Abstract

A first-order optical system (represented by its 4×4 ABCD matrix) is given in order to obtain a beam that preserves its spatial orientation of the transverse profile under free propagation from a beam with rotating irradiance distribution in free space. Within the formalism of the second-order irradiance moments, this transverse orientation is analyzed in terms of the evolution of the principal axes of the field irradiance distribution. It is shown that the spatial profile of the beam emerging from the proposed optical system does not rotate when light freely propagates. The improvement of the joint near-field and far-field beam spread product at the output of this optical system is also studied.

© 2006 Optical Society of America

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  1. R. Simon, N. Mukunda, and E. C. G. Sudarshan, “Partially coherent beams and a generalized ABCD-law,” Opt. Commun. 65, 322–328 (1988).
    [Crossref]
  2. S. Lavi, R. Prochaska, and E. Keren, “Generalized beam parameters and transformation law for partially coherent light,” Appl. Opt. 27, 3696–3703 (1988).
    [Crossref] [PubMed]
  3. M. J. Bastiaans, “Propagation laws for the second-order moments of the Wigner distribution function in first-order optical systems,” Optik 82, 173–181 (1989).
  4. A. E. Siegman, “New developments in laser resonators” in Laser Resonators, Proc. SPIE 1224, 2–14 (1990).
    [Crossref]
  5. J. Serna, R. Martínez-Herrero, and P. M. Mejías, “Parametric characterization of general partially coherent beams propagating through ABCD optical systems,” J. Opt. Soc. Am. A 8, 1094–1098 (1991).
    [Crossref]
  6. H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, 1027–1049 (1992).
    [Crossref]
  7. ISO 11146, Laser and laser related equipment-Test methods for laser beam widths, divergence angles and beam propagation ratios: ISO 11146-1:2005, Part 1: Stigmatic and simple astigmatic beams; ISO11146-2:2005, Part 2: General astigmatic beams; ISO/TR 11146-3:2004, Part 3: Intrinsic and geometrical laser beam classification, propagation, and details of test method; ISO/TR 11146-3:2004/Cor1:2005 (International Organization for Standardization, Geneva, Switzerland, 2005).
  8. F. Encinas-Sanz, J. Serna, C. Martínez, R. Martínez-Herrero, and P. M. Mejías, “Time-varying beam quality factor and mode evolution in TEA CO2 laser pulses,” IEEE J. Quantum Electron. 34, 1835–1838 (1998).
    [Crossref]
  9. P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarized laser beams,” Prog. Quantum Electron. 26, 65–130 (2002), and references therein.
    [Crossref]
  10. J. A. Arnaud and H. Kogelnik, “Light beams with general astigmatism,” Appl. Opt. 8, 1687–1693 (1969).
    [Crossref] [PubMed]
  11. J. Serna and G. Nemes, “Decoupling of coherent Gaussian beams with general astimatism,” Opt. Lett. 18, 1174–1176 (1993).
    [Crossref]
  12. G. Nemes and A. E. Siegman, “Measurement of all ten second-order moments of an astigmatic beam by use of rotating simple astigmatic (anamorphic) optics,” J. Opt. Soc. Am A 11, 2257–2264 (1994).
    [Crossref]
  13. G. Nemes, “Synthesis of general astigmatic optical systems, the detwisting procedure and the beam quality factors for general astigmatic laser beams,” in Proceedings of the Second Workshop on Laser Beam CharacterizationH. Weber, N. Reng, J. Ludtke, and P. M. Mejías, eds., Festkorper-Laser Institut Berlin GmbH, Berlin, Germany, 1994, pp. 93–104.
  14. J. Serna, P. M. Mejías, and R. Martínez-Herrero, “Rotation of partially coherent beams through free space,” Opt. Quantum Electron. 24, 873–880 (1992).
    [Crossref]
  15. G. Nemes and J. Serna, “Do not use spherical lenses and free spaces to characterize beams: a possible improvement of the ISO/DIS 11146 document,” in Proceedings of the Fourth Workshop on Laser Beam and Optics Characterization, A. Giesen and M. Morin, eds. (Verein Deutscher Ingenieure-Technologiezentrum, Düseldorf, Germany, 1997), pp. 29–49.
  16. G. Nemes and J. Serna, “Laser beam characterization with use of second order moments: an overview,” in Diode Pumped Solid State Lasers: Applications and IssuesM. W. Dowley, ed., OSA TOPS17, 200–207 (1998).
  17. J. Serna, F. Encinas, and G. Nemes, “Complete spatial characterization of a pulsed doughnut-type beam by use of spherical optics and a cylindrical lens,” J. Opt. Soc. Am. A 18, 1726–1733 (2001).
    [Crossref]
  18. M. J. Bastiaans, “Wigner distribution function and its applications to first-order optics,” J. Opt. Soc. Am. 69, 1710–1716 (1979).
    [Crossref]
  19. A. Walther, “Radiometry and coherence,” J. Opt. Soc. Am. 58, 1256–1259 (1968).
    [Crossref]
  20. A. T. Friberg, E. Tervonen, and T. Turunen, “Interpretation and experimental demonstration of twisted Gauss-Schell-mode beams,” J. Opt. Soc. Am A 11, 1818–1826 (1994).
    [Crossref]
  21. A. T. Friberg, C. Gao, B. Eppich, and H. Weber, “Generation of partially coherent fields with twist,” Proc. SPIE 3110, 317–318 (1997).
    [Crossref]
  22. R. Simon and K. Bernardo Wolf, “Fractional Fourier transform in two dimensions,” J. Opt. Soc. Am. A 17, 2368–2381 (2000).
    [Crossref]

