Sons, New York. 2nd ed.
    • (1975) Quantum Elctronics , pp. 99-129
    • Yariv, A.1
  • 131
    • 84882235780 scopus 로고
    • ch. 2, Academic Press, New York
    • Arnaud J.A. Beam and Fiber Optics 1976, 54-79. ch. 2, Academic Press, New York.
    • (1976) Beam and Fiber Optics , pp. 54-79
    • Arnaud, J.A.1
  • 132
    • 0003434416 scopus 로고
    • chs. 16-17, Univ. Book, London
    • Siegman A.E. Lasers 1986, 626-697. chs. 16-17, Univ. Book, London.
    • (1986) Lasers , pp. 626-697
    • Siegman, A.E.1
  • 133
    • 0004275892 scopus 로고
    • John Wiley & Sons, Mill Valley
    • Milonni P.W., Eberly J.H. Lasers 1988, 484-508. John Wiley & Sons, Mill Valley.
    • (1988) Lasers , pp. 484-508
    • Milonni, P.W.1    Eberly, J.H.2
  • 136
    • 84882074032 scopus 로고
    • Abacus Press, London, ch. 5; in particular, for the methods to compute the exponential function of matrices see
    • Deif A.S. Advanced Matrix Theory for Scientists and Engineers 1982, 176-182. Abacus Press, London, ch. 5; in particular, for the methods to compute the exponential function of matrices see.
    • (1982) Advanced Matrix Theory for Scientists and Engineers , pp. 176-182
    • Deif, A.S.1
  • 137
    • 77956658172 scopus 로고
    • Fourier optics from the perspective of the Heisenberg group
    • ch. 2, Springer-Verlag, Turnbridge Wells, J.S.....A. Mondragón, K.B. Wolf (Eds.)
    • Raszillier H., Schempp W. Fourier optics from the perspective of the Heisenberg group. Lie Methods in Optics 1986, 29-43. ch. 2, Springer-Verlag, Turnbridge Wells. J.S.....A. Mondragón, K.B. Wolf (Eds.).
    • (1986) Lie Methods in Optics , pp. 29-43
    • Raszillier, H.1    Schempp, W.2
  • 138
    • 84975568512 scopus 로고
    • Factorization of the phase-space transformation produced by an arbitrary refracting surface
    • Navarro-Saad M., Wolf K.B. Factorization of the phase-space transformation produced by an arbitrary refracting surface. J. Opt. Soc. Am. A 1986, 3:340-346.
    • (1986) J. Opt. Soc. Am. A , vol.3 , pp. 340-346
    • Navarro-Saad, M.1    Wolf, K.B.2
  • 139
    • 0042977563 scopus 로고
    • The Hamiltonian formulation of optics
    • Sekiguchi T., Wolf K.B. The Hamiltonian formulation of optics. Am. J. Phys. 1987, 55:830-835.
    • (1987) Am. J. Phys. , vol.55 , pp. 830-835
    • Sekiguchi, T.1    Wolf, K.B.2
  • 140
    • 0011523537 scopus 로고
    • Symmetry in Lie optics
    • Wolf K.B. Symmetry in Lie optics. Ann. Phys. 1986, 172:1-25.
    • (1986) Ann. Phys. , vol.172 , pp. 1-25
    • Wolf, K.B.1
  • 141
    • 36149031525 scopus 로고
    • Geometry and dynamics in refracting systems
    • Wolf K.B., Krötzsch G. Geometry and dynamics in refracting systems. Eur. J. Phys. 1995, 16:14-20.
    • (1995) Eur. J. Phys. , vol.16 , pp. 14-20
    • Wolf, K.B.1    Krötzsch, G.2
  • 143
    • 0038246169 scopus 로고
    • The two-dimensional symplectic and metaplectic groups and their universal cover
    • Plenum Press, New York, B. Gruber (Ed.)
    • Simon R., Mukunda N. The two-dimensional symplectic and metaplectic groups and their universal cover. Symmetries in Science VI 1993, 659-689. Plenum Press, New York. B. Gruber (Ed.).
    • (1993) Symmetries in Science VI , pp. 659-689
    • Simon, R.1    Mukunda, N.2
  • 144
    • 3843102440 scopus 로고
    • Generalization of the principal plane concept in matrix optics
    • Arsenault H.H. Generalization of the principal plane concept in matrix optics. Am. J. Phys. 1980, 48:397-399.
    • (1980) Am. J. Phys. , vol.48 , pp. 397-399
    • Arsenault, H.H.1
  • 145
    • 0020102107 scopus 로고
    • First-order optics - a canonical operator representation: lossless systems
    • Nazarathy M., Shamir J. First-order optics - a canonical operator representation: lossless systems. J. Opt. Soc. Am. 1982, 72:356-364.
    • (1982) J. Opt. Soc. Am. , vol.72 , pp. 356-364
    • Nazarathy, M.1    Shamir, J.2
  • 146
    • 0020834596 scopus 로고
    • Factorization of the transfer matrix for symmetrical optical systems
    • Arsenault H.H., Macukow B. Factorization of the transfer matrix for symmetrical optical systems. J. Opt. Soc. Am. 1983, 73:1350-1359.
    • (1983) J. Opt. Soc. Am. , vol.73 , pp. 1350-1359
    • Arsenault, H.H.1    Macukow, B.2
  • 147
    • 0020834878 scopus 로고
    • Matrix decomposition for nonsymmetrical optical systems
    • Macukow B., Arsenault H.H. Matrix decomposition for nonsymmetrical optical systems. J. Opt. Soc. Am. 1983, 73:1360-1366.
    • (1983) J. Opt. Soc. Am. , vol.73 , pp. 1360-1366
    • Macukow, B.1    Arsenault, H.H.2
  • 148
    • 0001332130 scopus 로고
    • Realization of first order optical systems using thin lenses
    • Sudarshan E.C.G., Mukunda N., Simon R. Realization of first order optical systems using thin lenses. Optica Acta 1985, 32:855-872.
    • (1985) Optica Acta , vol.32 , pp. 855-872
    • Sudarshan, E.C.G.1    Mukunda, N.2    Simon, R.3
  • 149
    • 0034132255 scopus 로고    scopus 로고
    • Structure of the set of paraxial optical systems
    • Simon R., Wolf K.B. Structure of the set of paraxial optical systems. J. Opt. Soc. Am. A 2000, 17:342-355.
    • (2000) J. Opt. Soc. Am. A , vol.17 , pp. 342-355
    • Simon, R.1    Wolf, K.B.2
  • 151
    • 0007347727 scopus 로고
    • Lie algebraic solution of linear differential equations
    • Wei J., Norman E. Lie algebraic solution of linear differential equations. J. Math Phys. 1963, 4:575-581.
    • (1963) J. Math Phys. , vol.4 , pp. 575-581
    • Wei, J.1    Norman, E.2
  • 152
    • 0042638530 scopus 로고
    • Exponential operators and parameter differentiation in quantum physics
    • Wilcox R.M. Exponential operators and parameter differentiation in quantum physics. J. Math. Phys. 1967, 8:962-982.
    • (1967) J. Math. Phys. , vol.8 , pp. 962-982
    • Wilcox, R.M.1
  • 153
    • 14344271665 scopus 로고
    • Baker-Campbell-Hausdorff relations and unitarity of SU(2) and SU(1,1) squeeze operators
    • Truax D.T. Baker-Campbell-Hausdorff relations and unitarity of SU(2) and SU(1,1) squeeze operators. Phys. Rev. D 1985, 31:1988-1991.
    • (1985) Phys. Rev. D , vol.31 , pp. 1988-1991
    • Truax, D.T.1
  • 154
    • 51249176676 scopus 로고
    • An algebraic view to the operatorial ordering and its applications to optics
    • Dattoli G., Gallardo J.C., Torre A. An algebraic view to the operatorial ordering and its applications to optics. Riv. Nuovo Cim. 1988, 11:11.
    • (1988) Riv. Nuovo Cim. , vol.11 , pp. 11
    • Dattoli, G.1    Gallardo, J.C.2    Torre, A.3
  • 155
    • 51249176676 scopus 로고
    • An algebraic view to the operatorial ordering and its applications to optics
    • Dattoli G., Gallardo J.C., Torre A. An algebraic view to the operatorial ordering and its applications to optics. Riv. Nuovo Cim. 1988, 11:1-79.
    • (1988) Riv. Nuovo Cim. , vol.11 , pp. 1-79
    • Dattoli, G.1    Gallardo, J.C.2    Torre, A.3
  • 156
    • 0040158328 scopus 로고
    • A general view to Lie algebraic methods in applied mathematics, optics and transport systems for charged beam accelerators
    • World Sc. Publ., Berlin, G. Maino, L. Fronzoni, M. Pettini (Eds.)
    • Dattoli G., Torre A. A general view to Lie algebraic methods in applied mathematics, optics and transport systems for charged beam accelerators. Dynamical Symmetries and Chaotic Behaviour in Physical Systems 1991, 21-89. World Sc. Publ., Berlin. G. Maino, L. Fronzoni, M. Pettini (Eds.).
    • (1991) Dynamical Symmetries and Chaotic Behaviour in Physical Systems , pp. 21-89
    • Dattoli, G.1    Torre, A.2
  • 157
    • 0027639265 scopus 로고
    • Decomposition formulas for SU (1,1) and SU (2) Lie algebras and their applications in quantum optics
    • Ban M. Decomposition formulas for SU (1,1) and SU (2) Lie algebras and their applications in quantum optics. J. Opt. Soc. Am. B 1993, 10:1347-1359.
    • (1993) J. Opt. Soc. Am. B , vol.10 , pp. 1347-1359
    • Ban, M.1
  • 158
    • 53449083270 scopus 로고    scopus 로고
    • Lie algebra treatment of two and three-mode interaction Hamiltonians
    • Torre A. Lie algebra treatment of two and three-mode interaction Hamiltonians. Recent Res. Devel. Quantum Electronics 2000, 2:111-131.
    • (2000) Recent Res. Devel. Quantum Electronics , vol.2 , pp. 111-131
    • Torre, A.1
  • 159
    • 36749113095 scopus 로고
    • Lie series and invariant functions for analytic symplectic maps
    • Dragt A.J., Finn J.M. Lie series and invariant functions for analytic symplectic maps. J. Math. Phys. 1976, 17:2215-2227.
    • (1976) J. Math. Phys. , vol.17 , pp. 2215-2227
    • Dragt, A.J.1    Finn, J.M.2
  • 160
    • 0003264910 scopus 로고
    • Lectures on nonlinear orbit dynamics
    • Amer. Inst. Phys., Singapore, R.A. Carrigan, F.R. Huson, M. Month (Eds.)
    • Dragt A.J. Lectures on nonlinear orbit dynamics. Physics of High Energy Particle Accelerators, AIP Conference Proceedings 1982, 147-313. Amer. Inst. Phys., Singapore. R.A. Carrigan, F.R. Huson, M. Month (Eds.).
    • (1982) Physics of High Energy Particle Accelerators, AIP Conference Proceedings , pp. 147-313
    • Dragt, A.J.1
  • 161
    • 0020102825 scopus 로고
    • Lie algebraic theory of geometrical optics and optical aberrations
    • Dragt A.J. Lie algebraic theory of geometrical optics and optical aberrations. J. Opt. Soc. Am. 1982, 72:372-378.
    • (1982) J. Opt. Soc. Am. , vol.72 , pp. 372-378
    • Dragt, A.J.1
  • 162
    • 0039615415 scopus 로고
    • Foundations of a Lie algebraic theory of geometrical optics
    • Springer-Verlag, New York, ch. 4, J. Sánchez Mondragon, K.B. Wolf (Eds.)
    • Dragt A.J., Forrest E., Wolf K.B. Foundations of a Lie algebraic theory of geometrical optics. Lie Methods in Optics 1986, 105-157. Springer-Verlag, New York, ch. 4. J. Sánchez Mondragon, K.B. Wolf (Eds.).
    • (1986) Lie Methods in Optics , pp. 105-157
    • Dragt, A.J.1    Forrest, E.2    Wolf, K.B.3
  • 163
    • 0001515953 scopus 로고
    • Immersion of the Fourier transform in a continuous group of functional transformations
    • Condon E.U. Immersion of the Fourier transform in a continuous group of functional transformations. Proc. Natl. Acad. Sci. USA 1937, 23:158-164.
    • (1937) Proc. Natl. Acad. Sci. USA , vol.23 , pp. 158-164
    • Condon, E.U.1
  • 164
    • 77958407025 scopus 로고
    • The fractional order Fourier transform and its application to quantum mechanics
    • Namias V. The fractional order Fourier transform and its application to quantum mechanics. J. Inst. Maths. Applics. 1980, 25:241-265.
    • (1980) J. Inst. Maths. Applics. , vol.25 , pp. 241-265
    • Namias, V.1
  • 165
    • 0027652515 scopus 로고
    • Fourier transforms of fractional order and their optical interpretation:I
    • Mendlovic D., Ozaktas H.M. Fourier transforms of fractional order and their optical interpretation:I. J. Opt. Soc. Am. A 1993, 10:1875-1881.
    • (1993) J. Opt. Soc. Am. A , vol.10 , pp. 1875-1881
    • Mendlovic, D.1    Ozaktas, H.M.2
  • 166
    • 0027740848 scopus 로고
    • Fourier transforms of fractional order and their optical interpretation: II
    • Mendlovic D., Ozaktas H.M. Fourier transforms of fractional order and their optical interpretation: II. J. Opt. Soc. Am. A 1993, 10:2522-2531.
    • (1993) J. Opt. Soc. Am. A , vol.10 , pp. 2522-2531
    • Mendlovic, D.1    Ozaktas, H.M.2
  • 167
    • 0027682286 scopus 로고
    • Image rotation, Wigner rotation, and the fractional order Fourier transform
    • Lohmann A.W. Image rotation, Wigner rotation, and the fractional order Fourier transform. J. Opt. Soc. Am. A 1993, 10:2181-2186.
    • (1993) J. Opt. Soc. Am. A , vol.10 , pp. 2181-2186
    • Lohmann, A.W.1
  • 168
    • 0028509784 scopus 로고
    • Graded-index fibers, Wigner distribution functions, and the fractional Fourier transform
    • Mendlovic D., Ozaktas H.M., Lohmann A.W. Graded-index fibers, Wigner distribution functions, and the fractional Fourier transform. Appl. Opt. 1994, 33:6188-6193.
    • (1994) Appl. Opt. , vol.33 , pp. 6188-6193
    • Mendlovic, D.1    Ozaktas, H.M.2    Lohmann, A.W.3
  • 169
    • 0028483920 scopus 로고
    • A simple realization of fractional Fourier transformation and relation to harmonic oscillator Green's function
    • Agarwal G.S., Simon R. A simple realization of fractional Fourier transformation and relation to harmonic oscillator Green's function. Opt. Commun. 1994, 110:23-26.
    • (1994) Opt. Commun. , vol.110 , pp. 23-26
    • Agarwal, G.S.1    Simon, R.2
  • 170
    • 77956711851 scopus 로고    scopus 로고
    • Fractional transformations in optics
    • ch. 4, Elsevier, Berlin, E. Wolf (Ed.)
    • Lohmann A.W., Mendlovic D., Zalevsky Z. Fractional transformations in optics. Progress in Optics 1997, 263-342. ch. 4, Elsevier, Berlin. E. Wolf (Ed.).
    • (1997) Progress in Optics , pp. 263-342
    • Lohmann, A.W.1    Mendlovic, D.2    Zalevsky, Z.3
  • 171
    • 77957719167 scopus 로고    scopus 로고
    • Introduction to the fractional Fourier transform and its applications
    • ch. 4, Academic Press, Amsterdam, P.W. Hawkes (Ed.)
    • Ozaktas H.M., Kutay M.A., Mendlovic D. Introduction to the fractional Fourier transform and its applications. Advances in Imaging and Electron Physics 1999, 239-291. ch. 4, Academic Press, Amsterdam. P.W. Hawkes (Ed.).
    • (1999) Advances in Imaging and Electron Physics , pp. 239-291
    • Ozaktas, H.M.1    Kutay, M.A.2    Mendlovic, D.3
  • 172
    • 77956712784 scopus 로고    scopus 로고
    • The fractional Fourier transform and some of its applications to optics
    • ch. 7, Elsevier, San Diego, E. Wolf (Ed.)
    • Torre A. The fractional Fourier transform and some of its applications to optics. Progress in Optics 2002, 521-586. ch. 7, Elsevier, San Diego. E. Wolf (Ed.).
    • (2002) Progress in Optics , pp. 521-586
    • Torre, A.1
  • 174
    • 84967871354 scopus 로고
    • Dirac's light-cone coordinate system
    • Kim Y.S., Noz M.E. Dirac's light-cone coordinate system. Am. J. Phys. 1982, 50:721-724.
    • (1982) Am. J. Phys. , vol.50 , pp. 721-724
    • Kim, Y.S.1    Noz, M.E.2
  • 175
    • 33645820068 scopus 로고
    • Illustrative examples of the symplectic group
    • Kim Y.S., Noz M.E. Illustrative examples of the symplectic group. Am. J. Phys. 1983, 51:368-375.
    • (1983) Am. J. Phys. , vol.51 , pp. 368-375
    • Kim, Y.S.1    Noz, M.E.2
  • 176
    • 0000557916 scopus 로고
    • Linear canonical transformations of coherent and squeezed states in the Wigner phase space
    • Han D., Kim Y.S., Noz M.E. Linear canonical transformations of coherent and squeezed states in the Wigner phase space. Phys. Rev. A 1988, 37:807-814.
    • (1988) Phys. Rev. A , vol.37 , pp. 807-814
    • Han, D.1    Kim, Y.S.2    Noz, M.E.3
  • 177
    • 0000652537 scopus 로고
    • II Quantitative analysis
    • II Quantitative analysis. Phys. Rev. A 1989, 40:902-912.
    • (1989) Phys. Rev. A , vol.40 , pp. 902-912
  • 179
    • 4243892486 scopus 로고
    • Simulating the Wigner angle with a parametric amplifier
    • Aravind P.K. Simulating the Wigner angle with a parametric amplifier. Phys. Rev. A 1990, 42:4077-4084.
    • (1990) Phys. Rev. A , vol.42 , pp. 4077-4084
    • Aravind, P.K.1
  • 180
    • 4243315676 scopus 로고
    • Measuring the Wigner rotation with electron beams
    • Ciocci F., Dattoli G., Mari C., Torre A. Measuring the Wigner rotation with electron beams. Phys. Rev. A 1992, 46:5149-5153.
    • (1992) Phys. Rev. A , vol.46 , pp. 5149-5153
    • Ciocci, F.1    Dattoli, G.2    Mari, C.3    Torre, A.4
  • 181
    • 0001180439 scopus 로고    scopus 로고
    • Wigner rotations and Iwasawa decompositions in polarization optics
    • Han D., Kim Y.S., Noz M.E. Wigner rotations and Iwasawa decompositions in polarization optics. Phys. Rev. E 1999, 60:1036-1041.
    • (1999) Phys. Rev. E , vol.60 , pp. 1036-1041
    • Han, D.1    Kim, Y.S.2    Noz, M.E.3
  • 182
    • 0002175702 scopus 로고    scopus 로고
    • Multilayer optics as an analog computer for testing special relativity
    • Monzón J.J., Sánchez-Soto L.L. Multilayer optics as an analog computer for testing special relativity. Phys. Lett. A 1999, 262:18-26.
    • (1999) Phys. Lett. A , vol.262 , pp. 18-26
    • Monzón, J.J.1    Sánchez-Soto, L.L.2
  • 184
    • 2942642546 scopus 로고
    • On the representations of Lie algebras
    • Iwasawa K. On the representations of Lie algebras. Jpn. J. Math. 1948, 19:513-523.
    • (1948) Jpn. J. Math. , vol.19 , pp. 513-523
    • Iwasawa, K.1
  • 185
    • 0000995338 scopus 로고
    • On some types of topological groups
    • Iwasawa K. On some types of topological groups. Ann. Math. 1948, 50:507-558.
    • (1948) Ann. Math. , vol.50 , pp. 507-558
    • Iwasawa, K.1
  • 187
    • 84916282453 scopus 로고
    • Addison Wesley, New York
    • 2(R) 1993, 659-689. Addison Wesley, New York.
