The Wigner function in paraxial optics I. Matrix methods in Fourier optics

Revista Mexicana de Fisica

Volumn 48, Issue 6, 2002, Pages 565-574

  Ortega Martínez, Roberto ^a   Román Moreno, Carlos J ^a   Leonor Rivera, Ana ^b  

^a UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

^b UNIVERSIDAD AUTÓNOMA DEL ESTADO DE MORELOS   (Mexico)

Author keywords

Fourier optics; Space phase measurements; Wave propagation

Indexed keywords

EID: 0038284717     PISSN: 0035001X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

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2. E. Wigner, On the quantum correction for thermodynamic equilibrium, Phys. Rev. 40 (1932) 749; J.E. Moyal, Quantum mechanics as a statistical theory, Proc. Cambridge Philos. Soc. 45 (1949) 99; J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill (Electrical and Computer Engineering Series, 2nd Edition, 1996), chapter 2, p30.
3. E. Wigner, On the quantum correction for thermodynamic equilibrium, Phys. Rev. 40 (1932) 749; J.E. Moyal, Quantum mechanics as a statistical theory, Proc. Cambridge Philos. Soc. 45 (1949) 99; J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill (Electrical and Computer Engineering Series, 2nd Edition, 1996), chapter 2, p30.
4. H. Bartelt and K.-H. Brenner, The Wigner function an alternative signal representation in optics, Israel J. Techn. 18 (1980) 260; H.O. Bartelt, K.-H. Brenner and A. Lohmann, The Wigner distribution function and its optical production, Opt. Comm. 32 (1980) 32; K.-H. Brenner and A. H. Lohmann, Wigner distribution function display of complex ID signals, Opt. Comm. 42 (1982) 310.
5. H. Bartelt and K.-H. Brenner, The Wigner function an alternative signal representation in optics, Israel J. Techn. 18 (1980) 260; H.O. Bartelt, K.-H. Brenner and A. Lohmann, The Wigner distribution function and its optical production, Opt. Comm. 32 (1980) 32; K.-H. Brenner and A. H. Lohmann, Wigner distribution function display of complex ID signals, Opt. Comm. 42 (1982) 310.
6. H. Bartelt and K.-H. Brenner, The Wigner function an alternative signal representation in optics, Israel J. Techn. 18 (1980) 260; H.O. Bartelt, K.-H. Brenner and A. Lohmann, The Wigner distribution function and its optical production, Opt. Comm. 32 (1980) 32; K.-H. Brenner and A. H. Lohmann, Wigner distribution function display of complex ID signals, Opt. Comm. 42 (1982) 310.
7. This distribution results from a uniformly-weighted superposition of plane waves traveling in the forward half sphere of directions, and interfering constructively at the image point.
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11. M. Moshinsky and C. Quesne, "Oscillator Systems," in Proceedings of the 15th Solvay Conference in Physics (1970) (Gordon and Breach, New York, 1974); ibid., J. Math. Phys 12 (1971) 1772; ibid., J. Math. Phys 12 (1971) 1780; M. Moshinsky, SIAM J. Appl. Math. 25 (1973) 193.
12. M. Moshinsky and C. Quesne, "Oscillator Systems," in Proceedings of the 15th Solvay Conference in Physics (1970) (Gordon and Breach, New York, 1974); ibid., J. Math. Phys 12 (1971) 1772; ibid., J. Math. Phys 12 (1971) 1780; M. Moshinsky, SIAM J. Appl. Math. 25 (1973) 193.
13. M. Moshinsky and C. Quesne, "Oscillator Systems," in Proceedings of the 15th Solvay Conference in Physics (1970) (Gordon and Breach, New York, 1974); ibid., J. Math. Phys 12 (1971) 1772; ibid., J. Math. Phys 12 (1971) 1780; M. Moshinsky, SIAM J. Appl. Math. 25 (1973) 193.
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18. E.C.G. Sudarshan, N. Mukunda and R. Simon, Opt. Acta 32 (1985) 855; K.B. Wolf and G. Krötzsch, "El problema de las tres lentes," Rev. Mex. Fís. submitted (2000).
19. G.W. Forbes, V.I. Man'ko, H.M. Ozaktas, R. Simon, K.B. Wolf, J. Opt. Soc. Am. A 17 (2000) 2272.
20. J.W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), 2nd ed., p. 148.
21. O.N. Stavroudis, The Optics of Rays, Wavefronts and Caustics (Academic Press, 1972), p. 95.