2002 (1)

P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarized laser beams,” Prog. Quantum Electron. 26, 65–130 (2002), and references therein.
[Crossref]

2001 (1)

2000 (1)

1998 (1)

F. Encinas-Sanz, J. Serna, C. Martínez, R. Martínez-Herrero, and P. M. Mejías, “Time-varying beam quality factor and mode evolution in TEA CO2 laser pulses,” IEEE J. Quantum Electron. 34, 1835–1838 (1998).
[Crossref]

1997 (1)

A. T. Friberg, C. Gao, B. Eppich, and H. Weber, “Generation of partially coherent fields with twist,” Proc. SPIE 3110, 317–318 (1997).
[Crossref]

1994 (2)

A. T. Friberg, E. Tervonen, and T. Turunen, “Interpretation and experimental demonstration of twisted Gauss-Schell-mode beams,” J. Opt. Soc. Am A 11, 1818–1826 (1994).
[Crossref]

G. Nemes and A. E. Siegman, “Measurement of all ten second-order moments of an astigmatic beam by use of rotating simple astigmatic (anamorphic) optics,” J. Opt. Soc. Am A 11, 2257–2264 (1994).
[Crossref]

1993 (1)

1992 (2)

J. Serna, P. M. Mejías, and R. Martínez-Herrero, “Rotation of partially coherent beams through free space,” Opt. Quantum Electron. 24, 873–880 (1992).
[Crossref]

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, 1027–1049 (1992).
[Crossref]

1991 (1)

1990 (1)

A. E. Siegman, “New developments in laser resonators” in Laser Resonators, Proc. SPIE 1224, 2–14 (1990).
[Crossref]

1989 (1)

M. J. Bastiaans, “Propagation laws for the second-order moments of the Wigner distribution function in first-order optical systems,” Optik 82, 173–181 (1989).

1988 (2)

R. Simon, N. Mukunda, and E. C. G. Sudarshan, “Partially coherent beams and a generalized ABCD-law,” Opt. Commun. 65, 322–328 (1988).
[Crossref]

S. Lavi, R. Prochaska, and E. Keren, “Generalized beam parameters and transformation law for partially coherent light,” Appl. Opt. 27, 3696–3703 (1988).
[Crossref] [PubMed]

1979 (1)

1969 (1)

1968 (1)

Arnaud, J. A.

Bastiaans, M. J.

