Abstract

The capability of a twisted nematic liquid crystal display to generate a set of equi-azimuth polarization states is used to achieve a phaseonly modulation regime. For this purpose, a liquid crystal display followed by a quarter-wave plate is launched between two polarizers. Theoretical support is provided by means of the Jones matrix calculus and the Poincaré sphere representation. Laboratory results for a commercial liquid crystal display are presented. A phase modulation deep of 270° is obtained at 514 nm with a residual intensity variation which is lower than 2.5 %.

© 2006 Optical Society of America

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References

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  1. V. Laude, "Twisted-nematic liquid-crystal pixelated active lens," Opt. Commun. 153, 134-152 (1998).
    [CrossRef]
  2. Z. Jaroszewicz, V. Climent, V. Duran, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, "Programmable axicon for variable inclination of the focal segment," J. Mod. Opt. 14, 2185-2190 (2004).
    [CrossRef]
  3. M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, "Optical particle trapping with computer-generated holograms written on a liquid-crystal display," Opt. Lett. 24, 608-610 (1999).
    [CrossRef]
  4. E. Schonbrun, R. Piestun, P. Jordan, J. Coopper, K. D. Wulff, J. Courtial, and M. Padgett, "3D interferometric optical tweezers using a single spatial light modulator," Opt. Express 13, 3777-3786 (2005).
    [CrossRef] [PubMed]
  5. C. H. Gooch and H. A. Tarry, "Optical-properties of twisted nematic liquid-crystal structures with twist angles less than 90 degrees," J. Phys. D 8, 1575-1584 (1975).
    [CrossRef]
  6. N. Mukohzaka, N. Yoshida, H. Toyoda, Y. Kobayashi, and T. Hara, "Diffraction efficiency analysis of a parallel-aligned nematic-liquid-crystal spatial light-modulator," Appl. Opt. 33, 2804-2811 (1994).
    [CrossRef] [PubMed]
  7. N. Konforti, E. Maron, and S. T. Wu, "Phase-only modulation with twisted nematic liquid-crystal spatial light modulators," Opt. Lett. 13, 251-253 (1988).
    [CrossRef] [PubMed]
  8. J. L. Pezzaniti and R. A. Chipman, "Phase-only modulation of a twisted nematic liquid-crystal TV by use of the eigenpolarization states," Opt. Lett. 18, 1567-1569 (1993).
    [CrossRef] [PubMed]
  9. J. A. Davis, I. Moreno, and T. Tsai, "Polarization eigenstates for twisted-nematic liquid-crystal displays," Appl. Opt. 37, 937-945 (1998).
    [CrossRef]
  10. K. H. Lu and B. E. A. Saleh, "Theory and design of the liquid-crystal TV as a spatial phase modulator," Opt. Eng. 29, 240-246 (1990).
    [CrossRef]
  11. I. Moreno, P. Velásquez, C. R. Fernández-Pousa, M. M. Sánchez-López, and F. Mateos, "Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display," J. Appl. Phys. 94, 3697-3702 (2003).
    [CrossRef]
  12. H. Hurwitz and R. C. Jones, "A new calculus for the treatment of optical systems II. Proof of three general equivalence Theorems," J. Opt. Soc. Am. 31, 493-499 (1941).
  13. V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, "Cell parameter determination of a twisted-nematic liquid crystal display by single-wavelength polarimetry," J. Appl. Phys. 97,043101 (2005).
    [CrossRef]
  14. V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, "Equivalent retarder-rotator approach to on-state twisted nematic liquid crystal displays," J. Appl. Phys. (accepted).
  15. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 1st edition, (Elsevier, Amsterdam, 1987), Chap. 1.
  16. M. Johnson, "Poincaré sphere representation of birefringent networks," Appl. Opt. 20, 2075-2080 (1981).
    [CrossRef] [PubMed]
  17. J. P. Guigay, "On Fresnel diffraction by one-dimensional periodic objects, with application to structure determination of phase objects," Opt. Acta 18, 677-682 (1971).
    [CrossRef]
  18. V. Arrizón and J. Ojeda-Castañeda, "Irradiance at Fresnel planes of a phase grating," J. Opt. Soc. Am. A 9, 1801-1806 (1992).
    [CrossRef]
  19. Z. Jaroszewicz, A. Kolodziejczyk, A. Kowalik, and R. Restrepo, "Determination of the step height of the binary phase grating from its Fresnel images," Optik 111, 207-210 (2000).
  20. A. Serrano-Heredia, G. W. Lu, P. Purwosumarto, and F. T. S. Yu, "Measurement of the phase modulation in liquid crystal television based on the fractional-Talbot effect," Opt. Eng. 35, 2680-2684 (1996).
    [CrossRef]
  21. A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, "Characterization of the retardance of a wave plate to increase the robutness of amplitude-only and phase-only modulations of a liquid cristal display," J. Mod. Opt. 52, 633-650 (2005).
    [CrossRef]