    • (1993) 2(R) , pp. 659-689
    • Lang, S.1
  • 188
    • 0027310025 scopus 로고
    • Iwasawa decomposition for SU(1,1) and the Güoy effect for squeezed states
    • Simon R., Mukunda N. Iwasawa decomposition for SU(1,1) and the Güoy effect for squeezed states. Opt. Commun. 1993, 95:39-45.
    • (1993) Opt. Commun. , vol.95 , pp. 39-45
    • Simon, R.1    Mukunda, N.2
  • 189
    • 0001442483 scopus 로고    scopus 로고
    • Iwasawa decomposition in first-order optics: universal treatment of shape-invariant propagation for coherent and partially coherent beams
    • Simon R., Mukunda N. Iwasawa decomposition in first-order optics: universal treatment of shape-invariant propagation for coherent and partially coherent beams. J. Opt. Soc. Am. A 1998, 15:2146-2155.
    • (1998) J. Opt. Soc. Am. A , vol.15 , pp. 2146-2155
    • Simon, R.1    Mukunda, N.2
  • 195
    • 77956666518 scopus 로고    scopus 로고
    • Phase space correspondence between classical optics and quantum mechanics
    • ch. 5, Elsevier, Boston, E. Wolf (Ed.)
    • Dragoman D. Phase space correspondence between classical optics and quantum mechanics. Progress in Optics 2002, 433-496. ch. 5, Elsevier, Boston. E. Wolf (Ed.).
    • (2002) Progress in Optics , pp. 433-496
    • Dragoman, D.1
  • 203
    • 0002399221 scopus 로고
    • A method of solution of problems of electromagnetic wave propagation along the earth's surface
    • (in Russian)
    • Leontovich M.A. A method of solution of problems of electromagnetic wave propagation along the earth's surface. Bulletin de l'Académie des Sciences de l'URSS, sér. phys 1944, 8:16-22. (in Russian).
    • (1944) Bulletin de l'Académie des Sciences de l'URSS, sér. phys , vol.8 , pp. 16-22
    • Leontovich, M.A.1
  • 204
    • 0003368479 scopus 로고
    • Solution of the problem of propagation of electromagnetic waves along the earth's surface by the method of parabolic equations
    • Leontovich M.A., Fock V.A. Solution of the problem of propagation of electromagnetic waves along the earth's surface by the method of parabolic equations. Sov. J. Phys. 1946, 10:13-20.
    • (1946) Sov. J. Phys. , vol.10 , pp. 13-20
    • Leontovich, M.A.1    Fock, V.A.2
  • 206
    • 84882227342 scopus 로고
    • Theory of radiowave propagation in an inhomogeneous (stratified) atmosphere for a raised source
    • Pergamon Press, Oxford, ch. 14
    • Fock V.A. Theory of radiowave propagation in an inhomogeneous (stratified) atmosphere for a raised source. Electromagnetic Diffraction and Propagation Problems 1965, 276-307. Pergamon Press, Oxford, ch. 14.
    • (1965) Electromagnetic Diffraction and Propagation Problems , pp. 276-307
    • Fock, V.A.1
  • 207
  • 208
    • 0001002474 scopus 로고
    • Theory of electromagnetic fieds
    • Davis L.W. Theory of electromagnetic fieds. Phys. Rev. A 1979, 19:1177-1179.
    • (1979) Phys. Rev. A , vol.19 , pp. 1177-1179
    • Davis, L.W.1
  • 209
    • 0018458499 scopus 로고
    • Gaussian beam propagation beyond the paraxial approximation
    • Agrawal G.P., Pattanayak D.N. Gaussian beam propagation beyond the paraxial approximation. J. Opt. Soc. Am. 1979, 69:575-578.
    • (1979) J. Opt. Soc. Am. , vol.69 , pp. 575-578
    • Agrawal, G.P.1    Pattanayak, D.N.2
  • 210
    • 33749579427 scopus 로고
    • From Maxwell to optical resonators
    • Addison-Wesley, Oxford, S.F. Jacobs, M.O. Scully, M. Sargent, C.D. Cantrell (Eds.)
    • Louisell W.H. From Maxwell to optical resonators. Laser Induced Fusion and X-ray Laser Studies 1976, 369-485. Addison-Wesley, Oxford. S.F. Jacobs, M.O. Scully, M. Sargent, C.D. Cantrell (Eds.).
    • (1976) Laser Induced Fusion and X-ray Laser Studies , pp. 369-485
    • Louisell, W.H.1
  • 211
    • 0032185285 scopus 로고    scopus 로고
    • Electromagnetic Gaussian beam
    • Seshadri S.R. Electromagnetic Gaussian beam. J. Opt. Soc. Am. A 1998, 15:2712-2719.
    • (1998) J. Opt. Soc. Am. A , vol.15 , pp. 2712-2719
    • Seshadri, S.R.1
  • 212
    • 0041449672 scopus 로고    scopus 로고
    • Higher-order corrections to the electric field vector of a Gaussian beam
    • Kim H.-C., Lee Y.H. Higher-order corrections to the electric field vector of a Gaussian beam. J. Opt. Soc. Am. A 1999, 16:2232-2238.
    • (1999) J. Opt. Soc. Am. A , vol.16 , pp. 2232-2238
    • Kim, H.-C.1    Lee, Y.H.2
  • 213
    • 0003031527 scopus 로고    scopus 로고
    • Corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media
    • Cao Q. Corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media. J. Opt. Soc. Am. A 1999, 16:2494-2499.
    • (1999) J. Opt. Soc. Am. A , vol.16 , pp. 2494-2499
    • Cao, Q.1
  • 214
    • 0033905976 scopus 로고    scopus 로고
    • Vectorial free-space optical propagation: a simple approach for generating all-order non paraxial corrections
    • Ciattoni A., Crosignani B., Porto P.Di Vectorial free-space optical propagation: a simple approach for generating all-order non paraxial corrections. Opt. Comm. 2000, 177:9-13.
    • (2000) Opt. Comm. , vol.177 , pp. 9-13
    • Ciattoni, A.1    Crosignani, B.2    Porto, P.D.3
  • 215
    • 85010108924 scopus 로고
    • Gaussian beam as a bundle of complex rays
    • Deschamps G.A. Gaussian beam as a bundle of complex rays. Electron. Lett. 1971, 7:684-685.
    • (1971) Electron. Lett. , vol.7 , pp. 684-685
    • Deschamps, G.A.1
  • 216
    • 0001279925 scopus 로고
    • Gaussian beam modes by multipoles with complex source points
    • Shin S.Y., Felsen L.B. Gaussian beam modes by multipoles with complex source points. J. Opt. Soc. Am. 1977, 67:699-700.
    • (1977) J. Opt. Soc. Am. , vol.67 , pp. 699-700
    • Shin, S.Y.1    Felsen, L.B.2
  • 217
    • 84936184503 scopus 로고
    • Complex-source pulsed-beam fields
    • Heyman E., Felsen L.B. Complex-source pulsed-beam fields. J. Opt. Soc. Am. A 1989, 6:806-817.
    • (1989) J. Opt. Soc. Am. A , vol.6 , pp. 806-817
    • Heyman, E.1    Felsen, L.B.2
  • 218
    • 0000119449 scopus 로고    scopus 로고
    • Electromagnetic Gaussian beams beyond the paraxial approximation
    • Sheppard C.J.R., Saghafi S. Electromagnetic Gaussian beams beyond the paraxial approximation. J. Opt. Soc. Am. A 1999, 16:1381-1386.
    • (1999) J. Opt. Soc. Am. A , vol.16 , pp. 1381-1386
    • Sheppard, C.J.R.1    Saghafi, S.2
  • 219
    • 84975559474 scopus 로고
    • Gaussian amplitude functions that are exact solutions to the scalar Helmholtz equation
    • Landesman B.T., Barrett H.H. Gaussian amplitude functions that are exact solutions to the scalar Helmholtz equation. J. Opt. Soc. Am. A 1988, 5:1610-1619.
    • (1988) J. Opt. Soc. Am. A , vol.5 , pp. 1610-1619
    • Landesman, B.T.1    Barrett, H.H.2
  • 220
    • 0001403087 scopus 로고    scopus 로고
    • Scalar field of nonparaxial Gaussian beams
    • Ulanowski Z., Ludlow I.K. Scalar field of nonparaxial Gaussian beams. Opt. Lett. 2000, 25:1792-1794.
    • (2000) Opt. Lett. , vol.25 , pp. 1792-1794
    • Ulanowski, Z.1    Ludlow, I.K.2
  • 221
    • 2942748401 scopus 로고    scopus 로고
    • Exact nonparaxial beams of the scalar Helmholtz equation
    • Rodríguez-Morales G., Chávez-Cerda S. Exact nonparaxial beams of the scalar Helmholtz equation. Opt. Lett. 2004, 29:430-432.
    • (2004) Opt. Lett. , vol.29 , pp. 430-432
    • Rodríguez-Morales, G.1    Chávez-Cerda, S.2
  • 224
    • 0015397187 scopus 로고
    • Ray techniques in electromagnetics
    • Deschamps G.A. Ray techniques in electromagnetics. Proc. IEEE 1972, 60:1022-1035.
    • (1972) Proc. IEEE , vol.60 , pp. 1022-1035
    • Deschamps, G.A.1
  • 225
    • 0008460865 scopus 로고
    • Phase-space representations of wave equations with applications to the eikonal approximation for short-wavelength waves
    • McDonald S.W. Phase-space representations of wave equations with applications to the eikonal approximation for short-wavelength waves. Phys. Rep. 1988, 158:337-416.
    • (1988) Phys. Rep. , vol.158 , pp. 337-416
    • McDonald, S.W.1
  • 226
    • 33645667614 scopus 로고
    • Geometrical theory of diffraction
    • Keller J.B. Geometrical theory of diffraction. J. Opt. Soc. Am. 1962, 52:116-119.
    • (1962) J. Opt. Soc. Am. , vol.52 , pp. 116-119
    • Keller, J.B.1
  • 227
    • 84882204430 scopus 로고
    • Sur le passage de l'Optique géométrique à l'Optique ondulatoire
    • Chako N. Sur le passage de l'Optique géométrique à l'Optique ondulatoire. Compt. Rend. 1960, 251:852-853.
    • (1960) Compt. Rend. , vol.251 , pp. 852-853
    • Chako, N.1
  • 228
    • 0000552337 scopus 로고
    • Formal quantum theory of light rays
    • Gloge D., Marcuse D. Formal quantum theory of light rays. J. Opt. Soc. Am. 1969, 59:1629-1631.
    • (1969) J. Opt. Soc. Am. , vol.59 , pp. 1629-1631
    • Gloge, D.1    Marcuse, D.2
  • 229
    • 0014710285 scopus 로고
    • Propagation of light beams in continuously focusing lens-like media
    • Eichmann G. Propagation of light beams in continuously focusing lens-like media. Proc. IRE 1970, 58:837-839.
    • (1970) Proc. IRE , vol.58 , pp. 837-839
    • Eichmann, G.1
  • 230
    • 0015009108 scopus 로고
    • Quasi-geometric optics of media with inhomogeneous index of refraction
    • Eichmann G. Quasi-geometric optics of media with inhomogeneous index of refraction. J. Opt. Soc. Am. 1971, 61:161-168.
    • (1971) J. Opt. Soc. Am. , vol.61 , pp. 161-168
    • Eichmann, G.1
  • 231
    • 0037651911 scopus 로고
    • Modes in general gaussian optical systems using quantum-mechanics formalism
    • Feldmann M. Modes in general gaussian optical systems using quantum-mechanics formalism. J. Opt. Soc. Am. 1971, 61:446-449.
    • (1971) J. Opt. Soc. Am. , vol.61 , pp. 446-449
    • Feldmann, M.1
  • 232
    • 0037908574 scopus 로고
    • Maxwell's equations from geometrical optics
    • Pradhan T. Maxwell's equations from geometrical optics. Phys. Lett. A 1987, 122:397-398.
    • (1987) Phys. Lett. A , vol.122 , pp. 397-398
    • Pradhan, T.1
  • 233
    • 0346833218 scopus 로고
    • Operational notation for the analysis and synthesis of optical data-processing systems
    • Vander Lugt A. Operational notation for the analysis and synthesis of optical data-processing systems. Proc. IEEE 1966, 54:1055-1063.
    • (1966) Proc. IEEE , vol.54 , pp. 1055-1063
    • Vander Lugt, A.1
  • 234
    • 0042727781 scopus 로고
    • General theory of linear, coherent, optical data-processing systems
    • Butterweck H.J. General theory of linear, coherent, optical data-processing systems. J. Opt. Soc. Am. 1977, 67:60-70.
    • (1977) J. Opt. Soc. Am. , vol.67 , pp. 60-70
    • Butterweck, H.J.1
  • 235
    • 0018983067 scopus 로고
    • Fourier optics described by operator algebra
    • Nazarathy M., Shamir J. Fourier optics described by operator algebra. J. Opt. Soc. Am. 1980, 70:150-159.
    • (1980) J. Opt. Soc. Am. , vol.70 , pp. 150-159
    • Nazarathy, M.1    Shamir, J.2
  • 236
    • 0019733101 scopus 로고
    • Principles of optical data-processing
    • ch. 4, North-Holland, New York, E. Wolf (Ed.)
    • Butterweck H.J. Principles of optical data-processing. Progress in Optics 1981, 211-280. ch. 4, North-Holland, New York. E. Wolf (Ed.).
    • (1981) Progress in Optics , pp. 211-280
    • Butterweck, H.J.1
  • 237
    • 0020192753 scopus 로고
    • First-order optics - a canonical operator representation: lossless systems
    • First-order optics: operator representation for systems with loss or gain
    • Nazarathy M., Shamir J. First-order optics - a canonical operator representation: lossless systems. J. Opt. Soc. Am. J. Opt. Soc. Am. 1982, 72:1398-1408.
    • (1982) J. Opt. Soc. Am. J. Opt. Soc. Am. , vol.72 , pp. 1398-1408
    • Nazarathy, M.1    Shamir, J.2
  • 238
    • 77956658172 scopus 로고
    • Fourier optics from the perspective of the Heisenberg group
    • ch. 2, Springer-Verlag, Amsterdam, J. Sánchez Mondragón, K.B. Wolf (Eds.)
    • Raszillier H., Schempp W. Fourier optics from the perspective of the Heisenberg group. Lie Methods in Optics 1986, 29-43. ch. 2, Springer-Verlag, Amsterdam. J. Sánchez Mondragón, K.B. Wolf (Eds.).
    • (1986) Lie Methods in Optics , pp. 29-43
    • Raszillier, H.1    Schempp, W.2
  • 239
    • 0038450087 scopus 로고
    • Canonical transforms for paraxial wave optics
    • ch. 5, Springer-Verlag, Berlin, J.S.....A. Mondragón, K.B. Wolf (Eds.)
    • Castaños O., López-Moreno E., Wolf K.B. Canonical transforms for paraxial wave optics. Lie Methods in Optics 1986, 159-182. ch. 5, Springer-Verlag, Berlin. J.S.....A. Mondragón, K.B. Wolf (Eds.).
    • (1986) Lie Methods in Optics , pp. 159-182
    • Castaños, O.1    López-Moreno, E.2    Wolf, K.B.3
  • 240
    • 0028458834 scopus 로고
    • Algebraic approach to characterizing paraxial optical systems
    • Wittig K., Giesen A., Hügel H. Algebraic approach to characterizing paraxial optical systems. Appl. Opt. 1994, 33:3837-3848.
    • (1994) Appl. Opt. , vol.33 , pp. 3837-3848
    • Wittig, K.1    Giesen, A.2    Hügel, H.3
  • 241
    • 0000587862 scopus 로고    scopus 로고
    • Optical phase space, Wigner representation, and invariant quality parameters
    • Simon R., Mukunda N. Optical phase space, Wigner representation, and invariant quality parameters. J. Opt. Soc. Am. A 2000, 17:2440-2463.
    • (2000) J. Opt. Soc. Am. A , vol.17 , pp. 2440-2463
    • Simon, R.1    Mukunda, N.2
  • 250
    • 0040302995 scopus 로고
    • The Heisenberg-Weyl ring in quantum mechanics
    • Academic Press, New York, E.M. Loebl (Ed.)
    • Wolf K.B. The Heisenberg-Weyl ring in quantum mechanics. Group Theory and Its Applications 1975, 189-247. Academic Press, New York. E.M. Loebl (Ed.).
    • (1975) Group Theory and Its Applications , pp. 189-247
    • Wolf, K.B.1
  • 251
    • 84912415971 scopus 로고
    • On the formation of quantum-mechanical operators
    • Shewell J.R. On the formation of quantum-mechanical operators. Am. J. Phys. 1959, 27:16-21.
    • (1959) Am. J. Phys. , vol.27 , pp. 16-21
    • Shewell, J.R.1
  • 252
    • 36149027461 scopus 로고
    • Function in Quantum Mechanics which corresponds to a given function in Classical Mechanics
    • Daughaday H., Nigam B.P. Function in Quantum Mechanics which corresponds to a given function in Classical Mechanics. Phys. Rev. B 1964, 139:1436-1442.
    • (1964) Phys. Rev. B , vol.139 , pp. 1436-1442
    • Daughaday, H.1    Nigam, B.P.2
  • 253
    • 0001031543 scopus 로고
    • Calculus for functions of non-commuting operators and general phase-space methods in quantum mechanics. I. Mapping theorems and ordering of functions of non commuting operators
    • Agarwal G.S., Wolf E. Calculus for functions of non-commuting operators and general phase-space methods in quantum mechanics. I. Mapping theorems and ordering of functions of non commuting operators. Phys. Rev. D 1970, 2:2161-2186.
    • (1970) Phys. Rev. D , vol.2 , pp. 2161-2186
    • Agarwal, G.S.1    Wolf, E.2
  • 254
    • 0007378611 scopus 로고
    • Lie serie, Lie transformations, and their applications
    • Springer-Verlag, New York, ch. 3, J.S.....A. Mondragón, K.B. Wolf (Eds.)
    • Steinberg S. Lie serie, Lie transformations, and their applications. Lie Methods in Optics 1986, 45-104. Springer-Verlag, New York, ch. 3. J.S.....A. Mondragón, K.B. Wolf (Eds.).
    • (1986) Lie Methods in Optics , pp. 45-104
    • Steinberg, S.1
  • 260
    • 0012230760 scopus 로고
    • Elements of Euclidean optics
    • ch. 6, Springer-Verlag, New York, K.B. Wolf (Ed.)
    • Wolf K.B. Elements of Euclidean optics. Lie Methods in Optics II 1989, 115-162. ch. 6, Springer-Verlag, New York. K.B. Wolf (Ed.).
    • (1989) Lie Methods in Optics II , pp. 115-162
    • Wolf, K.B.1
  • 263
    • 0003733504 scopus 로고
    • Here, the electrical-optical devices analogy is expressely evidenced, McGraw-Hill, New York
    • Papoulis A. Systems and Transforms with Applications in Optics 1968, Here, the electrical-optical devices analogy is expressely evidenced, McGraw-Hill, New York.
    • (1968) Systems and Transforms with Applications in Optics
    • Papoulis, A.1
  • 267
    • 0018519010 scopus 로고
    • The Wigner distribution function and Hamilton's characteristics of a geometric-optical system
    • Bastiaans M.J. The Wigner distribution function and Hamilton's characteristics of a geometric-optical system. Opt. Comm. 1979, 30:321-326.
    • (1979) Opt. Comm. , vol.30 , pp. 321-326
    • Bastiaans, M.J.1
  • 268
    • 0000293183 scopus 로고
    • Theory of communication. I: The analysis of information
    • Gabor D. Theory of communication. I: The analysis of information. J. of the IEE 1946, 93:429-441.
    • (1946) J. of the IEE , vol.93 , pp. 429-441
    • Gabor, D.1
  • 269
    • 0000293183 scopus 로고
    • Theory of communication. II: The analysis of hearing
    • Gabor D. Theory of communication. II: The analysis of hearing. J. of the IEE 1946, 93:442-445.