M. J. Bastiaans, “Propagation laws for the second-order moments of the Wigner distribution function in first-order optical systems,” Optik 82, 173–181 (1989).

M. J. Bastiaans, “Wigner distribution function and its applications to first-order optics,” J. Opt. Soc. Am. 69, 1710–1716 (1979).
[Crossref]

Bernardo Wolf, K.

Encinas, F.

Encinas-Sanz, F.

F. Encinas-Sanz, J. Serna, C. Martínez, R. Martínez-Herrero, and P. M. Mejías, “Time-varying beam quality factor and mode evolution in TEA CO2 laser pulses,” IEEE J. Quantum Electron. 34, 1835–1838 (1998).
[Crossref]

Eppich, B.

A. T. Friberg, C. Gao, B. Eppich, and H. Weber, “Generation of partially coherent fields with twist,” Proc. SPIE 3110, 317–318 (1997).
[Crossref]

Friberg, A. T.

A. T. Friberg, C. Gao, B. Eppich, and H. Weber, “Generation of partially coherent fields with twist,” Proc. SPIE 3110, 317–318 (1997).
[Crossref]

A. T. Friberg, E. Tervonen, and T. Turunen, “Interpretation and experimental demonstration of twisted Gauss-Schell-mode beams,” J. Opt. Soc. Am A 11, 1818–1826 (1994).
[Crossref]

Gao, C.

A. T. Friberg, C. Gao, B. Eppich, and H. Weber, “Generation of partially coherent fields with twist,” Proc. SPIE 3110, 317–318 (1997).
[Crossref]

Keren, E.

Kogelnik, H.

Lavi, S.

Martínez, C.

F. Encinas-Sanz, J. Serna, C. Martínez, R. Martínez-Herrero, and P. M. Mejías, “Time-varying beam quality factor and mode evolution in TEA CO2 laser pulses,” IEEE J. Quantum Electron. 34, 1835–1838 (1998).
[Crossref]

Martínez-Herrero, R.

P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarized laser beams,” Prog. Quantum Electron. 26, 65–130 (2002), and references therein.
[Crossref]

F. Encinas-Sanz, J. Serna, C. Martínez, R. Martínez-Herrero, and P. M. Mejías, “Time-varying beam quality factor and mode evolution in TEA CO2 laser pulses,” IEEE J. Quantum Electron. 34, 1835–1838 (1998).
[Crossref]

J. Serna, P. M. Mejías, and R. Martínez-Herrero, “Rotation of partially coherent beams through free space,” Opt. Quantum Electron. 24, 873–880 (1992).
[Crossref]

J. Serna, R. Martínez-Herrero, and P. M. Mejías, “Parametric characterization of general partially coherent beams propagating through ABCD optical systems,” J. Opt. Soc. Am. A 8, 1094–1098 (1991).
[Crossref]

Mejías, P. M.

P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarized laser beams,” Prog. Quantum Electron. 26, 65–130 (2002), and references therein.
[Crossref]

F. Encinas-Sanz, J. Serna, C. Martínez, R. Martínez-Herrero, and P. M. Mejías, “Time-varying beam quality factor and mode evolution in TEA CO2 laser pulses,” IEEE J. Quantum Electron. 34, 1835–1838 (1998).
[Crossref]

J. Serna, P. M. Mejías, and R. Martínez-Herrero, “Rotation of partially coherent beams through free space,” Opt. Quantum Electron. 24, 873–880 (1992).
[Crossref]

J. Serna, R. Martínez-Herrero, and P. M. Mejías, “Parametric characterization of general partially coherent beams propagating through ABCD optical systems,” J. Opt. Soc. Am. A 8, 1094–1098 (1991).
[Crossref]

Movilla, J. M.

P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarized laser beams,” Prog. Quantum Electron. 26, 65–130 (2002), and references therein.
[Crossref]

Mukunda, N.

R. Simon, N. Mukunda, and E. C. G. Sudarshan, “Partially coherent beams and a generalized ABCD-law,” Opt. Commun. 65, 322–328 (1988).
[Crossref]

Nemes, G.