2005

E. Schonbrun, R. Piestun, P. Jordan, J. Coopper, K. D. Wulff, J. Courtial, and M. Padgett, "3D interferometric optical tweezers using a single spatial light modulator," Opt. Express 13, 3777-3786 (2005).
[CrossRef] [PubMed]

V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, "Cell parameter determination of a twisted-nematic liquid crystal display by single-wavelength polarimetry," J. Appl. Phys. 97,043101 (2005).
[CrossRef]

A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, "Characterization of the retardance of a wave plate to increase the robutness of amplitude-only and phase-only modulations of a liquid cristal display," J. Mod. Opt. 52, 633-650 (2005).
[CrossRef]

2004

Z. Jaroszewicz, V. Climent, V. Duran, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, "Programmable axicon for variable inclination of the focal segment," J. Mod. Opt. 14, 2185-2190 (2004).
[CrossRef]

2003

I. Moreno, P. Velásquez, C. R. Fernández-Pousa, M. M. Sánchez-López, and F. Mateos, "Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display," J. Appl. Phys. 94, 3697-3702 (2003).
[CrossRef]

2000

Z. Jaroszewicz, A. Kolodziejczyk, A. Kowalik, and R. Restrepo, "Determination of the step height of the binary phase grating from its Fresnel images," Optik 111, 207-210 (2000).

1999

1998

1996

A. Serrano-Heredia, G. W. Lu, P. Purwosumarto, and F. T. S. Yu, "Measurement of the phase modulation in liquid crystal television based on the fractional-Talbot effect," Opt. Eng. 35, 2680-2684 (1996).
[CrossRef]

1994

1993

1992

1990

K. H. Lu and B. E. A. Saleh, "Theory and design of the liquid-crystal TV as a spatial phase modulator," Opt. Eng. 29, 240-246 (1990).
[CrossRef]

1988

1981

1975

C. H. Gooch and H. A. Tarry, "Optical-properties of twisted nematic liquid-crystal structures with twist angles less than 90 degrees," J. Phys. D 8, 1575-1584 (1975).
[CrossRef]

1971

J. P. Guigay, "On Fresnel diffraction by one-dimensional periodic objects, with application to structure determination of phase objects," Opt. Acta 18, 677-682 (1971).
[CrossRef]

1941

Arrizón, V.

Burvall, A.

Z. Jaroszewicz, V. Climent, V. Duran, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, "Programmable axicon for variable inclination of the focal segment," J. Mod. Opt. 14, 2185-2190 (2004).
[CrossRef]

Campos, J.

A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, "Characterization of the retardance of a wave plate to increase the robutness of amplitude-only and phase-only modulations of a liquid cristal display," J. Mod. Opt. 52, 633-650 (2005).
[CrossRef]

Cazorla, C.

A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, "Characterization of the retardance of a wave plate to increase the robutness of amplitude-only and phase-only modulations of a liquid cristal display," J. Mod. Opt. 52, 633-650 (2005).
[CrossRef]

Chipman, R. A.

Climent, V.

Z. Jaroszewicz, V. Climent, V. Duran, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, "Programmable axicon for variable inclination of the focal segment," J. Mod. Opt. 14, 2185-2190 (2004).
[CrossRef]

Coopper, J.

Courtial, J.

Davis, J. A.

Duran, V.

Z. Jaroszewicz, V. Climent, V. Duran, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, "Programmable axicon for variable inclination of the focal segment," J. Mod. Opt. 14, 2185-2190 (2004).
[CrossRef]

Durán, V.

V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, "Cell parameter determination of a twisted-nematic liquid crystal display by single-wavelength polarimetry," J. Appl. Phys. 97,043101 (2005).
[CrossRef]

V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, "Equivalent retarder-rotator approach to on-state twisted nematic liquid crystal displays," J. Appl. Phys. (accepted).