    • (1946) J. of the IEE , vol.93 , pp. 442-445
    • Gabor, D.1
  • 270
    • 0000293183 scopus 로고
    • Theory of communication. III: Frequency compression and expansion
    • Gabor D. Theory of communication. III: Frequency compression and expansion. J. of the IEE 1946, 93:445-457.
    • (1946) J. of the IEE , vol.93 , pp. 445-457
    • Gabor, D.1
  • 271
    • 0001736588 scopus 로고
    • Light and Information
    • North-Holland, New York, ch. 4, E. Wolf (Ed.)
    • Gabor D. Light and Information. Progress in Optics 1961, 109-153. North-Holland, New York, ch. 4. E. Wolf (Ed.).
    • (1961) Progress in Optics , pp. 109-153
    • Gabor, D.1
  • 272
    • 84882172968 scopus 로고    scopus 로고
    • http://www.hpl.hp.com/research/mmsl/presentations/3d/GeometryTutorial.pdf.
  • 273
    • 0042216804 scopus 로고
    • Operator method in physical optics
    • Stoler D. Operator method in physical optics. J. Opt. Soc. Am. 1981, 71:334-339.
    • (1981) J. Opt. Soc. Am. , vol.71 , pp. 334-339
    • Stoler, D.1
  • 274
    • 0037908613 scopus 로고
    • Metaplectic group and Fourier optics
    • Bacry H., Cadilhac M. Metaplectic group and Fourier optics. Phys. Rev. A 1981, 23:2533-2536.
    • (1981) Phys. Rev. A , vol.23 , pp. 2533-2536
    • Bacry, H.1    Cadilhac, M.2
  • 277
    • 24244435788 scopus 로고
    • Algebraic view of the optical propagation in a nonhomogeneous medium
    • Dattoli G., Solimeno S., Torre A. Algebraic view of the optical propagation in a nonhomogeneous medium. Phys. Rev. A 1987, 35:1668-1672.
    • (1987) Phys. Rev. A , vol.35 , pp. 1668-1672
    • Dattoli, G.1    Solimeno, S.2    Torre, A.3
  • 278
    • 51249176676 scopus 로고
    • An algebraic view to the operatorial ordering and its applications to optics
    • Dattoli G., Gallardo J.C., Torre A. An algebraic view to the operatorial ordering and its applications to optics. Riv. Nuovo Cim. 1988, 11(11):1-79.
    • (1988) Riv. Nuovo Cim. , vol.11 , Issue.11 , pp. 1-79
    • Dattoli, G.1    Gallardo, J.C.2    Torre, A.3
  • 279
    • 0040158328 scopus 로고
    • A general view to Lie algebraic methods in applied mathematics, optics and transport systems for charged beam accelerators
    • World Sc. Publ., Singapore, G. Maino, L. Fronzoni, M. Pettini (Eds.)
    • Dattoli G., Torre A. A general view to Lie algebraic methods in applied mathematics, optics and transport systems for charged beam accelerators. Dynamical Symmetrics and Chaotic Behaviour in Physical Systems 1991, 21-89. World Sc. Publ., Singapore. G. Maino, L. Fronzoni, M. Pettini (Eds.).
    • (1991) Dynamical Symmetrics and Chaotic Behaviour in Physical Systems , pp. 21-89
    • Dattoli, G.1    Torre, A.2
  • 280
    • 34250594733 scopus 로고
    • Sur certains groupes d'opérateurs unitaires
    • Weil A. Sur certains groupes d'opérateurs unitaires. Acta Math 1964, 111:143-211.
    • (1964) Acta Math , vol.111 , pp. 143-211
    • Weil, A.1
  • 281
    • 2342543452 scopus 로고
    • Springer-Verlag, Singapore
    • Collected Papers 1980, Vol. 3:1-69. Springer-Verlag, Singapore.
    • (1980) Collected Papers , vol.3 , pp. 1-69
  • 282
    • 33947183980 scopus 로고
    • Some recent results on the metaplectic representation
    • Springer-Verlag, Heidelberg, P. Kramer, A. Rieckers (Eds.)
    • Sternberg S. Some recent results on the metaplectic representation. Group Theoretical Methods in Physics 1978, 117-143. Springer-Verlag, Heidelberg. P. Kramer, A. Rieckers (Eds.).
    • (1978) Group Theoretical Methods in Physics , pp. 117-143
    • Sternberg, S.1
  • 283
    • 49049151627 scopus 로고
    • The metaplectic representation, Weyl operators, and spectral theory
    • Guillemin V., Sternberg S. The metaplectic representation, Weyl operators, and spectral theory. J. Functional Anal. 1981, 42:129-225.
    • (1981) J. Functional Anal. , vol.42 , pp. 129-225
    • Guillemin, V.1    Sternberg, S.2
  • 285
    • 0039519349 scopus 로고
    • The metaplectic group within the Heisenberg-Weyl ring
    • García-Bullé M., Lassner W., Wolf K.B. The metaplectic group within the Heisenberg-Weyl ring. J. Math. Phys. 1986, 27:29-36.
    • (1986) J. Math. Phys. , vol.27 , pp. 29-36
    • García-Bullé, M.1    Lassner, W.2    Wolf, K.B.3
  • 286
    • 33645082904 scopus 로고
    • The semiclassical evolution of wave packets
    • Littlejohn R.G. The semiclassical evolution of wave packets. Phys. Rep. 1986, 138:198-291.
    • (1986) Phys. Rep. , vol.138 , pp. 198-291
    • Littlejohn, R.G.1
  • 287
    • 0038246169 scopus 로고
    • The two-dimensional symplectic and metaplectic groups and their universal cover
    • Plenum Press, New York, B. Gruber (Ed.)
    • Simon R., Mukunda N. The two-dimensional symplectic and metaplectic groups and their universal cover. Symmetries in Science VI 1993, 659-689. Plenum Press, New York. B. Gruber (Ed.).
    • (1993) Symmetries in Science VI , pp. 659-689
    • Simon, R.1    Mukunda, N.2
  • 288
    • 0000587862 scopus 로고    scopus 로고
    • Optical phase space, Wigner representation, and invariant quality parameters
    • Simon R., Mukunda N. Optical phase space, Wigner representation, and invariant quality parameters. J. Opt. Soc. Am. A 2000, 17:2440-2463.
    • (2000) J. Opt. Soc. Am. A , vol.17 , pp. 2440-2463
    • Simon, R.1    Mukunda, N.2
  • 289
    • 0036431446 scopus 로고    scopus 로고
    • On the integral representations for metaplectic operators
    • ter Morsche H., Oonincx P.J. On the integral representations for metaplectic operators. J. Fourier Anal. & Appl. 2002, 8:245-257.
    • (2002) J. Fourier Anal. & Appl. , vol.8 , pp. 245-257
    • ter Morsche, H.1    Oonincx, P.J.2
  • 290
    • 0001459151 scopus 로고
    • Diffraction-integral written in terms of matrix-optics
    • Collins S.A. Diffraction-integral written in terms of matrix-optics. J. Opt. Soc. Am. 1970, 60:1168-1177.
    • (1970) J. Opt. Soc. Am. , vol.60 , pp. 1168-1177
    • Collins, S.A.1
  • 291
    • 0242518299 scopus 로고
    • Univ. Science Book, New York, ch. 20
    • Siegman A.E. Lasers 1986, 777-782. Univ. Science Book, New York, ch. 20.
    • (1986) Lasers , pp. 777-782
    • Siegman, A.E.1
  • 292
    • 0013369202 scopus 로고
    • Dual optical systems
    • Papoulis A. Dual optical systems. J. Opt. Soc. Am. 1968, 58:653-654.
    • (1968) J. Opt. Soc. Am. , vol.58 , pp. 653-654
    • Papoulis, A.1
  • 293
    • 0042727781 scopus 로고
    • General theory of linear, coherent, optical data-processing systems
    • Butterweck H.J. General theory of linear, coherent, optical data-processing systems. J. Opt. Soc. Am. 1977, 67:60-70.
    • (1977) J. Opt. Soc. Am. , vol.67 , pp. 60-70
    • Butterweck, H.J.1
  • 294
    • 0019733101 scopus 로고
    • Principles of optical data-processing
    • ch. 4, North-Holland, Mill Valley, E. Wolf (Ed.)
    • Butterweck H.J. Principles of optical data-processing. Progress in Optics 1981, Vol. XIX:211-280. ch. 4, North-Holland, Mill Valley. E. Wolf (Ed.).
    • (1981) Progress in Optics , vol.XIX , pp. 211-280
    • Butterweck, H.J.1
  • 295
    • 0242482022 scopus 로고
    • Ein neues Dualitätsprinzip in der Optik
    • Lohmann A. Ein neues Dualitätsprinzip in der Optik. Optik 1954, 11:478-488.
    • (1954) Optik , vol.11 , pp. 478-488
    • Lohmann, A.1
  • 296
    • 0242650417 scopus 로고
    • Duality in optics
    • For the English translation, see
    • Lohmann A. Duality in optics. Optik 1992, 89:93-97. For the English translation, see.
    • (1992) Optik , vol.89 , pp. 93-97
    • Lohmann, A.1
  • 300
    • 77958407025 scopus 로고
    • The fractional order Fourier transform and its application to quantum mechanics
    • Namias S.V. The fractional order Fourier transform and its application to quantum mechanics. J. Inst. Maths. Applics 1980, 25:241-265.
    • (1980) J. Inst. Maths. Applics , vol.25 , pp. 241-265
    • Namias, S.V.1
  • 301
    • 0028483920 scopus 로고
    • A simple realization of fractional Fourier transformation and relation to harmonic oscillator Green's function
    • Agarwal G.S., Simon R. A simple realization of fractional Fourier transformation and relation to harmonic oscillator Green's function. Opt. Comm. 1994, 110:23-26.
    • (1994) Opt. Comm. , vol.110 , pp. 23-26
    • Agarwal, G.S.1    Simon, R.2
  • 302
    • 0032083511 scopus 로고    scopus 로고
    • An alternative point of view to the theory of fractional Fourier transform
    • Dattoli G., Torre A., Mazzacurati G. An alternative point of view to the theory of fractional Fourier transform. IMA J. Appl. Math. 1998, 60:215-224.
    • (1998) IMA J. Appl. Math. , vol.60 , pp. 215-224
    • Dattoli, G.1    Torre, A.2    Mazzacurati, G.3
  • 303
    • 84975558681 scopus 로고
    • Optical interpretation of a complex-order Fourier transform
    • Shih C.-C. Optical interpretation of a complex-order Fourier transform. Opt. Lett. 1995, 20:1178-1180.
    • (1995) Opt. Lett. , vol.20 , pp. 1178-1180
    • Shih, C.-C.1
  • 304
    • 0000701950 scopus 로고    scopus 로고
    • Optical fractional order Fourier transforms with complex orders
    • Bernardo L.M., Soares O.O.D. Optical fractional order Fourier transforms with complex orders. Appl. Opt. 1996, 35:3163-3166.
    • (1996) Appl. Opt. , vol.35 , pp. 3163-3166
    • Bernardo, L.M.1    Soares, O.O.D.2
  • 305
    • 0001201391 scopus 로고    scopus 로고
    • Extended fractional Fourier transform
    • Hua J., Liu L., Li G. Extended fractional Fourier transform. J. Opt. Soc. Am. A 1997, 14:3316-3322.
    • (1997) J. Opt. Soc. Am. A , vol.14 , pp. 3316-3322
    • Hua, J.1    Liu, L.2    Li, G.3
  • 306
    • 84882160065 scopus 로고
    • Van Nostrand-Reinhold, New York, ch. 3
    • Marcuse D. Light Transmission Optics 1972, 107-109. Van Nostrand-Reinhold, New York, ch. 3.
    • (1972) Light Transmission Optics , pp. 107-109
    • Marcuse, D.1
  • 307
    • 0020102107 scopus 로고
    • First-order optics - a canonical operator representation: lossless systems
    • Nazarathy M., Shamir J. First-order optics - a canonical operator representation: lossless systems. J. Opt. Soc. Am. 1982, 72:356-364.
    • (1982) J. Opt. Soc. Am. , vol.72 , pp. 356-364
    • Nazarathy, M.1    Shamir, J.2
  • 308
    • 0008447017 scopus 로고
    • On a certain class of unitary transformations
    • Infeld L., Plebanski J. On a certain class of unitary transformations. Acta Phys. Polon. 1954, 14:41-75.
    • (1954) Acta Phys. Polon. , vol.14 , pp. 41-75
    • Infeld, L.1    Plebanski, J.2
  • 309
    • 84980077803 scopus 로고
    • On a Hilbert space of analytic functions and an associated integral transform. I
    • Bargmann V. On a Hilbert space of analytic functions and an associated integral transform. I. Comm. Pure & Appl. Math. 1961, 14:187-214.
    • (1961) Comm. Pure & Appl. Math. , vol.14 , pp. 187-214
    • Bargmann, V.1
  • 310
    • 84981759229 scopus 로고
    • On a Hilbert space of analytic functions and an associated integral transform. II. A family of related function spaces application to distribution theory
    • Bargmann V. On a Hilbert space of analytic functions and an associated integral transform. II. A family of related function spaces application to distribution theory. Comm. Pure & Appl. Math. 1967, 20:1-101.
    • (1967) Comm. Pure & Appl. Math. , vol.20 , pp. 1-101
    • Bargmann, V.1
  • 311
    • 36849112629 scopus 로고
    • Linear canonical transformations and their unitary representations
    • Moshinsky M., Quesne C. Linear canonical transformations and their unitary representations. J. Math. Phys. 1971, 12:1772-1780.
    • (1971) J. Math. Phys. , vol.12 , pp. 1772-1780
    • Moshinsky, M.1    Quesne, C.2
  • 312
    • 36849112326 scopus 로고
    • Canonical transformations and matrix elements
    • Quesne C., Moshinsky M. Canonical transformations and matrix elements. J. Math. Phys. 1971, 12:1780-1783.
    • (1971) J. Math. Phys. , vol.12 , pp. 1780-1783
    • Quesne, C.1    Moshinsky, M.2
  • 313
    • 0038246224 scopus 로고
    • Canonical transformations and quantum mechanics
    • Moshinsky M. Canonical transformations and quantum mechanics. SIAM J. Appl. Math. 1973, 25:1772-1780.
    • (1973) SIAM J. Appl. Math. , vol.25 , pp. 1772-1780
    • Moshinsky, M.1
  • 314
    • 36849106652 scopus 로고
    • Canonical transforms. I. Complex linear transforms
    • Wolf K.B. Canonical transforms. I. Complex linear transforms. J. Math. Phys. 1974, 15:1295-1301.
    • (1974) J. Math. Phys. , vol.15 , pp. 1295-1301
    • Wolf, K.B.1
  • 315
    • 36849101979 scopus 로고
    • Canonical transforms. II. Complex radial transforms
    • Wolf K.B. Canonical transforms. II. Complex radial transforms. J. Math. Phys. 1974, 15:2102-2111.
    • (1974) J. Math. Phys. , vol.15 , pp. 2102-2111
    • Wolf, K.B.1
  • 316
    • 0001356372 scopus 로고
    • Complex extensions of canonical transformations and quantum mechanics
    • Academic Press, Princeton, E.M. Loebl (Ed.)
    • Kramer P., Moshinsky M., Seligman T.H. Complex extensions of canonical transformations and quantum mechanics. Group Theory and Its Applications 1975, Vol. 3:249-332. Academic Press, Princeton. E.M. Loebl (Ed.).
    • (1975) Group Theory and Its Applications , vol.3 , pp. 249-332
    • Kramer, P.1    Moshinsky, M.2    Seligman, T.H.3
  • 320
    • 33745014742 scopus 로고
    • On the quantum correction for thermodynamic equilibrium
    • Wigner E.P. On the quantum correction for thermodynamic equilibrium. Phys. Rev. 1932, 40:749-759.
    • (1932) Phys. Rev. , vol.40 , pp. 749-759
    • Wigner, E.P.1
  • 321
    • 0000760091 scopus 로고
    • Quantum-mechanical distribution function revisited
    • MIT Press, Providence, W. Yourgrau, A. van der Merwe (Eds.)
    • Wigner E.P. Quantum-mechanical distribution function revisited. Perspectives in Quantum Theory 1971, 25-36. MIT Press, Providence. W. Yourgrau, A. van der Merwe (Eds.).
    • (1971) Perspectives in Quantum Theory , pp. 25-36
    • Wigner, E.P.1
  • 324
    • 33745040449 scopus 로고
    • On the principles of elementary quantum mechanics
    • Groenewold H.J. On the principles of elementary quantum mechanics. Physica 1946, 12:405-460.
    • (1946) Physica , vol.12 , pp. 405-460
    • Groenewold, H.J.1
  • 325
    • 84952911698 scopus 로고
    • Quantum mechanics as a statistical theory
    • Moyal J.E. Quantum mechanics as a statistical theory. Proc. Cambridge Phil. Soc. 1949, 45:99-124.
    • (1949) Proc. Cambridge Phil. Soc. , vol.45 , pp. 99-124
    • Moyal, J.E.1
  • 326
    • 0001236724 scopus 로고
    • Some topics in quantum statistics. The Wigner function and transport theory
    • North-Holland, New York, J. de Boer, G.E. Uhlenbeck (Eds.)
    • Mori H., Oppenheim I., Ross J. Some topics in quantum statistics. The Wigner function and transport theory. Studies in Statistical Mechanics 1962, 212-298. North-Holland, New York. J. de Boer, G.E. Uhlenbeck (Eds.).
    • (1962) Studies in Statistical Mechanics , pp. 212-298
    • Mori, H.1    Oppenheim, I.2    Ross, J.3
  • 327
    • 0000910767 scopus 로고
    • A theory of generalized functions, with applications to Wigner distribution and Weyl correspondence
    • de Bruijn N.G. A theory of generalized functions, with applications to Wigner distribution and Weyl correspondence. Nieuw Archief voor Wiskunde 1973, Vol XXI(3):205-280.
    • (1973) Nieuw Archief voor Wiskunde , vol.XXI , Issue.3 , pp. 205-280
    • de Bruijn, N.G.1
  • 328
    • 0000684635 scopus 로고
    • Semi-classical mechanics in phase-space: a study of Wigner's function
    • Berry M.V. Semi-classical mechanics in phase-space: a study of Wigner's function. Phil. Trans. Roy. Soc. 1977, 287:237-271.
    • (1977) Phil. Trans. Roy. Soc. , vol.287 , pp. 237-271
    • Berry, M.V.1
  • 329
    • 0008084056 scopus 로고
    • Weyl's association, Wigner's function and affine geometry
    • Balazs N.L. Weyl's association, Wigner's function and affine geometry. Physica 1980, 102A:236-254.
    • (1980) Physica , vol.102 A , pp. 236-254
    • Balazs, N.L.1
  • 330
    • 49049137470 scopus 로고
    • The Wigner function
    • Dahl J.P. The Wigner function. Physica 1982, 114A:439-444.
    • (1982) Physica , vol.114 A , pp. 439-444
    • Dahl, J.P.1
  • 331
    • 33646353810 scopus 로고
    • The Wigner distribution function - 50th birthday
    • O'Connell R.F. The Wigner distribution function - 50th birthday. Found. Phys. 1983, 13:83-92.
    • (1983) Found. Phys. , vol.13 , pp. 83-92
    • O'Connell, R.F.1
  • 332
    • 84931510621 scopus 로고
    • The Wigner representation of quantum mechanics
    • Tatarskií V.I. The Wigner representation of quantum mechanics. Sov. Phys. Usp. 1983, 26:311-327.
    • (1983) Sov. Phys. Usp. , vol.26 , pp. 311-327
    • Tatarskií, V.I.1
  • 333
    • 0001555225 scopus 로고
    • Wigner's function and other distribution functions in the Mock phase spaces
    • Balazs N.L., Jennings B.K. Wigner's function and other distribution functions in the Mock phase spaces. Phys. Rep. 1984, 104:347-391.
    • (1984) Phys. Rep. , vol.104 , pp. 347-391
    • Balazs, N.L.1    Jennings, B.K.2
  • 335
    • 77956666518 scopus 로고    scopus 로고
    • Phase space correspondence between classical optics and quantum mechanics
    • ch. 5, Elsevier, Amsterdam, E. Wolf (Ed.)