J. Serna, F. Encinas, and G. Nemes, “Complete spatial characterization of a pulsed doughnut-type beam by use of spherical optics and a cylindrical lens,” J. Opt. Soc. Am. A 18, 1726–1733 (2001).
[Crossref]

G. Nemes and A. E. Siegman, “Measurement of all ten second-order moments of an astigmatic beam by use of rotating simple astigmatic (anamorphic) optics,” J. Opt. Soc. Am A 11, 2257–2264 (1994).
[Crossref]

J. Serna and G. Nemes, “Decoupling of coherent Gaussian beams with general astimatism,” Opt. Lett. 18, 1174–1176 (1993).
[Crossref]

G. Nemes, “Synthesis of general astigmatic optical systems, the detwisting procedure and the beam quality factors for general astigmatic laser beams,” in Proceedings of the Second Workshop on Laser Beam CharacterizationH. Weber, N. Reng, J. Ludtke, and P. M. Mejías, eds., Festkorper-Laser Institut Berlin GmbH, Berlin, Germany, 1994, pp. 93–104.

G. Nemes and J. Serna, “Do not use spherical lenses and free spaces to characterize beams: a possible improvement of the ISO/DIS 11146 document,” in Proceedings of the Fourth Workshop on Laser Beam and Optics Characterization, A. Giesen and M. Morin, eds. (Verein Deutscher Ingenieure-Technologiezentrum, Düseldorf, Germany, 1997), pp. 29–49.

G. Nemes and J. Serna, “Laser beam characterization with use of second order moments: an overview,” in Diode Pumped Solid State Lasers: Applications and IssuesM. W. Dowley, ed., OSA TOPS17, 200–207 (1998).

Piquero, G.

P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarized laser beams,” Prog. Quantum Electron. 26, 65–130 (2002), and references therein.
[Crossref]

Prochaska, R.

Serna, J.

J. Serna, F. Encinas, and G. Nemes, “Complete spatial characterization of a pulsed doughnut-type beam by use of spherical optics and a cylindrical lens,” J. Opt. Soc. Am. A 18, 1726–1733 (2001).
[Crossref]

F. Encinas-Sanz, J. Serna, C. Martínez, R. Martínez-Herrero, and P. M. Mejías, “Time-varying beam quality factor and mode evolution in TEA CO2 laser pulses,” IEEE J. Quantum Electron. 34, 1835–1838 (1998).
[Crossref]

J. Serna and G. Nemes, “Decoupling of coherent Gaussian beams with general astimatism,” Opt. Lett. 18, 1174–1176 (1993).
[Crossref]

J. Serna, P. M. Mejías, and R. Martínez-Herrero, “Rotation of partially coherent beams through free space,” Opt. Quantum Electron. 24, 873–880 (1992).
[Crossref]

J. Serna, R. Martínez-Herrero, and P. M. Mejías, “Parametric characterization of general partially coherent beams propagating through ABCD optical systems,” J. Opt. Soc. Am. A 8, 1094–1098 (1991).
[Crossref]

G. Nemes and J. Serna, “Laser beam characterization with use of second order moments: an overview,” in Diode Pumped Solid State Lasers: Applications and IssuesM. W. Dowley, ed., OSA TOPS17, 200–207 (1998).

G. Nemes and J. Serna, “Do not use spherical lenses and free spaces to characterize beams: a possible improvement of the ISO/DIS 11146 document,” in Proceedings of the Fourth Workshop on Laser Beam and Optics Characterization, A. Giesen and M. Morin, eds. (Verein Deutscher Ingenieure-Technologiezentrum, Düseldorf, Germany, 1997), pp. 29–49.

Siegman, A. E.

G. Nemes and A. E. Siegman, “Measurement of all ten second-order moments of an astigmatic beam by use of rotating simple astigmatic (anamorphic) optics,” J. Opt. Soc. Am A 11, 2257–2264 (1994).
[Crossref]

A. E. Siegman, “New developments in laser resonators” in Laser Resonators, Proc. SPIE 1224, 2–14 (1990).
[Crossref]

Simon, R.