Fernández-Pousa, C. R.

I. Moreno, P. Velásquez, C. R. Fernández-Pousa, M. M. Sánchez-López, and F. Mateos, "Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display," J. Appl. Phys. 94, 3697-3702 (2003).
[CrossRef]

Friberg, A. T.

Z. Jaroszewicz, V. Climent, V. Duran, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, "Programmable axicon for variable inclination of the focal segment," J. Mod. Opt. 14, 2185-2190 (2004).
[CrossRef]

Gooch, C. H.

C. H. Gooch and H. A. Tarry, "Optical-properties of twisted nematic liquid-crystal structures with twist angles less than 90 degrees," J. Phys. D 8, 1575-1584 (1975).
[CrossRef]

Guigay, J. P.

J. P. Guigay, "On Fresnel diffraction by one-dimensional periodic objects, with application to structure determination of phase objects," Opt. Acta 18, 677-682 (1971).
[CrossRef]

Haist, T.

Hara, T.

Hurwitz, H.

Jaroszewicz, Z.

V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, "Cell parameter determination of a twisted-nematic liquid crystal display by single-wavelength polarimetry," J. Appl. Phys. 97,043101 (2005).
[CrossRef]

Z. Jaroszewicz, V. Climent, V. Duran, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, "Programmable axicon for variable inclination of the focal segment," J. Mod. Opt. 14, 2185-2190 (2004).
[CrossRef]

Z. Jaroszewicz, A. Kolodziejczyk, A. Kowalik, and R. Restrepo, "Determination of the step height of the binary phase grating from its Fresnel images," Optik 111, 207-210 (2000).

V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, "Equivalent retarder-rotator approach to on-state twisted nematic liquid crystal displays," J. Appl. Phys. (accepted).

Johnson, M.

Jones, R. C.

Jordan, P.

Kobayashi, Y.

Kolodziejczyk, A.

Z. Jaroszewicz, V. Climent, V. Duran, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, "Programmable axicon for variable inclination of the focal segment," J. Mod. Opt. 14, 2185-2190 (2004).
[CrossRef]

Z. Jaroszewicz, A. Kolodziejczyk, A. Kowalik, and R. Restrepo, "Determination of the step height of the binary phase grating from its Fresnel images," Optik 111, 207-210 (2000).

Konforti, N.

Kowalik, A.

Z. Jaroszewicz, A. Kolodziejczyk, A. Kowalik, and R. Restrepo, "Determination of the step height of the binary phase grating from its Fresnel images," Optik 111, 207-210 (2000).

Lancis, J.

V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, "Cell parameter determination of a twisted-nematic liquid crystal display by single-wavelength polarimetry," J. Appl. Phys. 97,043101 (2005).
[CrossRef]

Z. Jaroszewicz, V. Climent, V. Duran, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, "Programmable axicon for variable inclination of the focal segment," J. Mod. Opt. 14, 2185-2190 (2004).
[CrossRef]

V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, "Equivalent retarder-rotator approach to on-state twisted nematic liquid crystal displays," J. Appl. Phys. (accepted).

Laude, V.

V. Laude, "Twisted-nematic liquid-crystal pixelated active lens," Opt. Commun. 153, 134-152 (1998).
[CrossRef]

Lu, G. W.

A. Serrano-Heredia, G. W. Lu, P. Purwosumarto, and F. T. S. Yu, "Measurement of the phase modulation in liquid crystal television based on the fractional-Talbot effect," Opt. Eng. 35, 2680-2684 (1996).
[CrossRef]

Lu, K. H.

K. H. Lu and B. E. A. Saleh, "Theory and design of the liquid-crystal TV as a spatial phase modulator," Opt. Eng. 29, 240-246 (1990).
[CrossRef]

Maron, E.

Márquez, A.

A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, "Characterization of the retardance of a wave plate to increase the robutness of amplitude-only and phase-only modulations of a liquid cristal display," J. Mod. Opt. 52, 633-650 (2005).
[CrossRef]

Mateos, F.

I. Moreno, P. Velásquez, C. R. Fernández-Pousa, M. M. Sánchez-López, and F. Mateos, "Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display," J. Appl. Phys. 94, 3697-3702 (2003).
[CrossRef]

Moreno, I.