    • Dragoman D. Phase space correspondence between classical optics and quantum mechanics. Progress in Optics 2002, 433-496. ch. 5, Elsevier, Amsterdam. E. Wolf (Ed.).
    • (2002) Progress in Optics , pp. 433-496
    • Dragoman, D.1
  • 337
    • 0004161009 scopus 로고
    • ch. VI-VII, North-Holland, Singapore, The properties of the Weyl transform and the Wigner distribution function are specifically described in he appendix of ch. VI, pp. 341-364.
    • De Groot S.R., Suttorp L.G. Foundations of Electrodynamics 1972, 317-406. ch. VI-VII, North-Holland, Singapore, The properties of the Weyl transform and the Wigner distribution function are specifically described in he appendix of ch. VI, pp. 341-364.
    • (1972) Foundations of Electrodynamics , pp. 317-406
    • De Groot, S.R.1    Suttorp, L.G.2
  • 338
    • 0001843298 scopus 로고
    • Théorie et applications de la notion de signal analitique
    • Ville J. Théorie et applications de la notion de signal analitique. Cables et Transmissions 1948, 2A:61-74.
    • (1948) Cables et Transmissions , vol.2 A , pp. 61-74
    • Ville, J.1
  • 339
    • 0001068842 scopus 로고
    • Signal energy distribution in time and frequency
    • Rihaczek A.W. Signal energy distribution in time and frequency. IEEE Trans. Inf. Theory 1968, IT-14:369-374.
    • (1968) IEEE Trans. Inf. Theory , vol.IT-14 , pp. 369-374
    • Rihaczek, A.W.1
  • 340
    • 0019054579 scopus 로고
    • The Wigner distribution - a tool for time-frequency signal analysis. I: continuous-time signals
    • Claasen T.C.A.M., Mecklenbräuker W.F.G. The Wigner distribution - a tool for time-frequency signal analysis. I: continuous-time signals. Philips J. Res. 1980, 35:217-250.
    • (1980) Philips J. Res. , vol.35 , pp. 217-250
    • Claasen, T.C.A.M.1    Mecklenbräuker, W.F.G.2
  • 341
    • 0019067203 scopus 로고
    • The Wigner distribution - a tool for time-frequency signal analysis. II: discrete-time signals
    • Claasen T.C.A.M., Mecklenbräuker W.F.G. The Wigner distribution - a tool for time-frequency signal analysis. II: discrete-time signals. Philips J. Res. 1980, 35:276-300.
    • (1980) Philips J. Res. , vol.35 , pp. 276-300
    • Claasen, T.C.A.M.1    Mecklenbräuker, W.F.G.2
  • 342
    • 0001458386 scopus 로고
    • The Wigner distribution - a tool for time-frequency signal analysis. III: relations with other time-frequency signal transformations
    • Claasen T.C.A.M., Mecklenbräuker W.F.G. The Wigner distribution - a tool for time-frequency signal analysis. III: relations with other time-frequency signal transformations. Philips J. Res. 1980, 35:372-389.
    • (1980) Philips J. Res. , vol.35 , pp. 372-389
    • Claasen, T.C.A.M.1    Mecklenbräuker, W.F.G.2
  • 343
    • 0001517377 scopus 로고
    • A unified definition for the discrete-time, discrete-frequency, and discrete-time/frequency Wigner distributions
    • Peyrin F., Prost R. A unified definition for the discrete-time, discrete-frequency, and discrete-time/frequency Wigner distributions. IEEE Trans. on Acoust., Speech and Signal Process. 1986, 34:858-867.
    • (1986) IEEE Trans. on Acoust., Speech and Signal Process. , vol.34 , pp. 858-867
    • Peyrin, F.1    Prost, R.2
  • 344
    • 0024705330 scopus 로고
    • Time-frequency distributions-A Review
    • Cohen L. Time-frequency distributions-A Review. Proc. IEEE 1989, 77:941-981.
    • (1989) Proc. IEEE , vol.77 , pp. 941-981
    • Cohen, L.1
  • 348
    • 0017957904 scopus 로고
    • Wigner distribution function applied to optical signals and systems
    • Bastiaans M.J. Wigner distribution function applied to optical signals and systems. Opt. Comm. 1978, 25:26-30.
    • (1978) Opt. Comm. , vol.25 , pp. 26-30
    • Bastiaans, M.J.1
  • 349
    • 0018519010 scopus 로고
    • The Wigner distribution function and Hamilton's characteristics of a geometrical-optical system
    • Bastiaans M.J. The Wigner distribution function and Hamilton's characteristics of a geometrical-optical system. Opt. Comm. 1979, 30:321-326.
    • (1979) Opt. Comm. , vol.30 , pp. 321-326
    • Bastiaans, M.J.1
  • 350
    • 0000010577 scopus 로고
    • Wigner distribution function and its application to first-order optics
    • Bastiaans M.J. Wigner distribution function and its application to first-order optics. J. Opt. Soc. Am. 1979, 69:1710-1716.
    • (1979) J. Opt. Soc. Am. , vol.69 , pp. 1710-1716
    • Bastiaans, M.J.1
  • 351
    • 5244278515 scopus 로고
    • The Wigner distribution function and its applications to optics
    • ch. 9, AIP, Amsterdam, M.A. Machado, L.M. Narducci (Eds.) Optics in Four Dimensions-1980
    • Bastiaans M.J. The Wigner distribution function and its applications to optics. AIP Conf. Proc. 1981, 65:292-312. ch. 9, AIP, Amsterdam. M.A. Machado, L.M. Narducci (Eds.).
    • (1981) AIP Conf. Proc. , vol.65 , pp. 292-312
    • Bastiaans, M.J.1
  • 352
    • 0009951381 scopus 로고
    • Signal description by means of a local frequency spectrum
    • SPIE, New York, W.T. Rhodes, J.R. Fienup, B.E.A. Saleh (Eds.)
    • Bastiaans M.J. Signal description by means of a local frequency spectrum. Transformations in Optical Signal Processing 1981, 49-62. SPIE, New York. W.T. Rhodes, J.R. Fienup, B.E.A. Saleh (Eds.).
    • (1981) Transformations in Optical Signal Processing , pp. 49-62
    • Bastiaans, M.J.1
  • 354
    • 0003562442 scopus 로고    scopus 로고
    • Application of the Wigner distribution function in optics
    • Elsevier, W. Mecklenbräuker, F. Hlawatsch (Eds.)
    • Bastiaans M.J. Application of the Wigner distribution function in optics. The Wigner Distribution: Theory and Applications in Signal Processing 1997, 375-426. Elsevier. W. Mecklenbräuker, F. Hlawatsch (Eds.).
    • (1997) The Wigner Distribution: Theory and Applications in Signal Processing , pp. 375-426
    • Bastiaans, M.J.1
  • 355
    • 1542362002 scopus 로고
    • Image filtering and analysis through the Wigner distribution
    • Academic Press, Amsterdam, P.W. Hawkes (Ed.)
    • Cristóbal G., Gonzalo C., Bescós J. Image filtering and analysis through the Wigner distribution. Advances in Electronics and Electron Physics 1991, 309-397. Academic Press, Amsterdam. P.W. Hawkes (Ed.).
    • (1991) Advances in Electronics and Electron Physics , pp. 309-397
    • Cristóbal, G.1    Gonzalo, C.2    Bescós, J.3
  • 356
    • 0011777486 scopus 로고    scopus 로고
    • The Wigner distribution function in Optics and Optoelectronics
    • ch. 1, Elsevier, San Diego, E. Wolf (Ed.)
    • Dragoman D. The Wigner distribution function in Optics and Optoelectronics. Progress in Optics 1997, 1-56. ch. 1, Elsevier, San Diego. E. Wolf (Ed.).
    • (1997) Progress in Optics , pp. 1-56
    • Dragoman, D.1
  • 357
    • 84882078690 scopus 로고    scopus 로고
    • Wigner Distribution and Phase Space in Optics
    • 12, G.W. Forbes, V.I. Man'ko, H.M. Ozaktas, R. Simon, K.B. Wolf (Eds.)
    • Wigner Distribution and Phase Space in Optics. J. Opt. Soc. Am. A 2000, 17:2273-2542. 12. G.W. Forbes, V.I. Man'ko, H.M. Ozaktas, R. Simon, K.B. Wolf (Eds.).
    • (2000) J. Opt. Soc. Am. A , vol.17 , pp. 2273-2542
  • 358
    • 18344373564 scopus 로고
    • Ordered expansions in boson amplitude operators
    • Cahill K.E., Glauber R.J. Ordered expansions in boson amplitude operators. Phys. Rev. 1969, 177:1857-1881.
    • (1969) Phys. Rev. , vol.177 , pp. 1857-1881
    • Cahill, K.E.1    Glauber, R.J.2
  • 359
    • 4243358746 scopus 로고
    • Density operators and quasiprobability distributions
    • Density operators and quasiprobability distributions. Phys. Rev. 1969, 177:1882-1902.
    • (1969) Phys. Rev. , vol.177 , pp. 1882-1902
  • 364
    • 0022062890 scopus 로고
    • Brightness, coherence and propagation characteristics of synchrotron radiation
    • Kim K.-J. Brightness, coherence and propagation characteristics of synchrotron radiation. Nucl. Instr. & Meth. in Phys. Res. A 1986, 246:71-76.
    • (1986) Nucl. Instr. & Meth. in Phys. Res. A , vol.246 , pp. 71-76
    • Kim, K.-J.1
  • 365
    • 0242539260 scopus 로고
    • A generalized display of the contrast transfer function in transmission electron microscopy
    • Castaño V.M. A generalized display of the contrast transfer function in transmission electron microscopy. Optik 1988, 81:35-37.
    • (1988) Optik , vol.81 , pp. 35-37
    • Castaño, V.M.1
  • 366
    • 84882195546 scopus 로고    scopus 로고
    • "A note on Wigner-phase space and electron beam transport",
    • ENEA RT/INN/91/30
    • G. Dattoli, C. Mari and A. Torre, "A note on Wigner-phase space and electron beam transport", ENEA RT/INN/91/30.
    • Dattoli, G.1    Mari, C.2    Torre, A.3
  • 367
    • 0242539258 scopus 로고
    • Image displacements in transmission electron microscopy: a phase space approach
    • Castaño V.M., Santiago P., Gómez A. Image displacements in transmission electron microscopy: a phase space approach. Optik 1993, 95:31-33.
    • (1993) Optik , vol.95 , pp. 31-33
    • Castaño, V.M.1    Santiago, P.2    Gómez, A.3
  • 369
    • 0002396383 scopus 로고
    • Quasi-probability distributions for arbitrary operators
    • Springer-Verlag, Singapore, Y.S. Kim, W.W. Zachary (Eds.)
    • SCully M.O., Cohen L. Quasi-probability distributions for arbitrary operators. The Physics of Phase Space 1987, 253-260. Springer-Verlag, Singapore. Y.S. Kim, W.W. Zachary (Eds.).
    • (1987) The Physics of Phase Space , pp. 253-260
    • SCully, M.O.1    Cohen, L.2
  • 370
    • 4243275762 scopus 로고
    • Quantum-mechanical phase space: a generalization of Wigner phase-space formulation to arbitrary coordinate systems
    • Pimpale A., Razavy M. Quantum-mechanical phase space: a generalization of Wigner phase-space formulation to arbitrary coordinate systems. Phys. Rev. 1988, 38:6046-6054.
    • (1988) Phys. Rev. , vol.38 , pp. 6046-6054
    • Pimpale, A.1    Razavy, M.2
  • 371
    • 0001680187 scopus 로고
    • Wigner function for number and phase
    • Vaccaro J.A., Pegg D.T. Wigner function for number and phase. Phys. Rev. A 1990, 41:5156-6054.
    • (1990) Phys. Rev. A , vol.41 , pp. 5156-6054
    • Vaccaro, J.A.1    Pegg, D.T.2
  • 372
    • 0005268501 scopus 로고
    • Quantum mechanical distribution functions: conditions for uniqueness
    • O'Connell R.F., Wigner E.P. Quantum mechanical distribution functions: conditions for uniqueness. Phys. Lett. A 1981, 83:145-148.
    • (1981) Phys. Lett. A , vol.83 , pp. 145-148
    • O'Connell, R.F.1    Wigner, E.P.2
  • 374
    • 0021546780 scopus 로고
    • Interference terms in the Wigner distribution
    • Elsevier, New York, V. Cappellini, A.G. Constantinides (Eds.)
    • Hlawatsch F. Interference terms in the Wigner distribution. Digital Signal Processing-84 1984, 363-367. Elsevier, New York. V. Cappellini, A.G. Constantinides (Eds.).
    • (1984) Digital Signal Processing-84 , pp. 363-367
    • Hlawatsch, F.1
  • 375
    • 0020251715 scopus 로고
    • On the locus and spread of pseudo-density functions in the time-frequency plane
    • Janssen A.J.E.M. On the locus and spread of pseudo-density functions in the time-frequency plane. Philips J. Res. 1982, 37:79-110.
    • (1982) Philips J. Res. , vol.37 , pp. 79-110
    • Janssen, A.J.E.M.1
  • 376
    • 84941867096 scopus 로고
    • What is a multicomponent signal?
    • Cohen L. What is a multicomponent signal?. Proc. IEEE, ICASSP 1992, 5(92):113-116.
    • (1992) Proc. IEEE, ICASSP , vol.5 , Issue.92 , pp. 113-116
    • Cohen, L.1
  • 377
    • 0001218355 scopus 로고
    • When is the Wigner quasi-probability density non-negative?
    • Hudson R.L. When is the Wigner quasi-probability density non-negative?. Rep. Math. Phys. 1974, 6:249-252.
    • (1974) Rep. Math. Phys. , vol.6 , pp. 249-252
    • Hudson, R.L.1
  • 378
    • 36749105794 scopus 로고
    • Positive quantum joint distributions
    • Cohen L., Zaparovanny Y.I. Positive quantum joint distributions. J. Math. Phys. 1980, 21:794-796.
    • (1980) J. Math. Phys. , vol.21 , pp. 794-796
    • Cohen, L.1    Zaparovanny, Y.I.2
  • 379
    • 0000406855 scopus 로고
    • Some properties of non-negative quantummechanical distribution function
    • O'Connell R.F., Wigner E.P. Some properties of non-negative quantummechanical distribution function. Phys. Lett. A 1981, 85:121-126.
    • (1981) Phys. Lett. A , vol.85 , pp. 121-126
    • O'Connell, R.F.1    Wigner, E.P.2
  • 380
    • 36749120013 scopus 로고
    • When is the Wigner function of multi-dimensional systems non-negative?
    • Soto F., Claverie P. When is the Wigner function of multi-dimensional systems non-negative?. J. Math. Phys 1983, 24:97-100.
    • (1983) J. Math. Phys , vol.24 , pp. 97-100
    • Soto, F.1    Claverie, P.2
  • 381
    • 0038584758 scopus 로고
    • A note on Hudson's theorem about functions with non-negative Wigner distributions
    • Janssen A.J.E.M. A note on Hudson's theorem about functions with non-negative Wigner distributions. SIAM J. Math. Anal. 1984, 15:170-176.
    • (1984) SIAM J. Math. Anal. , vol.15 , pp. 170-176
    • Janssen, A.J.E.M.1
  • 382
    • 0001035508 scopus 로고
    • Positivity properties of phase-plane distribution functions
    • Janssen A.J.E.M. Positivity properties of phase-plane distribution functions. J. Math. Phys. 1984, 25:2240-2252.
    • (1984) J. Math. Phys. , vol.25 , pp. 2240-2252
    • Janssen, A.J.E.M.1
  • 384
    • 0001381047 scopus 로고
    • Some formal properties of the density matrix
    • Husimi K. Some formal properties of the density matrix. Proc. Phys. Math. Soc. Japan 1940, 22:264-314.
    • (1940) Proc. Phys. Math. Soc. Japan , vol.22 , pp. 264-314
    • Husimi, K.1
  • 385
    • 49649138458 scopus 로고
    • A non-negative Wigner-type distribution
    • Cartwright N.D. A non-negative Wigner-type distribution. Physica 1976, 83A:210-212.
    • (1976) Physica , vol.83 A , pp. 210-212
    • Cartwright, N.D.1
  • 387
    • 0039220120 scopus 로고
    • A comment on the smoothed Wigner function
    • Smith T.B. A comment on the smoothed Wigner function. Phys. Lett. A 1988, 127:75-78.
    • (1988) Phys. Lett. A , vol.127 , pp. 75-78
    • Smith, T.B.1
  • 388
    • 0033735614 scopus 로고    scopus 로고
    • The origin of negative values of the Wigner distribution function
    • Dragoman D. The origin of negative values of the Wigner distribution function. Optik 2000, 111:179-183.
    • (2000) Optik , vol.111 , pp. 179-183
    • Dragoman, D.1
  • 389
    • 0040225070 scopus 로고
    • Dynamical maps and nonnegative phase-space distribution functions in quantum mechanics
    • Jagannathan R., Simon R., Sudarshan E.C.G., Vasudevan R. Dynamical maps and nonnegative phase-space distribution functions in quantum mechanics. Phys. Lett. A 1987, 120:161-164.
    • (1987) Phys. Lett. A , vol.120 , pp. 161-164
    • Jagannathan, R.1    Simon, R.2    Sudarshan, E.C.G.3    Vasudevan, R.4
  • 390
    • 0039173177 scopus 로고
    • Conditions for the convolution of two Wigner distributions to be itself a Wigner distribution
    • Narcowich F.J. Conditions for the convolution of two Wigner distributions to be itself a Wigner distribution. J. Math. Phys. 1988, 29:2036-2041.
    • (1988) J. Math. Phys. , vol.29 , pp. 2036-2041
    • Narcowich, F.J.1
  • 391
    • 0043243214 scopus 로고
    • Wigner distribution and ambiguity function
    • AIP, Amsterdam, M.A. Machado, L.M. Narducci (Eds.) Optics in Four Dimensions-1980
    • Szu H.H., Blodgett J.A. Wigner distribution and ambiguity function. AIP Conf. Proc. 1981, 65:355-381. AIP, Amsterdam. M.A. Machado, L.M. Narducci (Eds.).
    • (1981) AIP Conf. Proc. , vol.65 , pp. 355-381
    • Szu, H.H.1    Blodgett, J.A.2
  • 392
    • 0007318650 scopus 로고
    • Necessary and sufficient conditions for a phase-space function to be a Wigner distribution
    • Narcowich F.J., O'Connell R.F. Necessary and sufficient conditions for a phase-space function to be a Wigner distribution. Phys. Rev. A 1986, 34:1-6.
    • (1986) Phys. Rev. A , vol.34 , pp. 1-6
    • Narcowich, F.J.1    O'Connell, R.F.2
  • 393
    • 3543014288 scopus 로고
    • New interpretation of the scalar product in Hilbert space
    • Aharonov Y., Albert D.Z., Au C.K. New interpretation of the scalar product in Hilbert space. Phys. Rev. Lett. 1981, 47:1029-1031.
    • (1981) Phys. Rev. Lett. , vol.47 , pp. 1029-1031
    • Aharonov, Y.1    Albert, D.Z.2    Au, C.K.3
  • 394
    • 3542994375 scopus 로고
    • New interpretation of the scalar product in Hilbert space
    • O'Connell R.F., Rajagopal A.K. New interpretation of the scalar product in Hilbert space. Phys. Rev. Lett. 1981, 48:525-526.
    • (1981) Phys. Rev. Lett. , vol.48 , pp. 525-526
    • O'Connell, R.F.1    Rajagopal, A.K.2
  • 395
    • 0040782039 scopus 로고
    • Quantum interference, superposition states of light, and nonclassical effects
    • ch. 1, Elsevier, New York, E. Wolf (Ed.)
    • Buzek V., Knight P.L. Quantum interference, superposition states of light, and nonclassical effects. Progress in Optics 1995, 1-158. ch. 1, Elsevier, New York. E. Wolf (Ed.).
    • (1995) Progress in Optics , pp. 1-158
    • Buzek, V.1    Knight, P.L.2
  • 396
    • 0028395999 scopus 로고
    • Efficiency of light launching into waveguides
    • Onciul D. Efficiency of light launching into waveguides. Optik 1994, 96:20-24.