R. Simon and K. Bernardo Wolf, “Fractional Fourier transform in two dimensions,” J. Opt. Soc. Am. A 17, 2368–2381 (2000).
[Crossref]

R. Simon, N. Mukunda, and E. C. G. Sudarshan, “Partially coherent beams and a generalized ABCD-law,” Opt. Commun. 65, 322–328 (1988).
[Crossref]

Sudarshan, E. C. G.

R. Simon, N. Mukunda, and E. C. G. Sudarshan, “Partially coherent beams and a generalized ABCD-law,” Opt. Commun. 65, 322–328 (1988).
[Crossref]

Tervonen, E.

A. T. Friberg, E. Tervonen, and T. Turunen, “Interpretation and experimental demonstration of twisted Gauss-Schell-mode beams,” J. Opt. Soc. Am A 11, 1818–1826 (1994).
[Crossref]

Turunen, T.

A. T. Friberg, E. Tervonen, and T. Turunen, “Interpretation and experimental demonstration of twisted Gauss-Schell-mode beams,” J. Opt. Soc. Am A 11, 1818–1826 (1994).
[Crossref]

Walther, A.

Weber, H.

A. T. Friberg, C. Gao, B. Eppich, and H. Weber, “Generation of partially coherent fields with twist,” Proc. SPIE 3110, 317–318 (1997).
[Crossref]

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, 1027–1049 (1992).
[Crossref]

Appl. Opt. (2)

IEEE J. Quantum Electron. (1)

F. Encinas-Sanz, J. Serna, C. Martínez, R. Martínez-Herrero, and P. M. Mejías, “Time-varying beam quality factor and mode evolution in TEA CO2 laser pulses,” IEEE J. Quantum Electron. 34, 1835–1838 (1998).
[Crossref]

J. Opt. Soc. Am A (2)

G. Nemes and A. E. Siegman, “Measurement of all ten second-order moments of an astigmatic beam by use of rotating simple astigmatic (anamorphic) optics,” J. Opt. Soc. Am A 11, 2257–2264 (1994).
[Crossref]

A. T. Friberg, E. Tervonen, and T. Turunen, “Interpretation and experimental demonstration of twisted Gauss-Schell-mode beams,” J. Opt. Soc. Am A 11, 1818–1826 (1994).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

Opt. Commun. (1)

R. Simon, N. Mukunda, and E. C. G. Sudarshan, “Partially coherent beams and a generalized ABCD-law,” Opt. Commun. 65, 322–328 (1988).
[Crossref]

Opt. Lett. (1)

Opt. Quantum Electron. (2)

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, 1027–1049 (1992).
[Crossref]

J. Serna, P. M. Mejías, and R. Martínez-Herrero, “Rotation of partially coherent beams through free space,” Opt. Quantum Electron. 24, 873–880 (1992).
[Crossref]

Optik (1)

M. J. Bastiaans, “Propagation laws for the second-order moments of the Wigner distribution function in first-order optical systems,” Optik 82, 173–181 (1989).

Proc. SPIE (2)

A. E. Siegman, “New developments in laser resonators” in Laser Resonators, Proc. SPIE 1224, 2–14 (1990).
[Crossref]

A. T. Friberg, C. Gao, B. Eppich, and H. Weber, “Generation of partially coherent fields with twist,” Proc. SPIE 3110, 317–318 (1997).
[Crossref]

Prog. Quantum Electron. (1)

P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarized laser beams,” Prog. Quantum Electron. 26, 65–130 (2002), and references therein.
[Crossref]

Other (4)

ISO 11146, Laser and laser related equipment-Test methods for laser beam widths, divergence angles and beam propagation ratios: ISO 11146-1:2005, Part 1: Stigmatic and simple astigmatic beams; ISO11146-2:2005, Part 2: General astigmatic beams; ISO/TR 11146-3:2004, Part 3: Intrinsic and geometrical laser beam classification, propagation, and details of test method; ISO/TR 11146-3:2004/Cor1:2005 (International Organization for Standardization, Geneva, Switzerland, 2005).