I. Moreno, P. Velásquez, C. R. Fernández-Pousa, M. M. Sánchez-López, and F. Mateos, "Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display," J. Appl. Phys. 94, 3697-3702 (2003).
[CrossRef]

J. A. Davis, I. Moreno, and T. Tsai, "Polarization eigenstates for twisted-nematic liquid-crystal displays," Appl. Opt. 37, 937-945 (1998).
[CrossRef]

Mukohzaka, N.

Ojeda-Castañeda, J.

Padgett, M.

Pezzaniti, J. L.

Piestun, R.

Purwosumarto, P.

A. Serrano-Heredia, G. W. Lu, P. Purwosumarto, and F. T. S. Yu, "Measurement of the phase modulation in liquid crystal television based on the fractional-Talbot effect," Opt. Eng. 35, 2680-2684 (1996).
[CrossRef]

Reicherter, M.

Restrepo, R.

Z. Jaroszewicz, A. Kolodziejczyk, A. Kowalik, and R. Restrepo, "Determination of the step height of the binary phase grating from its Fresnel images," Optik 111, 207-210 (2000).

Saleh, B. E. A.

K. H. Lu and B. E. A. Saleh, "Theory and design of the liquid-crystal TV as a spatial phase modulator," Opt. Eng. 29, 240-246 (1990).
[CrossRef]

Sánchez-López, M. M.

I. Moreno, P. Velásquez, C. R. Fernández-Pousa, M. M. Sánchez-López, and F. Mateos, "Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display," J. Appl. Phys. 94, 3697-3702 (2003).
[CrossRef]

Schonbrun, E.

Serrano-Heredia, A.

A. Serrano-Heredia, G. W. Lu, P. Purwosumarto, and F. T. S. Yu, "Measurement of the phase modulation in liquid crystal television based on the fractional-Talbot effect," Opt. Eng. 35, 2680-2684 (1996).
[CrossRef]

Tajahuerce, E.

V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, "Cell parameter determination of a twisted-nematic liquid crystal display by single-wavelength polarimetry," J. Appl. Phys. 97,043101 (2005).
[CrossRef]

V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, "Equivalent retarder-rotator approach to on-state twisted nematic liquid crystal displays," J. Appl. Phys. (accepted).

Tarry, H. A.

C. H. Gooch and H. A. Tarry, "Optical-properties of twisted nematic liquid-crystal structures with twist angles less than 90 degrees," J. Phys. D 8, 1575-1584 (1975).
[CrossRef]

Tiziani, H. J.

Toyoda, H.

Tsai, T.

Velásquez, P.

I. Moreno, P. Velásquez, C. R. Fernández-Pousa, M. M. Sánchez-López, and F. Mateos, "Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display," J. Appl. Phys. 94, 3697-3702 (2003).
[CrossRef]

Wagemann, E. U.

Wu, S. T.

Wulff, K. D.

Yoshida, N.

Yu, F. T. S.

A. Serrano-Heredia, G. W. Lu, P. Purwosumarto, and F. T. S. Yu, "Measurement of the phase modulation in liquid crystal television based on the fractional-Talbot effect," Opt. Eng. 35, 2680-2684 (1996).
[CrossRef]

Yzuel, M. J.

A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, "Characterization of the retardance of a wave plate to increase the robutness of amplitude-only and phase-only modulations of a liquid cristal display," J. Mod. Opt. 52, 633-650 (2005).
[CrossRef]

Appl. Opt.

J. Appl. Phys.

I. Moreno, P. Velásquez, C. R. Fernández-Pousa, M. M. Sánchez-López, and F. Mateos, "Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display," J. Appl. Phys. 94, 3697-3702 (2003).
[CrossRef]

V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, "Cell parameter determination of a twisted-nematic liquid crystal display by single-wavelength polarimetry," J. Appl. Phys. 97,043101 (2005).
[CrossRef]

V. Durán, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz, "Equivalent retarder-rotator approach to on-state twisted nematic liquid crystal displays," J. Appl. Phys. (accepted).