    • (1994) Optik , vol.96 , pp. 20-24
    • Onciul, D.1
  • 397
    • 0028479608 scopus 로고
    • Waveguide launching efficiency for multimode and partially coherent light sources
    • Onciul D. Waveguide launching efficiency for multimode and partially coherent light sources. Optik 1994, 97:75-77.
    • (1994) Optik , vol.97 , pp. 75-77
    • Onciul, D.1
  • 398
    • 0029375657 scopus 로고
    • Phase space representation of modes in optical waveguides
    • Dragoman D. Phase space representation of modes in optical waveguides. J. Mod. Opt. 1995, 42:1815-1823.
    • (1995) J. Mod. Opt. , vol.42 , pp. 1815-1823
    • Dragoman, D.1
  • 399
    • 84975562528 scopus 로고
    • Wigner distribution function representation of the coupling coefficient
    • Dragoman D. Wigner distribution function representation of the coupling coefficient. Appl. Opt. 1995, 35:6758-6763.
    • (1995) Appl. Opt. , vol.35 , pp. 6758-6763
    • Dragoman, D.1
  • 400
    • 0001801888 scopus 로고    scopus 로고
    • Fractional Talbot effect: analysis in phase space
    • Testorf M., Ojeda-Castañeda J. Fractional Talbot effect: analysis in phase space. J. Opt. Soc. Am. A 1996, 13:119-125.
    • (1996) J. Opt. Soc. Am. A , vol.13 , pp. 119-125
    • Testorf, M.1    Ojeda-Castañeda, J.2
  • 401
    • 0021958449 scopus 로고
    • Quasi ray-optical approach to longitudinal periodicities of free and bounded wavefields
    • Ojeda-Castañeda J., Sicre E.E. Quasi ray-optical approach to longitudinal periodicities of free and bounded wavefields. Opt. Acta 1985, 32:17-26.
    • (1985) Opt. Acta , vol.32 , pp. 17-26
    • Ojeda-Castañeda, J.1    Sicre, E.E.2
  • 402
    • 0020169626 scopus 로고
    • Wigner distribution function display of complex 1D signals
    • Brenner K.-H., Lohmann A.W. Wigner distribution function display of complex 1D signals. Opt. Comm. 1982, 42:310-314.
    • (1982) Opt. Comm. , vol.42 , pp. 310-314
    • Brenner, K.-H.1    Lohmann, A.W.2
  • 403
    • 0344864752 scopus 로고
    • The influence of wave aberrations on the Wigner distribution
    • Lohmann A.W., Ojeda-Castañeda J., Streibl N. The influence of wave aberrations on the Wigner distribution. Opt. Appl. 1983, 13:465-471.
    • (1983) Opt. Appl. , vol.13 , pp. 465-471
    • Lohmann, A.W.1    Ojeda-Castañeda, J.2    Streibl, N.3
  • 404
    • 0042952609 scopus 로고
    • A macroscopic theory of interference and diffraction of light from finite sources. II. Fields with a spectral range of arbitrary width
    • Wolf E. A macroscopic theory of interference and diffraction of light from finite sources. II. Fields with a spectral range of arbitrary width. Proc. Roy. Soc. (London) 1955, 230:246-265.
    • (1955) Proc. Roy. Soc. (London) , vol.230 , pp. 246-265
    • Wolf, E.1
  • 405
    • 0001479148 scopus 로고
    • 6th, ch. 10, Pergamon, Amsterdam
    • Born M., Wolf E. Principles of Optics 1980, 491-555. 6th, ch. 10, Pergamon, Amsterdam.
    • (1980) Principles of Optics , pp. 491-555
    • Born, M.1    Wolf, E.2
  • 407
  • 409
    • 84950652199 scopus 로고
    • The Wigner distribution function of partially coherent light
    • Bastiaans M.J. The Wigner distribution function of partially coherent light. Optica Acta 1981, 28:1215-1224.
    • (1981) Optica Acta , vol.28 , pp. 1215-1224
    • Bastiaans, M.J.1
  • 410
    • 84867571153 scopus 로고
    • Applications of the Wigner distribution function to partially coherent light
    • Bastiaans M.J. Applications of the Wigner distribution function to partially coherent light. J. Opt. Soc. Am. A 1986, 3:1227-1238.
    • (1986) J. Opt. Soc. Am. A , vol.3 , pp. 1227-1238
    • Bastiaans, M.J.1
  • 411
    • 0037905423 scopus 로고
    • Ambiguity function and Wigner distribution applied to partially coherent imagery
    • Brenner K.-H., Ojeda-Castañeda J. Ambiguity function and Wigner distribution applied to partially coherent imagery. Optica Acta 1984, 31:213-223.
    • (1984) Optica Acta , vol.31 , pp. 213-223
    • Brenner, K.-H.1    Ojeda-Castañeda, J.2
  • 412
    • 0000572780 scopus 로고
    • Radiometry and coherence
    • Walther E. Radiometry and coherence. J. Opt. Soc. Am. 1968, 58:1256-1259.
    • (1968) J. Opt. Soc. Am. , vol.58 , pp. 1256-1259
    • Walther, E.1
  • 413
    • 0000273864 scopus 로고
    • Radiometry and coherence
    • Walther E. Radiometry and coherence. J. Opt. Soc. Am. 1973, 63:1219-1226.
    • (1973) J. Opt. Soc. Am. , vol.63 , pp. 1219-1226
    • Walther, E.1
  • 414
    • 0017926394 scopus 로고
    • Coherence and radiometry
    • Wolf E. Coherence and radiometry. J. Opt. Soc. Am. 1978, 68:6-14.
    • (1978) J. Opt. Soc. Am. , vol.68 , pp. 6-14
    • Wolf, E.1
  • 416
    • 0000439939 scopus 로고    scopus 로고
    • Sinusoidal-Gaussian beams in complex optical systems
    • Casperson L.W., Hall D.G., Tovar A.A. Sinusoidal-Gaussian beams in complex optical systems. J. Opt. Soc. Am. A 1997, 14:3341-3348.
    • (1997) J. Opt. Soc. Am. A , vol.14 , pp. 3341-3348
    • Casperson, L.W.1    Hall, D.G.2    Tovar, A.A.3
  • 417
    • 0032046227 scopus 로고    scopus 로고
    • Hermite-sinusoidal-Gaussian beams in complex optical systems
    • Casperson L.W., Tovar A.A. Hermite-sinusoidal-Gaussian beams in complex optical systems. J. Opt. Soc. Am. A 1998, 15:954-961.
    • (1998) J. Opt. Soc. Am. A , vol.15 , pp. 954-961
    • Casperson, L.W.1    Tovar, A.A.2
  • 418
    • 0032159130 scopus 로고    scopus 로고
    • Production and propagation of Hermitesinusoidal-Gaussian laser beams
    • Tovar A.A., Casperson L.W. Production and propagation of Hermitesinusoidal-Gaussian laser beams. J. Opt. Soc. Am. A 1998, 15:2425-2432.
    • (1998) J. Opt. Soc. Am. A , vol.15 , pp. 2425-2432
    • Tovar, A.A.1    Casperson, L.W.2
  • 419
    • 0034428715 scopus 로고    scopus 로고
    • Propagation properties of Hermite-cosh-Gaussian laser beams
    • Belafhal A., Ibnchaikh M. Propagation properties of Hermite-cosh-Gaussian laser beams. Opt. Comm. 2000, 186:269-276.
    • (2000) Opt. Comm. , vol.186 , pp. 269-276
    • Belafhal, A.1    Ibnchaikh, M.2
  • 420
    • 0024032010 scopus 로고
    • Solid-state laser unstable resonators with tapered reflectivity mirrors: the supergaussian approach
    • De Silvestri S., Laporta P., Magni V., Svelto O. Solid-state laser unstable resonators with tapered reflectivity mirrors: the supergaussian approach. IEEE J. Quant. Electron. 1988, 24:1172-1177.
    • (1988) IEEE J. Quant. Electron. , vol.24 , pp. 1172-1177
    • De Silvestri, S.1    Laporta, P.2    Magni, V.3    Svelto, O.4
  • 421
    • 0028498516 scopus 로고
    • Propagation of super-Gaussian beams
    • Palma C., Bagini V. Propagation of super-Gaussian beams. Opt. Comm. 1994, 111:6-10.
    • (1994) Opt. Comm. , vol.111 , pp. 6-10
    • Palma, C.1    Bagini, V.2
  • 424
    • 0001871334 scopus 로고
    • Uncertainty principles in Fourier analysis
    • Academic Press, New York, O. Shisha (Ed.)
    • De Bruijn N.G. Uncertainty principles in Fourier analysis. Inequalities 1967, 57-71. Academic Press, New York. O. Shisha (Ed.).
    • (1967) Inequalities , pp. 57-71
    • De Bruijn, N.G.1
  • 425
    • 0017552006 scopus 로고
    • A unified approach to short-time Fourier analysis and synthesis
    • Allen J.B., Rabiner L.R. A unified approach to short-time Fourier analysis and synthesis. Proc. IEEE 1977, 65:1558-1564.
    • (1977) Proc. IEEE , vol.65 , pp. 1558-1564
    • Allen, J.B.1    Rabiner, L.R.2
  • 426
    • 0017851927 scopus 로고
    • On the use of windows for harmonic analysis with the discrete Fourier transform
    • Harris F.J. On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE 1978, 66:51-83.
    • (1978) Proc. IEEE , vol.66 , pp. 51-83
    • Harris, F.J.1
  • 427
    • 0021230773 scopus 로고
    • Signal description by means of a local frequency spectrum
    • W.T. Rhodes, J.R. Fienup, B.E.A. Saleh (Eds.) Transformations in Optical Signal Processing
    • Bastiaans M.J. Signal description by means of a local frequency spectrum. SPIE 1981, 373:49-62. W.T. Rhodes, J.R. Fienup, B.E.A. Saleh (Eds.).
    • (1981) SPIE , vol.373 , pp. 49-62
    • Bastiaans, M.J.1
  • 428
    • 0001942222 scopus 로고
    • Short-time Fourier transform
    • Prentice Hall, New York, J.S. Lim, A.V. Oppenheim (Eds.)
    • Nawab S.H., Quatieri T.F. Short-time Fourier transform. Advanced Topics in Signal Processing 1988, 289-337. Prentice Hall, New York. J.S. Lim, A.V. Oppenheim (Eds.).
    • (1988) Advanced Topics in Signal Processing , pp. 289-337
    • Nawab, S.H.1    Quatieri, T.F.2
  • 430
    • 0019008929 scopus 로고
    • Gabor's expansion of a signal into Gaussian elementary signals
    • Bastiaans M.J. Gabor's expansion of a signal into Gaussian elementary signals. Proc. IEEE 1980, 68:538-539.
    • (1980) Proc. IEEE , vol.68 , pp. 538-539
    • Bastiaans, M.J.1
  • 431
    • 0019585486 scopus 로고
    • A sampling theorem for the complex spectrogram, and Gabor's expansion of a signal in Gaussian elementary signals
    • Bastiaans M.J. A sampling theorem for the complex spectrogram, and Gabor's expansion of a signal in Gaussian elementary signals. Opt. Eng. 1981, 20:594-598.
    • (1981) Opt. Eng. , vol.20 , pp. 594-598
    • Bastiaans, M.J.1
  • 432
    • 0000860782 scopus 로고
    • Gabor's signal expansion and degrees of freedom of a signal
    • Bastiaans M.J. Gabor's signal expansion and degrees of freedom of a signal. Optica Acta 1982, 29:1223-1229.
    • (1982) Optica Acta , vol.29 , pp. 1223-1229
    • Bastiaans, M.J.1
  • 433
    • 0026244477 scopus 로고
    • Gabor's signal expansion applied to partially coherent light
    • Bastiaans M.J. Gabor's signal expansion applied to partially coherent light. Opt. Comm. 1991, 86:14-18.
    • (1991) Opt. Comm. , vol.86 , pp. 14-18
    • Bastiaans, M.J.1
  • 434
    • 0028493248 scopus 로고
    • Gabor's signal expansion and Zak transform
    • Bastiaans M.J. Gabor's signal expansion and Zak transform. Appl. Opt. 1994, 33:5241-5255.
    • (1994) Appl. Opt. , vol.33 , pp. 5241-5255
    • Bastiaans, M.J.1
  • 435
    • 0030103713 scopus 로고    scopus 로고
    • On the discrete Gabor transform and the discrete Zak transform
    • Bastiaans M.J., Geilen M.C.W. On the discrete Gabor transform and the discrete Zak transform. Signal Process. 1996, 49:151-166.
    • (1996) Signal Process. , vol.49 , pp. 151-166
    • Bastiaans, M.J.1    Geilen, M.C.W.2
  • 436
    • 0141582037 scopus 로고
    • Generalized phase space distribution functions
    • Cohen L. Generalized phase space distribution functions. J. Math. Phys. 1966, 7:781-786.
    • (1966) J. Math. Phys. , vol.7 , pp. 781-786
    • Cohen, L.1
  • 437
    • 36749108415 scopus 로고
    • Quantization problem and variational principle in the phase-space formulation of quantum mechanics
    • Cohen L. Quantization problem and variational principle in the phase-space formulation of quantum mechanics. J. Math. Phys. 1976, 17:1863-1866.
    • (1976) J. Math. Phys. , vol.17 , pp. 1863-1866
    • Cohen, L.1
  • 438
    • 0001458386 scopus 로고
    • The Wigner distribution - a tool for time-frequency signal analysis. III: relations with other time-frequency signal transformations
    • Claasen T.C.A.M., Mecklenbräuker W.F.G. The Wigner distribution - a tool for time-frequency signal analysis. III: relations with other time-frequency signal transformations. Philips J. Res. 1980, 35:372-389.
    • (1980) Philips J. Res. , vol.35 , pp. 372-389
    • Claasen, T.C.A.M.1    Mecklenbräuker, W.F.G.2
  • 439
    • 0024705330 scopus 로고
    • Time-frequency distributions - A review
    • Cohen L. Time-frequency distributions - A review. Proc. IEEE 1989, 77:941-981.
    • (1989) Proc. IEEE , vol.77 , pp. 941-981
    • Cohen, L.1
  • 440
    • 0023825353 scopus 로고
    • Joint spatial/spatial-frequency representation
    • Jacobson L.D., Wechsler H. Joint spatial/spatial-frequency representation. Signal Process. 1988, 14:37-68.
    • (1988) Signal Process. , vol.14 , pp. 37-68
    • Jacobson, L.D.1    Wechsler, H.2
  • 442
  • 445
    • 0024681555 scopus 로고
    • Improved time-frequency representation of multicomponent signal using exponential kernels
    • Choi H., Williams W.J. Improved time-frequency representation of multicomponent signal using exponential kernels. IEEE Trans. on Signal Process. 1989, 37:862-871.
    • (1989) IEEE Trans. on Signal Process. , vol.37 , pp. 862-871
    • Choi, H.1    Williams, W.J.2
  • 446
    • 0025463449 scopus 로고
    • The use of cone-shape kernels for generalized time-frequency representation of nonstationary signals
    • Zhao Y., Atlas L.E., Marks R.J. The use of cone-shape kernels for generalized time-frequency representation of nonstationary signals. IEEE Trans. on Signal Process. 1990, 38:1084-1091.
    • (1990) IEEE Trans. on Signal Process. , vol.38 , pp. 1084-1091
    • Zhao, Y.1    Atlas, L.E.2    Marks, R.J.3
  • 447
    • 0026187950 scopus 로고
    • Duality and classification of bilinear time-frequency signal representations
    • Hlawatsch F. Duality and classification of bilinear time-frequency signal representations. IEEE Trans. on Signal Process. 1991, 39:1564-1574.
    • (1991) IEEE Trans. on Signal Process. , vol.39 , pp. 1564-1574
    • Hlawatsch, F.1
  • 449
    • 0026817814 scopus 로고
    • Kernel design for reduced interference distributions
    • Jeong J., Williams W.J. Kernel design for reduced interference distributions. IEEE Trans. on Signal Process. 1992, 40:401-412.
    • (1992) IEEE Trans. on Signal Process. , vol.40 , pp. 401-412
    • Jeong, J.1    Williams, W.J.2
  • 451
  • 452
    • 0027577041 scopus 로고
    • A signal-dependent time-frequency representation: optimal kernel design
    • Baraniuk R.G., Jones D.L. A signal-dependent time-frequency representation: optimal kernel design. IEEE Trans. on Signal Process. 1993, 41:1589-1602.
    • (1993) IEEE Trans. on Signal Process. , vol.41 , pp. 1589-1602
    • Baraniuk, R.G.1    Jones, D.L.2
  • 453
    • 0028378116 scopus 로고
    • Bilinear time-frequency representations of signals: the shift-scale invariant class
    • Hlawatsch F., Urbanke R.L. Bilinear time-frequency representations of signals: the shift-scale invariant class. IEEE Trans. on Signal Process. 1994, 42:357-366.
    • (1994) IEEE Trans. on Signal Process. , vol.42 , pp. 357-366
    • Hlawatsch, F.1    Urbanke, R.L.2
  • 455
    • 0029222057 scopus 로고
    • On joint distribution of arbitrary variables
    • Baraniuk R.G., Cohen L. On joint distribution of arbitrary variables. IEEE Signal Lett. 1995, 2:10-12.
    • (1995) IEEE Signal Lett. , vol.2 , pp. 10-12
    • Baraniuk, R.G.1    Cohen, L.2
  • 457
    • 0001619688 scopus 로고
    • Smoothed pseudo-Wigner distribution, Choi-Williams distribution and cone-kernel representation: ambiguity-domain analysis and experimental comparison
    • Hlawatsch F., Manickam T.G., Urbanke R.L., Jones W. Smoothed pseudo-Wigner distribution, Choi-Williams distribution and cone-kernel representation: ambiguity-domain analysis and experimental comparison. Signal Process. 1995, 43:149-168.
    • (1995) Signal Process. , vol.43 , pp. 149-168
    • Hlawatsch, F.1    Manickam, T.G.2    Urbanke, R.L.3    Jones, W.4
  • 458
    • 0029253536 scopus 로고
    • Wide-band ambiguity functions and affine Wigner distributions
    • Shenoy R.G., Parks T.W. Wide-band ambiguity functions and affine Wigner distributions. Signal Process. 1995, 41:339-363.
    • (1995) Signal Process. , vol.41 , pp. 339-363
    • Shenoy, R.G.1    Parks, T.W.2
  • 459
    • 0029393329 scopus 로고
    • Design of time-frequency representations using a multiform, tiltable exponential kernel
    • Costa A.H., Boudreaux-Bartels G.F. Design of time-frequency representations using a multiform, tiltable exponential kernel. IEEE Trans. on Signal Process. 1995, 43:2283-2301.
    • (1995) IEEE Trans. on Signal Process. , vol.43 , pp. 2283-2301
    • Costa, A.H.1    Boudreaux-Bartels, G.F.2
  • 460
    • 0030142571 scopus 로고    scopus 로고
    • A general approach for obtaining joint representations in signal analysis-Part I: characteristic function operator method
    • Cohen L. A general approach for obtaining joint representations in signal analysis-Part I: characteristic function operator method. IEEE Trans. on Signal Process. 1996, 44:1080-1090.
    • (1996) IEEE Trans. on Signal Process. , vol.44 , pp. 1080-1090
    • Cohen, L.1
  • 461
    • 0030142570 scopus 로고    scopus 로고
    • A general approach for obtaining joint representations in signal analysis-Part II: general class, mean and local values, and bandwidth
    • Cohen L. A general approach for obtaining joint representations in signal analysis-Part II: general class, mean and local values, and bandwidth. IEEE Trans. on Signal Process. 1996, 44:1091-1098.
    • (1996) IEEE Trans. on Signal Process. , vol.44 , pp. 1091-1098
    • Cohen, L.1
  • 462
    • 0032181607 scopus 로고    scopus 로고
    • Joint distributions of arbitrary variables made easy
    • Baraniuk R.G. Joint distributions of arbitrary variables made easy. Multdim. Sys. and Signal Process. 1998, 9:341-348.