G. Nemes and J. Serna, “Do not use spherical lenses and free spaces to characterize beams: a possible improvement of the ISO/DIS 11146 document,” in Proceedings of the Fourth Workshop on Laser Beam and Optics Characterization, A. Giesen and M. Morin, eds. (Verein Deutscher Ingenieure-Technologiezentrum, Düseldorf, Germany, 1997), pp. 29–49.

G. Nemes and J. Serna, “Laser beam characterization with use of second order moments: an overview,” in Diode Pumped Solid State Lasers: Applications and IssuesM. W. Dowley, ed., OSA TOPS17, 200–207 (1998).

G. Nemes, “Synthesis of general astigmatic optical systems, the detwisting procedure and the beam quality factors for general astigmatic laser beams,” in Proceedings of the Second Workshop on Laser Beam CharacterizationH. Weber, N. Reng, J. Ludtke, and P. M. Mejías, eds., Festkorper-Laser Institut Berlin GmbH, Berlin, Germany, 1994, pp. 93–104.

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Equations (24)

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h ( r , η , z ) = + W ( r + s 2 , r s 2 ) exp ( i k η s ) d s ,
< x m y n u p v q > 1 I o + x m y n u p v q h r η z d r d η ,
Q = < x 2 + y 2 > < u 2 + v 2 > < xu + yv > 2 .
Q x = < x 2 > < u 2 > < xu > 2 ,
Q y = < y 2 > < v 2 > < yv > 2 .
tan 2 θ = < y 2 > f < v 2 > f < x 2 > f < u 2 > f < uv > f < x 2 + y 2 > f + < xy > f < u 2 + v 2 > f ,
S = 2 2 = a 0 1 a 0 0 b 0 1 b a 0 1 a 0 0 b 0 1 b ,
M = a 0 0 0 0 b 0 0 0 0 1 a 0 0 0 0 1 b .
F = 2 2 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 ,
tan 2 φ ( z ) = 2 < xy > < x 2 > < y 2 > ,
tan 2 φ ( z ) =
= 2 < xy > o + 2 kz ( < xv > o + < yu > o ) + 2 k 2 z 2 < uv > o < x 2 > o < y 2 > o + 2 kz ( < xu > o < yu > o ) + k 2 z 2 ( < u 2 > o < v 2 > o ) ,
< x 2 > o = 1 2 ( a 2 < x 2 > i + < u 2 > i a 2 + 2 < xu > i ) = < x 2 > i < u 2 > i + < xu > i
< y 2 > o = 1 2 ( b 2 < y 2 > i + < v 2 > i b 2 + 2 < yv > i ) = < y 2 > i < v 2 > i + < yv > i
< x 2 > o = < y 2 > o .
tan 2 φ ( z ) = , for any z ,
< x 2 > o + < y 2 > o = 2 < x 2 > i < u 2 > i + ( < xu > i < yu > i ) .
< u 2 > o + < v 2 > o = 2 < x 2 > i < u 2 > i ( < xu > i < yv > i ) ,
Q o = 4 < x 2 > i < u 2 > i ( < xu > i < yv > i ) 2 ,
Q o = 4 < x 2 > i < u 2 > i 4 < xu > i 2 = 4 Q x = 4 Q y .
Q i = 2 < x 2 > i < u 2 > i + < y 2 > i < u 2 > i + < x 2 > i < v 2 > i =
= 2 < x 2 > i < u 2 > i + < x 2 > i < u 2 > i 2 < v 2 > i + < x 2 > i < v 2 > i .
Q o Q i = 2< x 2 > i < u 2 > i < x 2 > i < u 2 > i 2 < v 2 > i < x 2 > i < v 2 > i 4 < xu > i 2 =
= < x 2 > i < v 2 > i ( < u 2 > i < v 2 > i ) 2 4 < xu > i 2 0 ,

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