    • (1998) Multdim. Sys. and Signal Process. , vol.9 , pp. 341-348
    • Baraniuk, R.G.1
  • 464
    • 84944486510 scopus 로고
    • The design of radar signals having both high range resolution and high velocity resolution
    • Klauder J.R. The design of radar signals having both high range resolution and high velocity resolution. Bell Syst. Tech. J. 1960, 39:809-820.
    • (1960) Bell Syst. Tech. J. , vol.39 , pp. 809-820
    • Klauder, J.R.1
  • 465
    • 84882058105 scopus 로고
    • ch. 8, McGraw-Hill, New York
    • Papoulis A. Signal Analysis 1977, 284-295. ch. 8, McGraw-Hill, New York.
    • (1977) Signal Analysis , pp. 284-295
    • Papoulis, A.1
  • 466
    • 0043243214 scopus 로고
    • Wigner distribution and ambiguity function
    • AIP, New York, M.A. Machado, L.M. Narducci (Eds.) Optics in Four Dimensions-1980
    • Szu H.H., Blodgett J.A. Wigner distribution and ambiguity function. AIP Conf. Proc. 1981, 65:355-381. AIP, New York. M.A. Machado, L.M. Narducci (Eds.).
    • (1981) AIP Conf. Proc. , vol.65 , pp. 355-381
    • Szu, H.H.1    Blodgett, J.A.2
  • 467
    • 0021461780 scopus 로고
    • The mutual time-frequency content of two signals
    • Szu H.H., Caulfield H.J. The mutual time-frequency content of two signals. Proc. IEEE 1984, 72:902-908.
    • (1984) Proc. IEEE , vol.72 , pp. 902-908
    • Szu, H.H.1    Caulfield, H.J.2
  • 468
    • 0016073256 scopus 로고
    • Ambiguity function in Fourier optics
    • Papoulis A. Ambiguity function in Fourier optics. J. Opt. Soc. Am. 1974, 64:779-788.
    • (1974) J. Opt. Soc. Am. , vol.64 , pp. 779-788
    • Papoulis, A.1
  • 469
    • 11744254135 scopus 로고
    • Reconstructions of images of partially coherent objects from samples of mutual intensity
    • Dutta K., Goodman J.W. Reconstructions of images of partially coherent objects from samples of mutual intensity. J. Opt. Soc. Am. 1977, 67:796-803.
    • (1977) J. Opt. Soc. Am. , vol.67 , pp. 796-803
    • Dutta, K.1    Goodman, J.W.2
  • 470
    • 0017997664 scopus 로고
    • The ambiguity function in diffraction and isoplanatic imaging by partially coherent beams
    • Guigay J.-P. The ambiguity function in diffraction and isoplanatic imaging by partially coherent beams. Opt. Comm. 1978, 26:136-138.
    • (1978) Opt. Comm. , vol.26 , pp. 136-138
    • Guigay, J.-P.1
  • 471
    • 0037905423 scopus 로고
    • Ambiguity function and Wigner distribution applied to partially coherent imagery
    • Brenner K.-H., Ojeda-Castañeda J. Ambiguity function and Wigner distribution applied to partially coherent imagery. Optica Acta 1984, 31:213-223.
    • (1984) Optica Acta , vol.31 , pp. 213-223
    • Brenner, K.-H.1    Ojeda-Castañeda, J.2
  • 472
  • 473
    • 0015615593 scopus 로고
    • Crosspath real-time optical correlator and ambiguity function processor
    • Said R.A.K., Cooper D.C. Crosspath real-time optical correlator and ambiguity function processor. Proc. IEE 1973, 120:423-428.
    • (1973) Proc. IEE , vol.120 , pp. 423-428
    • Said, R.A.K.1    Cooper, D.C.2
  • 474
    • 0017465255 scopus 로고
    • Ambiguity function display: an improved coherent processor
    • Marks R.J., Walkup J.F., Krile T.F. Ambiguity function display: an improved coherent processor. Appl. Opt. 1977, 16:746-750.
    • (1977) Appl. Opt. , vol.16 , pp. 746-750
    • Marks, R.J.1    Walkup, J.F.2    Krile, T.F.3
  • 475
    • 84882158034 scopus 로고
    • Addendum 1977, 16:1777.
    • (1977) Addendum , vol.16 , pp. 1777
  • 476
    • 0018469302 scopus 로고
    • Optical image plane correlator for ambiguity surface computation
    • Casasent D., Vijaya Kumar B.V.K. Optical image plane correlator for ambiguity surface computation. Appl. Opt. 1979, 18:1673-1678.
    • (1979) Appl. Opt. , vol.18 , pp. 1673-1678
    • Casasent, D.1    Vijaya Kumar, B.V.K.2
  • 477
    • 0018482723 scopus 로고
    • Space-variant ambiguity function processor
    • Psaltis d., Casasent D. Space-variant ambiguity function processor. Appl. Opt. 1979, 18:1869-1874.
    • (1979) Appl. Opt. , vol.18 , pp. 1869-1874
    • Psaltis, D.1    Casasent, D.2
  • 478
    • 84882088604 scopus 로고
    • Ambiguity function display using a single 1D input
    • Marks R.J., Hall M.W. Ambiguity function display using a single 1D input. Appl. Opt. 1979, 18:2539-2540.
    • (1979) Appl. Opt. , vol.18 , pp. 2539-2540
    • Marks, R.J.1    Hall, M.W.2
  • 479
    • 0018995792 scopus 로고
    • Ambiguity processing by joint Fourier transform holography
    • Lee T.C., Rebholz J., Tamura P.N., Lindquist J. Ambiguity processing by joint Fourier transform holography. Appl. Opt. 1980, 19:895-899.
    • (1980) Appl. Opt. , vol.19 , pp. 895-899
    • Lee, T.C.1    Rebholz, J.2    Tamura, P.N.3    Lindquist, J.4
  • 480
    • 84975624479 scopus 로고
    • Ambiguity-function generation using passive optical τ-shift technique
    • Tamura P.N., Rebholz J.J., Lee T.C. Ambiguity-function generation using passive optical τ-shift technique. Opt. Lett. 1980, 5:401-403.
    • (1980) Opt. Lett. , vol.5 , pp. 401-403
    • Tamura, P.N.1    Rebholz, J.J.2    Lee, T.C.3
  • 481
    • 36149054319 scopus 로고
    • Spatial filtering in optical-data processing
    • Birch K.G. Spatial filtering in optical-data processing. Rep. Prog. Phys. 1972, 35:1265-1314.
    • (1972) Rep. Prog. Phys. , vol.35 , pp. 1265-1314
    • Birch, K.G.1
  • 482
    • 0016114373 scopus 로고
    • Coherent Optical processing
    • Vander Lugt A. Coherent Optical processing. Proc. IEEE 1974, 62:1300-1319.
    • (1974) Proc. IEEE , vol.62 , pp. 1300-1319
    • Vander Lugt, A.1
  • 483
    • 0017266477 scopus 로고
    • Frequency-variant optical signal analysis
    • Rhodes W.T., Florence J.M. Frequency-variant optical signal analysis. Appl. Opt. 1976, 15:3073-3079.
    • (1976) Appl. Opt. , vol.15 , pp. 3073-3079
    • Rhodes, W.T.1    Florence, J.M.2
  • 484
    • 0017416631 scopus 로고
    • Operations achievable with coherent optical information processing systems
    • Goodman J.W. Operations achievable with coherent optical information processing systems. Proc. IEEE 1977, 65:29-38.
    • (1977) Proc. IEEE , vol.65 , pp. 29-38
    • Goodman, J.W.1
  • 486
    • 0017938083 scopus 로고
    • Astigmatic coherent processor analysis
    • Marks R.J., Bell S.V. Astigmatic coherent processor analysis. Opt. Eng. 1978, 17:167-169.
    • (1978) Opt. Eng. , vol.17 , pp. 167-169
    • Marks, R.J.1    Bell, S.V.2
  • 487
    • 0019010930 scopus 로고
    • Space-variant coherent optical processing
    • Walkup J.F. Space-variant coherent optical processing. Opt. Eng. 1980, 19:339-346.
    • (1980) Opt. Eng. , vol.19 , pp. 339-346
    • Walkup, J.F.1
  • 488
    • 0019011742 scopus 로고
    • Incoherent spatial filtering
    • Rhodes W.T. Incoherent spatial filtering. Opt. Eng. 1980, 19:323-330.
    • (1980) Opt. Eng. , vol.19 , pp. 323-330
    • Rhodes, W.T.1
  • 490
    • 0020140014 scopus 로고
    • Optical processing of one-dimensional signals
    • Bartelt H., Lohmann A.W. Optical processing of one-dimensional signals. Opt. Comm. 1982, 42:87-91.
    • (1982) Opt. Comm. , vol.42 , pp. 87-91
    • Bartelt, H.1    Lohmann, A.W.2
  • 491
    • 0022768173 scopus 로고
    • Optical computing: a field in flux
    • Bell T.E. Optical computing: a field in flux. IEEE Spectrum 1986, 23(no. 8):34-57.
    • (1986) IEEE Spectrum , vol.23 , Issue.8 , pp. 34-57
    • Bell, T.E.1
  • 492
    • 0041468625 scopus 로고
    • Information processing with spatially incoherent light
    • ch. 5, North Holland, New York, E. Wolf (Ed.)
    • Glaser I. Information processing with spatially incoherent light. Progress in Optics 1987, 389-509. ch. 5, North Holland, New York. E. Wolf (Ed.).
    • (1987) Progress in Optics , pp. 389-509
    • Glaser, I.1
  • 498
    • 84882048877 scopus 로고
    • Digital Optical Computing
    • special issue in
    • Digital Optical Computing. Opt. Eng. 1986, 25:1-116. special issue in.
    • (1986) Opt. Eng. , vol.25 , pp. 1-116
  • 499
    • 84975661907 scopus 로고
    • What classical optics can do for the digital optical computer
    • Lohmann A.W. What classical optics can do for the digital optical computer. Appl. Opt. 1986, 25:1543-1549.
    • (1986) Appl. Opt. , vol.25 , pp. 1543-1549
    • Lohmann, A.W.1
  • 500
    • 0024020037 scopus 로고
    • Digital optical computing
    • Brenner K.-H. Digital optical computing. Appl. Phys. B 1988, 46:111-120.
    • (1988) Appl. Phys. B , vol.46 , pp. 111-120
    • Brenner, K.-H.1
  • 502
  • 503
    • 0018039524 scopus 로고
    • Bilinear processing of 1D signals by use of linear 2D coherent optical processors
    • Saleh B.E.A. Bilinear processing of 1D signals by use of linear 2D coherent optical processors. Appl. Opt. 1978, 17:3408-3411.
    • (1978) Appl. Opt. , vol.17 , pp. 3408-3411
    • Saleh, B.E.A.1
  • 504
    • 0000098635 scopus 로고
    • Optical bilinear transformations: general properties
    • Saleh B.E.A. Optical bilinear transformations: general properties. Optica Acta 1979, 26:777-799.
    • (1979) Optica Acta , vol.26 , pp. 777-799
    • Saleh, B.E.A.1
  • 505
    • 0020168320 scopus 로고
    • Linearity of quasi-homogeneous partially coherent imagery
    • Saleh B.E.A. Linearity of quasi-homogeneous partially coherent imagery. J. Opt. Soc. Am. 1982, 72:1095-1096.
    • (1982) J. Opt. Soc. Am. , vol.72 , pp. 1095-1096
    • Saleh, B.E.A.1
  • 506
    • 0021199819 scopus 로고
    • Bilinear transformations in optical signal-processing
    • Saleh B.E.A. Bilinear transformations in optical signal-processing. Proc. Soc. Photo-Opt. Inst. 1984, 373:125-134.
    • (1984) Proc. Soc. Photo-Opt. Inst. , vol.373 , pp. 125-134
    • Saleh, B.E.A.1
  • 507
    • 27644461657 scopus 로고
    • Bilinear optical systems. The Wigner distribution function and ambiguity function representations
    • Ojeda-Castañeda J., Sicre E.E. Bilinear optical systems. The Wigner distribution function and ambiguity function representations. Optica Acta 1984, 31:255-260.
    • (1984) Optica Acta , vol.31 , pp. 255-260
    • Ojeda-Castañeda, J.1    Sicre, E.E.2
  • 508
    • 84975560616 scopus 로고
    • Wigner distribution function display: a supplement to ambiguity function display using a single 1D input
    • Bastiaans M.J. Wigner distribution function display: a supplement to ambiguity function display using a single 1D input. Appl. Opt. 1980, 19:192.
    • (1980) Appl. Opt. , vol.19 , pp. 192
    • Bastiaans, M.J.1
  • 509
    • 49149141092 scopus 로고
    • The Wigner distribution function and its optical production
    • Bartelt H.O., Brenner K.-H., Lohnmann A.W. The Wigner distribution function and its optical production. Opt. Comm. 1980, 32:32-38.
    • (1980) Opt. Comm. , vol.32 , pp. 32-38
    • Bartelt, H.O.1    Brenner, K.-H.2    Lohnmann, A.W.3
  • 510
    • 0020169626 scopus 로고
    • Wigner distribution function display of complex 1D signals
    • Brenner K.-H., Lohmann A.W. Wigner distribution function display of complex 1D signals. Opt. Comm. 1982, 42:310-314.
    • (1982) Opt. Comm. , vol.42 , pp. 310-314
    • Brenner, K.-H.1    Lohmann, A.W.2
  • 511
    • 0020189213 scopus 로고
    • Two-dimensional optical filtering of 1D signals
    • Eichmann G., Dong B.Z. Two-dimensional optical filtering of 1D signals. Appl. Opt. 1982, 21:3152-3156.
    • (1982) Appl. Opt. , vol.21 , pp. 3152-3156
    • Eichmann, G.1    Dong, B.Z.2
  • 512
    • 0000154288 scopus 로고
    • The Wigner distribution of two-dimensional signals. Coherent optical generation and display
    • Bamler R., Glünder H. The Wigner distribution of two-dimensional signals. Coherent optical generation and display. Optica Acta 1983, 30:1789-1803.
    • (1983) Optica Acta , vol.30 , pp. 1789-1803
    • Bamler, R.1    Glünder, H.2
  • 513
    • 0021515497 scopus 로고
    • Generation of the Wigner distribution function of two-dimensional singals by a parallel optical processor
    • Subotic N., Saleh B.E.A. Generation of the Wigner distribution function of two-dimensional singals by a parallel optical processor. Opt. Lett. 1984, 9:471-473.
    • (1984) Opt. Lett. , vol.9 , pp. 471-473
    • Subotic, N.1    Saleh, B.E.A.2
  • 514
    • 0001558566 scopus 로고
    • Optical generation of the Wigner distribution of 2D real signals
    • Conner M., Li Y. Optical generation of the Wigner distribution of 2D real signals. Appl. Opt. 1985, 24:3825-3829.
    • (1985) Appl. Opt. , vol.24 , pp. 3825-3829
    • Conner, M.1    Li, Y.2
  • 515
    • 0022681499 scopus 로고
    • The generation of a Wigner distribution function of complex signals by spatial filtering
    • Mateeva Ts., Sharlandjiev P. The generation of a Wigner distribution function of complex signals by spatial filtering. Opt. Comm. 1986, 57:153-155.
    • (1986) Opt. Comm. , vol.57 , pp. 153-155
    • Mateeva, T.1    Sharlandjiev, P.2
  • 516
    • 0022710886 scopus 로고
    • Simultaneous optical production of the sectional Wigner distribution function for a two-dimensional object
    • Iwai T., Gupta A.K., Asakura T. Simultaneous optical production of the sectional Wigner distribution function for a two-dimensional object. Opt. Comm. 1986, 58:15-19.
    • (1986) Opt. Comm. , vol.58 , pp. 15-19
    • Iwai, T.1    Gupta, A.K.2    Asakura, T.3
  • 517
    • 0022918627 scopus 로고
    • New optical system for the efficient display of Wigner distribution function using a single object transparency
    • Gupta A.K., Asakura T. New optical system for the efficient display of Wigner distribution function using a single object transparency. Opt. Comm. 1986, 60:265-268.
    • (1986) Opt. Comm. , vol.60 , pp. 265-268
    • Gupta, A.K.1    Asakura, T.2
  • 518
    • 0024053189 scopus 로고
    • Optical Wigner distribution and ambiguity function for complex signals and images
    • Li Y., Eichmann G., Conner M. Optical Wigner distribution and ambiguity function for complex signals and images. Opt. Comm. 1988, 67:177-179.
    • (1988) Opt. Comm. , vol.67 , pp. 177-179
    • Li, Y.1    Eichmann, G.2    Conner, M.3
  • 519
    • 84882103860 scopus 로고
    • Wigner distribution function/ambiguity function processor
    • Rakes A.A., Hester C., Inguva R., Kumar B.V.K. Wigner distribution function/ambiguity function processor. Proc. SPIE 1988, 936:260-269.
    • (1988) Proc. SPIE , vol.936 , pp. 260-269
    • Rakes, A.A.1    Hester, C.2    Inguva, R.3    Kumar, B.V.K.4
  • 520
    • 0037905425 scopus 로고    scopus 로고
    • Proposal for optical implementation of the Wigner distribution function
    • Shabtay G., Mendlovic D., Zalevsky Z. Proposal for optical implementation of the Wigner distribution function. Appl. Opt. 1998, 37:2142-2144.
    • (1998) Appl. Opt. , vol.37 , pp. 2142-2144
    • Shabtay, G.1    Mendlovic, D.2    Zalevsky, Z.3
  • 521
    • 0000640583 scopus 로고    scopus 로고
    • Heterodyne measurement of Wigner distributions for classical optical fields
    • Lee K.F., Reil F., Bali S., Wax A., Thomas J.E. Heterodyne measurement of Wigner distributions for classical optical fields. Opt. Lett. 1999, 24:1370-1372.
    • (1999) Opt. Lett. , vol.24 , pp. 1370-1372
    • Lee, K.F.1    Reil, F.2    Bali, S.3    Wax, A.4    Thomas, J.E.5
  • 522
    • 0011777486 scopus 로고    scopus 로고
    • The Wigner distribution function in Optics and Optoelectronics
    • ch. 1, Elsevier, Bellingham, USA, E. Wolf (Ed.)
    • Dragoman D. The Wigner distribution function in Optics and Optoelectronics. Progress in Optics 1997, 1-56. ch. 1, Elsevier, Bellingham, USA. E. Wolf (Ed.).
    • (1997) Progress in Optics , pp. 1-56
    • Dragoman, D.1
  • 523
    • 1542362002 scopus 로고
    • Image filtering and analysis through the Wigner distribution
    • Academic Press, Amsterdam, P.W. Hawkes (Ed.)
    • Cristóbal G., Gonzalo C., Bescós J. Image filtering and analysis through the Wigner distribution. Advances in Electronics and Electron Physics 1991, 309-397. Academic Press, Amsterdam. P.W. Hawkes (Ed.).
    • (1991) Advances in Electronics and Electron Physics , pp. 309-397
    • Cristóbal, G.1    Gonzalo, C.2    Bescós, J.3
  • 525
    • 0000441472 scopus 로고
    • The formulation of quantum mechanics in terms of ensemble in phase space
    • Takabayasi T. The formulation of quantum mechanics in terms of ensemble in phase space. Progr. Theor. Phys. 1954, 11:341-373.
    • (1954) Progr. Theor. Phys. , vol.11 , pp. 341-373
    • Takabayasi, T.1
  • 526
    • 33745055092 scopus 로고
    • Formulation of quantum mechanics based on the quasi-probability distribution induced on phase space
    • Baker G.A. Formulation of quantum mechanics based on the quasi-probability distribution induced on phase space. Phys. Rev. 1958, 109:2198-2206.
    • (1958) Phys. Rev. , vol.109 , pp. 2198-2206
    • Baker, G.A.1
  • 527
    • 0000104238 scopus 로고
    • Wigner representation of quantum operators and its applications to electrons in a magnetic field
    • Kubo R. Wigner representation of quantum operators and its applications to electrons in a magnetic field. J. Phys. Soc. Japn 1964, 19:2127-2139.
    • (1964) J. Phys. Soc. Japn , vol.19 , pp. 2127-2139
    • Kubo, R.1
  • 529
    • 77956679689 scopus 로고
    • On phase-space description of quantum mechanics
    • Ruggeri G.J. On phase-space description of quantum mechanics. Progr. Theor. Phys. 1971, 46:1703-1712.
    • (1971) Progr. Theor. Phys. , vol.46 , pp. 1703-1712
    • Ruggeri, G.J.1
  • 530
    • 36749116312 scopus 로고
    • Wigner phase space method. Analysis for semiclassical applications
    • Heller E.J. Wigner phase space method. Analysis for semiclassical applications. J. Chem. Phys. 1976, 65:1289-1298.
    • (1976) J. Chem. Phys. , vol.65 , pp. 1289-1298
    • Heller, E.J.1
  • 531
    • 0001545185 scopus 로고
    • On a quantum algebraic approach to a generalized phase space
    • Bohm D., Hiley B.J. On a quantum algebraic approach to a generalized phase space. Found. Phys. 1981, 11:179-203.
    • (1981) Found. Phys. , vol.11 , pp. 179-203
    • Bohm, D.1    Hiley, B.J.2
  • 532
    • 4243937369 scopus 로고
    • Wigner function as the expectation value of a parity operator
    • Royer A. Wigner function as the expectation value of a parity operator. Phys. Rev. A 1977, 15:449-450.
    • (1977) Phys. Rev. A , vol.15 , pp. 449-450
    • Royer, A.1
  • 534
    • 0038584779 scopus 로고
    • Gaussian Wigner distributions: a complete characterization
    • Simon R., Sudarshan E.C.G., Mukunda N. Gaussian Wigner distributions: a complete characterization. Phys. Lett. 1987, 124:223-228.
    • (1987) Phys. Lett. , vol.124 , pp. 223-228
    • Simon, R.1    Sudarshan, E.C.G.2    Mukunda, N.3
  • 535
    • 4244042893 scopus 로고
    • Gaussian-Wigner distributions in quantum mechanics and optics
    • Simon R., Sudarshan E.C.G., Mukunda N. Gaussian-Wigner distributions in quantum mechanics and optics. Phys. Rev. Lett. A 1987, 36:3868-3880.
    • (1987) Phys. Rev. Lett. A , vol.36 , pp. 3868-3880
    • Simon, R.1    Sudarshan, E.C.G.2    Mukunda, N.3
  • 536
    • 0002113773 scopus 로고
    • Wigner function in Liouville space: A canonical formalism
    • Royer A. Wigner function in Liouville space: A canonical formalism. Phys. Rev. A 1991, 43:44-56.
    • (1991) Phys. Rev. A , vol.43 , pp. 44-56
    • Royer, A.1
  • 537
    • 0004423664 scopus 로고
    • On quantum mechanical phase-space wave functions
    • Wlodarz J.J. On quantum mechanical phase-space wave functions. J. Chem. Phys. 1994, 100:7478-7480.
    • (1994) J. Chem. Phys. , vol.100 , pp. 7478-7480
    • Wlodarz, J.J.1
  • 538
    • 4243870641 scopus 로고
    • Theory and application of the quantum phase-space distribution functions
    • Lee H.-W. Theory and application of the quantum phase-space distribution functions. Phys. Rep. 1995, 259:147-211.
    • (1995) Phys. Rep. , vol.259 , pp. 147-211
    • Lee, H.-W.1
  • 539
    • 33745014742 scopus 로고
    • On the quantum correction for thermodynamic equilibrium
    • Wigner E.P. On the quantum correction for thermodynamic equilibrium. Phys. Rev. 1932, 40:749-759.
    • (1932) Phys. Rev. , vol.40 , pp. 749-759
    • Wigner, E.P.1
  • 540
    • 0000760091 scopus 로고
    • Quantum-mechanical distribution functions-Revisited
    • MIT Press, New York, W. Yourgrau, A.V.D. Merwe (Eds.)
    • Wigner E.P. Quantum-mechanical distribution functions-Revisited. Perspectives in Quantum Theory 1971, 25-36. MIT Press, New York. W. Yourgrau, A.V.D. Merwe (Eds.).
    • (1971) Perspectives in Quantum Theory , pp. 25-36
    • Wigner, E.P.1
  • 541
    • 0005268501 scopus 로고
    • Quantum-mechanical distribution functions: conditions for uniqueness
    • O'Connell R.F., Wigner E.P. Quantum-mechanical distribution functions: conditions for uniqueness. Phys. Lett. 1981, 83A:145-148.
    • (1981) Phys. Lett. , vol.83 A , pp. 145-148
    • O'Connell, R.F.1    Wigner, E.P.2
  • 542
    • 0002565536 scopus 로고
    • Quantum mechanics in phase space I. Unicity of the Wigner distribution function
    • Krüger J.G., Poffyn A. Quantum mechanics in phase space I. Unicity of the Wigner distribution function. Physica 1976, 85A:84-100.
    • (1976) Physica , vol.85 A , pp. 84-100
    • Krüger, J.G.1    Poffyn, A.2
  • 543
    • 0141582037 scopus 로고
    • Generalized phase-space distribution functions
    • Cohen L. Generalized phase-space distribution functions. J. Math. Phys. 1966, 7:781-786.
    • (1966) J. Math. Phys. , vol.7 , pp. 781-786
    • Cohen, L.1
  • 544
    • 2242420938 scopus 로고
    • Can quantum mechanics be formulated as a classical probabilistic theory?
    • Cohen L. Can quantum mechanics be formulated as a classical probabilistic theory?. Philos. Sc. 1966, 33:317-322.
    • (1966) Philos. Sc. , vol.33 , pp. 317-322
    • Cohen, L.1
  • 545
    • 25944459164 scopus 로고
    • Some nonclassical features of phase-space representations of quantum mechanics
    • Srinivas M.D., Wolf E. Some nonclassical features of phase-space representations of quantum mechanics. Phys. Rev. D 1975, 11:1477-1485.
    • (1975) Phys. Rev. D , vol.11 , pp. 1477-1485
    • Srinivas, M.D.1    Wolf, E.2
  • 546
    • 36749110097 scopus 로고
    • A generalization of Cohen's theorem
    • Groblicki R. A generalization of Cohen's theorem. J. Math Phys. 1983, 24:841-843.
    • (1983) J. Math Phys. , vol.24 , pp. 841-843
    • Groblicki, R.1
  • 547
    • 0033735614 scopus 로고    scopus 로고
    • The origin of negative values of the Wigner distribution function
    • Dragoman D. The origin of negative values of the Wigner distribution function. Optik 2000, 111:179-183.
    • (2000) Optik , vol.111 , pp. 179-183
    • Dragoman, D.1
  • 548
    • 7044241645 scopus 로고
    • Phase-space formulation of the dynamics of canonical variables
    • Metha C.L. Phase-space formulation of the dynamics of canonical variables. J. Math. Phys. 1964, 5:677-686.
    • (1964) J. Math. Phys. , vol.5 , pp. 677-686
    • Metha, C.L.1
  • 549
    • 0011685829 scopus 로고
    • Weyl transformation and the classical limit of quantum mechanics
    • Leaf B. Weyl transformation and the classical limit of quantum mechanics. J. Math. Phys. 1968, 9:65-72.
    • (1968) J. Math. Phys. , vol.9 , pp. 65-72
    • Leaf, B.1
  • 550
    • 25844476555 scopus 로고
    • Weyl transform in nonrelativistic quantum mechanics
    • Weyl transform in nonrelativistic quantum mechanics. J. Math. Phys. 1968, 9:769-781.
    • (1968) J. Math. Phys. , vol.9 , pp. 769-781
  • 551
    • 36749108415 scopus 로고
    • Quantization problem and variational principle in the phase-space formulation of quantum mechanics
    • Cohen L. Quantization problem and variational principle in the phase-space formulation of quantum mechanics. J. Math. Phys. 1976, 17:1863-1866.
    • (1976) J. Math. Phys. , vol.17 , pp. 1863-1866
    • Cohen, L.1
  • 552
    • 0040012271 scopus 로고
    • Phase space functions and correspondence rules
    • Springborg M. Phase space functions and correspondence rules. J. Phys. A: Math. Gen. 1983, 16:535-542.
    • (1983) J. Phys. A: Math. Gen. , vol.16 , pp. 535-542
    • Springborg, M.1
  • 553
    • 0032020166 scopus 로고    scopus 로고
    • The Weyl representation in classical and quantum mechanics
    • Ozorio De Almeida A.M. The Weyl representation in classical and quantum mechanics. Phys. Rep. 1998, 295:265-342.
    • (1998) Phys. Rep. , vol.295 , pp. 265-342
    • Ozorio De Almeida, A.M.1
  • 554
    • 0028378193 scopus 로고
    • The Weyl correspondence and time-frequency analysis
    • Shenoy R.G., Parks T.W. The Weyl correspondence and time-frequency analysis. IEEE Trans. Signal Process. 1994, 42:318-331.
    • (1994) IEEE Trans. Signal Process. , vol.42 , pp. 318-331
    • Shenoy, R.G.1    Parks, T.W.2
  • 555
    • 0027541609 scopus 로고
    • Phase-space representations as a tool for the evaluation of the polychromatic OTF
    • Furlan W.D., Saavedra G., Lancis J. Phase-space representations as a tool for the evaluation of the polychromatic OTF. Opt. Comm. 1993, 96:208-213.
    • (1993) Opt. Comm. , vol.96 , pp. 208-213
    • Furlan, W.D.1    Saavedra, G.2    Lancis, J.3
  • 556
    • 0031360280 scopus 로고    scopus 로고
    • Polychromatic axial behavior of aberrated optical systems: Wigner distribution function approach
    • Furlan W.D., Saavedra G., Silvestre E., Andrés P., Yzuel M.J. Polychromatic axial behavior of aberrated optical systems: Wigner distribution function approach. Appl. Opt. 1997, 36:9146-9151.
    • (1997) Appl. Opt. , vol.36 , pp. 9146-9151
    • Furlan, W.D.1    Saavedra, G.2    Silvestre, E.3    Andrés, P.4    Yzuel, M.J.5
  • 557
    • 0039577488 scopus 로고
    • Achromatic white self-imaging phenomenon: an appproach using the Wigner distribution function
    • Lancis J., Sicre E.E., Pons A., Saavedra G. Achromatic white self-imaging phenomenon: an appproach using the Wigner distribution function. J. Mod. Opt. 1995, 42:425-434.
    • (1995) J. Mod. Opt. , vol.42 , pp. 425-434
    • Lancis, J.1    Sicre, E.E.2    Pons, A.3    Saavedra, G.4
  • 558
    • 0034314745 scopus 로고    scopus 로고
    • Wigner algebra as a tool for the design of achromatic optical processing systems
    • Wang D., Pe'er A., Lohmann A.W., Friesem A.A. Wigner algebra as a tool for the design of achromatic optical processing systems. Opt. Eng. 2000, 39:3014-3024.
    • (2000) Opt. Eng. , vol.39 , pp. 3014-3024
    • Wang, D.1    Pe'er, A.2    Lohmann, A.W.3    Friesem, A.A.4
  • 559
    • 0000741812 scopus 로고
    • Facts relating to Optical Science
    • Talbot H.F. Facts relating to Optical Science. Phil. Mag. 1836, 9:401-407.
    • (1836) Phil. Mag. , vol.9 , pp. 401-407
    • Talbot, H.F.1
  • 560
    • 84970884391 scopus 로고
    • Beugungserscheinungen an Doppelrastern
    • Lau E. Beugungserscheinungen an Doppelrastern. Ann. Phys. 1948, 6:417-4237.
    • (1948) Ann. Phys. , vol.6 , pp. 417-4237
    • Lau, E.1
  • 561
    • 13244276710 scopus 로고
    • The self imaging phenomenon and its applications
    • ch. 1, Elsevier, Cambridge, E. Wolf (Ed.)
    • Patorski K. The self imaging phenomenon and its applications. Progress in Optics 1989, 1-108. ch. 1, Elsevier, Cambridge. E. Wolf (Ed.).
    • (1989) Progress in Optics , pp. 1-108
    • Patorski, K.1
  • 562
    • 0011763767 scopus 로고
    • Spatial periodicities in coherent and partially coherent fields
    • Lohmann A.W., Ojeda-Castañeda J., Streibl N. Spatial periodicities in coherent and partially coherent fields. Opt. Acta 1983, 30:1259-1266.
    • (1983) Opt. Acta , vol.30 , pp. 1259-1266
    • Lohmann, A.W.1    Ojeda-Castañeda, J.2    Streibl, N.3
  • 563
    • 0021958449 scopus 로고
    • Quasi ray-optical approach to longitudinal periodicities of free and bounded wavefields
    • Ojeda-Castañeda J., Sicre E.E. Quasi ray-optical approach to longitudinal periodicities of free and bounded wavefields. Opt. Acta 1985, 32:17-26.
    • (1985) Opt. Acta , vol.32 , pp. 17-26
    • Ojeda-Castañeda, J.1    Sicre, E.E.2
  • 564
    • 84882231646 scopus 로고    scopus 로고
    • http://dau.ing.univaq.it/omhat/Ref/talbib.htm.
  • 565
    • 9744255599 scopus 로고    scopus 로고
    • Simple principles of the Talbot effect
    • and references therein
    • Zhou C., Wang W., Dai E., Liu L. Simple principles of the Talbot effect. Optics & Phot. News 2004, 15(11):46-50. and references therein.
    • (2004) Optics & Phot. News , vol.15 , Issue.11 , pp. 46-50
    • Zhou, C.1    Wang, W.2    Dai, E.3    Liu, L.4
  • 566
    • 0027652515 scopus 로고
    • Fractional Fourier transformations and their optical implementation: I
    • Mendlovic D., Ozaktas H.M. Fractional Fourier transformations and their optical implementation: I. J. Opt. Soc. Am. A 1993, 10:1875-1880.
    • (1993) J. Opt. Soc. Am. A , vol.10 , pp. 1875-1880
    • Mendlovic, D.1    Ozaktas, H.M.2
  • 567
    • 0027740848 scopus 로고
    • Fractional Fourier transformations and their optical implementation: II
    • Mendlovic D., Ozaktas H.M. Fractional Fourier transformations and their optical implementation: II. J. Opt. Soc. Am. A 1993, 10:2522-2531.
    • (1993) J. Opt. Soc. Am. A , vol.10 , pp. 2522-2531
    • Mendlovic, D.1    Ozaktas, H.M.2
  • 568
    • 0027682286 scopus 로고
    • Image rotation, Wigner rotation and the fractional Fourier transform
    • Lohmann A.W. Image rotation, Wigner rotation and the fractional Fourier transform. J. Opt. Soc. Am. A 1993, 10:2181-2186.
    • (1993) J. Opt. Soc. Am. A , vol.10 , pp. 2181-2186
    • Lohmann, A.W.1
  • 569
    • 0028509784 scopus 로고
    • Graded-index fibers, Wigner distirbution functions, and the fractional Fourier transforms
    • Mendlovic D., Ozaktas H.M., Lohmann A.W. Graded-index fibers, Wigner distirbution functions, and the fractional Fourier transforms. Appl. Opt. 1994, 33:6188-6193.
    • (1994) Appl. Opt. , vol.33 , pp. 6188-6193
    • Mendlovic, D.1    Ozaktas, H.M.2    Lohmann, A.W.3
  • 570
    • 0028382656 scopus 로고
    • Convolution, filtering, and multiplexing in fractional Fourier domain and their relation to chirp and wavelet transforms
    • Ozatkas H.M., Barshan B., Mendlovic D., Onural L. Convolution, filtering, and multiplexing in fractional Fourier domain and their relation to chirp and wavelet transforms. J. Opt. Soc. Am. A 1994, 11:547-559.
    • (1994) J. Opt. Soc. Am. A , vol.11 , pp. 547-559
    • Ozatkas, H.M.1    Barshan, B.2    Mendlovic, D.3    Onural, L.4
  • 572
    • 0005487112 scopus 로고    scopus 로고
    • Optical illustration of a varied fractional-Fourier transform order and the Radon-Wigner display
    • Mendlovic D., Dorsch R.G., Lohmann A.W., Zalevsky Z., Ferreira C. Optical illustration of a varied fractional-Fourier transform order and the Radon-Wigner display. Appl. Opt. 1996, 35:3925-3929.
    • (1996) Appl. Opt. , vol.35 , pp. 3925-3929
    • Mendlovic, D.1    Dorsch, R.G.2    Lohmann, A.W.3    Zalevsky, Z.4    Ferreira, C.5
  • 574
    • 77956711851 scopus 로고    scopus 로고
    • Fractional transformations in optics
    • ch. 4, Elsevier, Amsterdam, E. Wolf (Ed.)
    • Lohmann A.W., Mendlovic D., Zalevsky Z. Fractional transformations in optics. Progress in Optics 1997, 263-342. ch. 4, Elsevier, Amsterdam. E. Wolf (Ed.).
    • (1997) Progress in Optics , pp. 263-342
    • Lohmann, A.W.1    Mendlovic, D.2    Zalevsky, Z.3
  • 575
    • 77956712784 scopus 로고    scopus 로고
    • The fractional Fourier transform and some of its applications to optics
    • ch. 7, Elsevier, Amsterdam, E. Wolf (Ed.)
    • Torre A. The fractional Fourier transform and some of its applications to optics. Progress in Optics 2002, 521-586. ch. 7, Elsevier, Amsterdam. E. Wolf (Ed.).
    • (2002) Progress in Optics , pp. 521-586
    • Torre, A.1
  • 578
    • 0001169360 scopus 로고
    • Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten
    • Radon J. Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten. Ber. Saechs. Akad. Wiss. (Leipzig), Math-Phys. K 1917, 69:262-277.
    • (1917) Ber. Saechs. Akad. Wiss. (Leipzig), Math-Phys. K , vol.69 , pp. 262-277
    • Radon, J.1
  • 579
    • 0003351604 scopus 로고
    • The Radon Transform
    • Birkhaüser, Chichester
    • Helgason S. The Radon Transform. Progress in Mathematics 1980, Vol. 5. Birkhaüser, Chichester.
    • (1980) Progress in Mathematics , vol.5
    • Helgason, S.1
  • 581
    • 77956979227 scopus 로고
    • The Radon transform and its applications
    • ch. III, Elsevier, New York, E. Wolf (Ed.)
    • Barrett H.H. The Radon transform and its applications. Progress in Optics 1984, 217-286. ch. III, Elsevier, New York. E. Wolf (Ed.).
    • (1984) Progress in Optics , pp. 217-286
    • Barrett, H.H.1
  • 582
    • 0030554620 scopus 로고    scopus 로고
    • The second revolution in medical imaging
    • Guy C.N. The second revolution in medical imaging. Contemp. Phys. 1996, 37:15-45.
    • (1996) Contemp. Phys. , vol.37 , pp. 15-45
    • Guy, C.N.1
  • 583
    • 0027003950 scopus 로고
    • Radon transform of the Wigner spectrum
    • F.T. Luk (Ed.) Advanced Signal Processing Algorithms, Architectures, and Implementations III
    • Wood J.C., Berry D.T. Radon transform of the Wigner spectrum. Proc. SPIE 1770 1992, 358-375. F.T. Luk (Ed.).
    • (1992) Proc. SPIE 1770 , pp. 358-375
    • Wood, J.C.1    Berry, D.T.2
  • 584
    • 0028483876 scopus 로고
    • Linear signal synthesis using the Radon-Wigner transform
    • Wood J.C., Berry D.T. Linear signal synthesis using the Radon-Wigner transform. IEEE Trans. Signal Process 1994, 42:2105-2111.
    • (1994) IEEE Trans. Signal Process , vol.42 , pp. 2105-2111
    • Wood, J.C.1    Berry, D.T.2
  • 585
    • 0028539817 scopus 로고
    • Radon transformation of time-frequency distributions for analysis of multicomponent signals
    • Radon transformation of time-frequency distributions for analysis of multicomponent signals. IEEE Trans. Signal Process 1994, 42:3166-3177.
    • (1994) IEEE Trans. Signal Process , vol.42 , pp. 3166-3177
  • 586
    • 0028459601 scopus 로고
    • Relationships between the Radon-Wigner and fractional Fourier transforms
    • Lohmann A.W., Soffer B.H. Relationships between the Radon-Wigner and fractional Fourier transforms. J. Opt. Soc. Am. A 1994, 11:1798-1801.
    • (1994) J. Opt. Soc. Am. A , vol.11 , pp. 1798-1801
    • Lohmann, A.W.1    Soffer, B.H.2
  • 587
    • 0001606283 scopus 로고    scopus 로고
    • The fractional Fourier transformation and the Wigner distribution
    • Mustard D. The fractional Fourier transformation and the Wigner distribution. Austral. Math. Soc. Ser B 1996, 38:209-219.
    • (1996) Austral. Math. Soc. Ser B , vol.38 , pp. 209-219
    • Mustard, D.1
  • 588
    • 5244370967 scopus 로고    scopus 로고
    • Radon-Wigner transform for optical field analysis
    • Dec. 9-12, Derha, India
    • Alieva T., Bastiaans M.J. Radon-Wigner transform for optical field analysis. Proc. Int. Conf. on Opt. and Optoelectron. 1998, Vol. 1:132-135. Dec. 9-12, Derha, India, http://www.sps.ele.tue.nl/members/M.J.Bastiaans/pdfs/icol98_5.pdf.
    • (1998) Proc. Int. Conf. on Opt. and Optoelectron. , vol.1 , pp. 132-135
    • Alieva, T.1    Bastiaans, M.J.2
  • 589
    • 23544460852 scopus 로고
    • Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase
    • Vogel K., Risken H. Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase. Phys. Rev. A 1989, 40:2487-2489.
    • (1989) Phys. Rev. A , vol.40 , pp. 2487-2489
    • Vogel, K.1    Risken, H.2
  • 590
    • 0027560182 scopus 로고
    • Measurements of the Wigner distirbution and the density matrix of a light mode using homodyne tomography. Application to squeezed states and the vacuum
    • Smithey D.T., Beck M., Raymer M.G., Faridani A. Measurements of the Wigner distirbution and the density matrix of a light mode using homodyne tomography. Application to squeezed states and the vacuum. Phys. Rev. Lett. 1993, 70:1244-1247.
    • (1993) Phys. Rev. Lett. , vol.70 , pp. 1244-1247
    • Smithey, D.T.1    Beck, M.2    Raymer, M.G.3    Faridani, A.4
  • 591
    • 12044254133 scopus 로고
    • Complex wave-field reconstruction using phase-space tomography
    • Raymer M.G., Beck M., McAlister D.F. Complex wave-field reconstruction using phase-space tomography. Phys. Rev. Lett. 1994, 72:1137-1140.
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 1137-1140
    • Raymer, M.G.1    Beck, M.2    McAlister, D.F.3
  • 592
    • 84975571252 scopus 로고
    • Optical phase retrieval by phase space tomography and fractional-order Fourier transforms
    • McAlister D.F., Beck M., Clarke L., Mayer A., Raymer M.G. Optical phase retrieval by phase space tomography and fractional-order Fourier transforms. Opt. Lett. 1995, 20:1181-1183.
    • (1995) Opt. Lett. , vol.20 , pp. 1181-1183
    • McAlister, D.F.1    Beck, M.2    Clarke, L.3    Mayer, A.4    Raymer, M.G.5
  • 593
    • 0000936650 scopus 로고    scopus 로고
    • Wave field determination using tomography of the ambiguity function
    • Tu J., Tamura S. Wave field determination using tomography of the ambiguity function. Phys. Rev. E 1997, 55:1946-1949.
    • (1997) Phys. Rev. E , vol.55 , pp. 1946-1949
    • Tu, J.1    Tamura, S.2
  • 594
    • 0001603729 scopus 로고    scopus 로고
    • Analytic relation for recovering the mutual intensity by means of intensity information
    • Tu J., Tamura S. Analytic relation for recovering the mutual intensity by means of intensity information. J. Opt. Soc. Am. A 1998, 15:202-206.
    • (1998) J. Opt. Soc. Am. A , vol.15 , pp. 202-206
    • Tu, J.1    Tamura, S.2
  • 595
    • 0036731197 scopus 로고    scopus 로고
    • Tomographic amplitude and phase recovery of vertical-cavity surface-emitting laser by use of the ambiguity function
    • Dragoman D., Dragoman M., Brenner K.-H. Tomographic amplitude and phase recovery of vertical-cavity surface-emitting laser by use of the ambiguity function. Opt. Lett. 2002, 27:1519-1521.
    • (2002) Opt. Lett. , vol.27 , pp. 1519-1521
    • Dragoman, D.1    Dragoman, M.2    Brenner, K.-H.3
  • 596
    • 0000532470 scopus 로고
    • A tomographic approach to Wigner's function
    • Bertrand J., Bertrand P. A tomographic approach to Wigner's function. Found. Phys. 1987, 17:397-405.
    • (1987) Found. Phys. , vol.17 , pp. 397-405
    • Bertrand, J.1    Bertrand, P.2
  • 597
    • 0031501967 scopus 로고    scopus 로고
    • Measuring the quantum mechanical wave function
    • Raymer M.G. Measuring the quantum mechanical wave function. Contemp. Phys. 1997, 38:343-355.
    • (1997) Contemp. Phys. , vol.38 , pp. 343-355
    • Raymer, M.G.1
  • 600
    • 3242805628 scopus 로고
    • General remarks concerning theories dealing with scattering and diffraction in random media
    • Bremmer H. General remarks concerning theories dealing with scattering and diffraction in random media. Radio Sc. 1973, 8:511-534.
    • (1973) Radio Sc. , vol.8 , pp. 511-534
    • Bremmer, H.1
  • 601
    • 84950608626 scopus 로고
    • Transport equations for the Wigner distribution function
    • Bastiaans M.J. Transport equations for the Wigner distribution function. Opt. Acta 1979, 26:1265-1272.
    • (1979) Opt. Acta , vol.26 , pp. 1265-1272
    • Bastiaans, M.J.1
  • 602
    • 0041901755 scopus 로고
    • Transport equations for the Wigner distribution function in an inhomogeneous and dispersive medium
    • Transport equations for the Wigner distribution function in an inhomogeneous and dispersive medium. Opt. Acta 1979, 26:1333-1344.
    • (1979) Opt. Acta , vol.26 , pp. 1333-1344
  • 603
    • 0346593936 scopus 로고
    • Statistische Mechanik bei Störung des Zustands eines physikalischen Systems durch die Beobachtung
    • F. Vieweg, Berlin
    • Bopp F. Statistische Mechanik bei Störung des Zustands eines physikalischen Systems durch die Beobachtung. Werner Heisenberg und die Physik unserer Zeit 1961, 128-149. F. Vieweg, Berlin.
    • (1961) Werner Heisenberg und die Physik unserer Zeit , pp. 128-149
    • Bopp, F.1
  • 604
    • 34250293071 scopus 로고
    • Quantum-mechanical operators and phase-space operators
    • Balazs N.L., Pauli H.C. Quantum-mechanical operators and phase-space operators. Z. Physik A 1977, 282:221-225.
    • (1977) Z. Physik A , vol.282 , pp. 221-225
    • Balazs, N.L.1    Pauli, H.C.2
  • 605
    • 4243204256 scopus 로고
    • Quantum mechanics in phase space: new approaches to the correspondence principle
    • Torres-Vega Go., Frederick J.H. Quantum mechanics in phase space: new approaches to the correspondence principle. J. Chem. Phys. 1990, 93:8862-8874.
    • (1990) J. Chem. Phys. , vol.93 , pp. 8862-8874
    • Torres-Vega, G.1    Frederick, J.H.2
  • 606
    • 84937655864 scopus 로고
    • Visual pattern recognition by moment invariants
    • Hu M.K. Visual pattern recognition by moment invariants. IRE Trans. Info. Theory 1962, IT-8:179-187.
    • (1962) IRE Trans. Info. Theory , vol.IT-8 , pp. 179-187
    • Hu, M.K.1
  • 607
    • 0019004314 scopus 로고
    • Optical calculation of irradiance moments
    • Teague M.R. Optical calculation of irradiance moments. Appl. Opt. 1980, 19:1353-1356.
    • (1980) Appl. Opt. , vol.19 , pp. 1353-1356
    • Teague, M.R.1
  • 608
    • 0019047147 scopus 로고
    • Image analysis via the general theory of moments
    • Teague M.R. Image analysis via the general theory of moments. J. Opt. Soc. Am. 1980, 70:920-930.
    • (1980) J. Opt. Soc. Am. , vol.70 , pp. 920-930
    • Teague, M.R.1
  • 614
    • 0019054579 scopus 로고
    • The Wigner distribution - a tool for time-frequency signal analysis. I: continuous-time signals
    • Classen T.C.A.M., Mecklenbräuker W.F.G. The Wigner distribution - a tool for time-frequency signal analysis. I: continuous-time signals. Philips J. Res. 1980, 35:217-250.
    • (1980) Philips J. Res. , vol.35 , pp. 217-250
    • Classen, T.C.A.M.1    Mecklenbräuker, W.F.G.2
  • 615
    • 0019014549 scopus 로고
    • Signal duration and the Fourier transform
    • Pohlig S.C. Signal duration and the Fourier transform. Proc. IEEE 1980, 68:629.
    • (1980) Proc. IEEE , vol.68 , pp. 629
    • Pohlig, S.C.1
  • 616
    • 0023704029 scopus 로고
    • Instantaneous mean quantities in time-frequency analysis
    • Cohen L. Instantaneous mean quantities in time-frequency analysis. Proc. IEEE 1988, ICASSP-88:2188-2191.
    • (1988) Proc. IEEE , vol.ICASSP-88 , pp. 2188-2191
    • Cohen, L.1
  • 618
    • 0031191052 scopus 로고    scopus 로고
    • Instantaneous frequency and the conditional mean frequency of a signal
    • Loughlin P.J., Tacer B. Instantaneous frequency and the conditional mean frequency of a signal. Signal Process 1997, 60:153-162.
    • (1997) Signal Process , vol.60 , pp. 153-162
    • Loughlin, P.J.1    Tacer, B.2
  • 619
    • 84937035392 scopus 로고
    • Estimating and interpreting the instantaneous frequency of a signal. I: Fundamentals
    • Boashash B. Estimating and interpreting the instantaneous frequency of a signal. I: Fundamentals. Proc. IEEE 1992, 80:520-538.
    • (1992) Proc. IEEE , vol.80 , pp. 520-538
    • Boashash, B.1
  • 620
    • 84941871268 scopus 로고
    • Estimating and interpreting the instantaneous frequency of a signal. II: Algorithms and applications
    • Boashash B. Estimating and interpreting the instantaneous frequency of a signal. II: Algorithms and applications. Proc. IEEE 1992, 80:540-568.
    • (1992) Proc. IEEE , vol.80 , pp. 540-568
    • Boashash, B.1
  • 624
    • 0000807048 scopus 로고
    • Propagation laws for the second-order moments of the Wigner distribution function in first-order optical systems
    • Bastiaans M.J. Propagation laws for the second-order moments of the Wigner distribution function in first-order optical systems. Optik 1989, 82:173-181.
    • (1989) Optik , vol.82 , pp. 173-181
    • Bastiaans, M.J.1
  • 625
    • 0009092454 scopus 로고
    • Second-order moments of the Wigner distribution function in first-order optical systems
    • Bastiaans M.J. Second-order moments of the Wigner distribution function in first-order optical systems. Optik 1991, 88:163-168.
    • (1991) Optik , vol.88 , pp. 163-168
    • Bastiaans, M.J.1
  • 626
    • 0009412617 scopus 로고
    • ABCD law for partially coherent Gaussian light, propagating through first-order optical systems
    • Bastiaans M.J. ABCD law for partially coherent Gaussian light, propagating through first-order optical systems. Opt. Quantum Electron. 1992, 24:S1011-S1019.
    • (1992) Opt. Quantum Electron. , vol.24
    • Bastiaans, M.J.1
  • 627
    • 0027544366 scopus 로고
    • Invariance properties of general astigmatic beams through first-order optical systems
    • Onciul D. Invariance properties of general astigmatic beams through first-order optical systems. J. Opt. Soc. Am. A 1993, 10:295-299.
    • (1993) J. Opt. Soc. Am. A , vol.10 , pp. 295-299
    • Onciul, D.1
  • 628
    • 0028531612 scopus 로고
    • Higher-order moments of the Wigner distribution function in first-order optical systems
    • Dragoman D. Higher-order moments of the Wigner distribution function in first-order optical systems. J. Opt. Soc. Am. A 1994, 11:2643-2646.
    • (1994) J. Opt. Soc. Am. A , vol.11 , pp. 2643-2646
    • Dragoman, D.1
  • 629
    • 0034169536 scopus 로고    scopus 로고
    • Focal shift, optical transfer function, and phase space representation
    • Sheppard C.J.R., Larkin K.G. Focal shift, optical transfer function, and phase space representation. J. Opt. Soc. Am. A 2000, 17:772-779.
    • (2000) J. Opt. Soc. Am. A , vol.17 , pp. 772-779
    • Sheppard, C.J.R.1    Larkin, K.G.2
  • 630
    • 0003172876 scopus 로고    scopus 로고
    • Universal invariants of quantum-mechanical and optical systems
    • Dodonov V.V., Man'ko O.V. Universal invariants of quantum-mechanical and optical systems. J. Opt. Soc. Am. A 2000, 17:2403-2410.
    • (2000) J. Opt. Soc. Am. A , vol.17 , pp. 2403-2410
    • Dodonov, V.V.1    Man'ko, O.V.2
  • 631
    • 0000587862 scopus 로고    scopus 로고
    • Optical phase space, Wigner representation, and invariant quality parameters
    • Simon R., Mukunda N. Optical phase space, Wigner representation, and invariant quality parameters. J. Opt. Soc. Am. A 2000, 17:2440-2463.
    • (2000) J. Opt. Soc. Am. A , vol.17 , pp. 2440-2463
    • Simon, R.1    Mukunda, N.2
  • 632
    • 0016073256 scopus 로고
    • Ambiguity function in Fourier optics
    • Papoulis A. Ambiguity function in Fourier optics. J. Opt. Soc. Am. 1974, 64:779-788.
    • (1974) J. Opt. Soc. Am. , vol.64 , pp. 779-788
    • Papoulis, A.1
  • 633
    • 0019075685 scopus 로고
    • Some observations on oral air flow during phonation
    • Teager H.M. Some observations on oral air flow during phonation. IEEE Trans. Acoust., Speech, Signal Process 1980, ASSP-28:599-601.
    • (1980) IEEE Trans. Acoust., Speech, Signal Process , vol.ASSP-28 , pp. 599-601
    • Teager, H.M.1
  • 634
    • 0003236089 scopus 로고
    • Evidence for nonlinear sound production mechanisms in the vocal tract
    • Kluwer, Englewood Cliffs, J. Hardcastle, A. Marchal (Eds.)
    • Teager H.M., Teager S.M. Evidence for nonlinear sound production mechanisms in the vocal tract. Speech Production and Speech Modelling 1990, 241-261. Kluwer, Englewood Cliffs. J. Hardcastle, A. Marchal (Eds.).
    • (1990) Speech Production and Speech Modelling , pp. 241-261
    • Teager, H.M.1    Teager, S.M.2
  • 635
    • 0002908893 scopus 로고
    • Some useful properties of Teager's energy operator
    • Kaiser J.F. Some useful properties of Teager's energy operator. IEEE ICASSP-93 1993, Vol. 3:149-152.
    • (1993) IEEE ICASSP-93 , vol.3 , pp. 149-152
    • Kaiser, J.F.1
  • 636
  • 637
    • 0001871334 scopus 로고
    • Uncertainty principle in Fourier analysis
    • Academic Press, Boston, O. Shisha (Ed.)
    • de Bruijn N.G. Uncertainty principle in Fourier analysis. Inequalities 1967, 57-71. Academic Press, Boston. O. Shisha (Ed.).
    • (1967) Inequalities , pp. 57-71
    • de Bruijn, N.G.1
  • 638
    • 0000910767 scopus 로고
    • A theory of generalized functions, with applications to Wigner distribution and Weyl correspondence
    • de Bruijn N.G. A theory of generalized functions, with applications to Wigner distribution and Weyl correspondence. Nieuw Archief voor Wiskunde 1973, 21(3):205-280.
    • (1973) Nieuw Archief voor Wiskunde , vol.21 , Issue.3 , pp. 205-280
    • de Bruijn, N.G.1
  • 639
    • 2442623404 scopus 로고    scopus 로고
    • The uncertainty principle: global, local, or both?
    • Loughlin P.J., Cohen L. The uncertainty principle: global, local, or both?. IEEE Trans. Signal Process. 2004, 52:1218-1227.
    • (2004) IEEE Trans. Signal Process. , vol.52 , pp. 1218-1227
    • Loughlin, P.J.1    Cohen, L.2
  • 640
    • 84882167893 scopus 로고    scopus 로고
    • http://www.stanford.edu/siegman/beam_quality_ref_list.html.
  • 643
    • 0025546679 scopus 로고
    • New developments in laser resonators
    • Siegman A.E. New developments in laser resonators. SPIE 1990, 1224:2-14.
    • (1990) SPIE , vol.1224 , pp. 2-14
    • Siegman, A.E.1
  • 644
    • 0001232834 scopus 로고
    • 2 concept characterizes beam quality
    • May
    • 2 concept characterizes beam quality. Laser Focus 1990, 173-183. May.
    • (1990) Laser Focus , pp. 173-183
    • Johnston, T.F.1
  • 646
    • 84975551215 scopus 로고
    • Beam propagation and the ABCD ray matrices
    • Bélanger P.-A. Beam propagation and the ABCD ray matrices. Opt. Lett. 1991, 16:196-198.
    • (1991) Opt. Lett. , vol.16 , pp. 196-198
    • Bélanger, P.-A.1
  • 647
    • 0026156369 scopus 로고
    • Defining the effective radius of curvature for a nonideal optical beam
    • Siegman A.E. Defining the effective radius of curvature for a nonideal optical beam. IEEE J. Quantum Electron. 1991, QE-27:1146-1148.
    • (1991) IEEE J. Quantum Electron. , vol.QE-27 , pp. 1146-1148
    • Siegman, A.E.1
  • 648
    • 0001135437 scopus 로고
    • Wave optical analysis of the phase space analyser
    • Weber H. Wave optical analysis of the phase space analyser. J. Mod. Opt. 1992, 39:543-559.
    • (1992) J. Mod. Opt. , vol.39 , pp. 543-559
    • Weber, H.1
  • 649
  • 650
    • 84975538293 scopus 로고
    • Method for direct measurement of the variance of laser beams
    • Champagne Y., Baré C., Bélanger P.-A. Method for direct measurement of the variance of laser beams. Opt. Lett. 1994, 19:505-507.
    • (1994) Opt. Lett. , vol.19 , pp. 505-507
    • Champagne, Y.1    Baré, C.2    Bélanger, P.-A.3
  • 651
    • 0029373906 scopus 로고
    • Method for direct measurement of realistic second-moment propagation parameters for nonideal laser beams
    • Champagne Y., Bélanger P.-A. Method for direct measurement of realistic second-moment propagation parameters for nonideal laser beams. Opt. Quantum Electron. 1995, 27:813-824.
    • (1995) Opt. Quantum Electron. , vol.27 , pp. 813-824
    • Champagne, Y.1    Bélanger, P.-A.2
  • 654
    • 34250360913 scopus 로고    scopus 로고
    • Laser and Gaussian beam propagation and transformation
    • Dekker, Berlin
    • Alda J. Laser and Gaussian beam propagation and transformation. Encyclopedia of Optical Engineering 2003, Dekker, Berlin.
    • (2003) Encyclopedia of Optical Engineering
    • Alda, J.1
  • 655
    • 0003853433 scopus 로고
    • as to positive definite matrices see ch. 4, pp. 103-106; as regards the Kronecker product see pp. 184-185, Abacus Press, New York
    • Deif A.S. Advanced Matrix Theory for Scientists and Engineers 1982, as to positive definite matrices see ch. 4, pp. 103-106; as regards the Kronecker product see pp. 184-185, Abacus Press, New York.
    • (1982) Advanced Matrix Theory for Scientists and Engineers
    • Deif, A.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.