J. Mod. Opt.

Z. Jaroszewicz, V. Climent, V. Duran, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, "Programmable axicon for variable inclination of the focal segment," J. Mod. Opt. 14, 2185-2190 (2004).
[CrossRef]

A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, "Characterization of the retardance of a wave plate to increase the robutness of amplitude-only and phase-only modulations of a liquid cristal display," J. Mod. Opt. 52, 633-650 (2005).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. D

C. H. Gooch and H. A. Tarry, "Optical-properties of twisted nematic liquid-crystal structures with twist angles less than 90 degrees," J. Phys. D 8, 1575-1584 (1975).
[CrossRef]

Opt. Acta

J. P. Guigay, "On Fresnel diffraction by one-dimensional periodic objects, with application to structure determination of phase objects," Opt. Acta 18, 677-682 (1971).
[CrossRef]

Opt. Commun.

V. Laude, "Twisted-nematic liquid-crystal pixelated active lens," Opt. Commun. 153, 134-152 (1998).
[CrossRef]

Opt. Eng.

K. H. Lu and B. E. A. Saleh, "Theory and design of the liquid-crystal TV as a spatial phase modulator," Opt. Eng. 29, 240-246 (1990).
[CrossRef]

A. Serrano-Heredia, G. W. Lu, P. Purwosumarto, and F. T. S. Yu, "Measurement of the phase modulation in liquid crystal television based on the fractional-Talbot effect," Opt. Eng. 35, 2680-2684 (1996).
[CrossRef]

Opt. Express

Opt. Lett.

Optik

Z. Jaroszewicz, A. Kolodziejczyk, A. Kowalik, and R. Restrepo, "Determination of the step height of the binary phase grating from its Fresnel images," Optik 111, 207-210 (2000).

Other

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 1st edition, (Elsevier, Amsterdam, 1987), Chap. 1.

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Figures (6)

Fig. 1.
Fig. 1.

Representation of measured equivalent parameters, the phase retardation, δeq , and the rotation angle, φeq , of a commercial TNLCD as a function of the addressed gray-level, g, for a wavelength of 514 nm.

Fig. 2.
Fig. 2.

Experimental setup for generating a set of EAPSs. P is the polarizer; LCD, the sample display; and QWP, the quarter-wave plate. θ 1 and θ 2 are, respectively, the polarizer and the quarter-wave plate angles with respect to the input molecular director of the LCD. Ψ D is the angle between the input molecular director and the horizontal axis of the laboratory.

Fig. 3.
Fig. 3.

Representation on the Poincaré sphere of the output polarization states for the different gray-levels, g, when the TNLCD behaves as EAPS generator.

Fig. 4.
Fig. 4.

Experimental setup for achieving phase-only modulation. P1 is the polarizer; LCD, the sample display; QWP, the quarter-wave plate; and P2, the analyzer. θ 1, θ 2 and θ 3 are, respectively, the polarizer, the quarter-wave plate and the analyzer angles with respect to the input molecular director of the LCD.

Fig. 5.
Fig. 5.

Fresnel images at a quarter of the Talbot distance of different binary phase gratings implemented with the TNLCD.

Fig. 6.
Fig. 6.

Modulation provided by the TNLCD in the phase-mostly configuration: a) Phase shift versus gray level and b) complex amplitude modulation.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

E ( α , ε ) = exp ( j δ ) ( cos α cos ε j sin α sin ε sin α cos ε + j cos α sin ε ) ,
E out = P ( ξ ) E ( α 0 , ε ) = exp ( j δ ) ( cos ( α 0 ξ ) cos ε j sin ( α 0 ξ ) sin ε 0 ) ,
T = cos 2 ( α 0 ξ ) cos 2 ε + sin 2 ( α 0 ξ ) sin 2 ε .
ξ = α 0 π 4 ,
E out = 1 2 exp [ j ( ε + δ ) ] ( 1 0 ) .
M TNLCD = exp ( i β ) R ( ϕ eq ) WP ( 2 δ eq, ϕ + ϕ eq 2 ) ,
( E x E y ) = exp ( i β ) P ( θ 3 ) WP ( π 2 , θ 2 ) R ( ϕ eq ) WP ( 2 δ eq , ϕ + ϕ eq 2 ) ( cos θ 1 sin θ 1 ) =
= exp ( i β ) ( a + ib 0 ) ,
a= 1 2 2 [cos( θ 1 θ 2 δ eq φ eq )+cos( θ 1 θ 2 + δ eq φ eq ) +2cos( θ 1 θ 2 +2 θ 3 φ )sin δ eq ],
b = 1 2 [ cos ( θ 1 + θ 2 2 θ 3 + ϕ eq ) cos δ eq cos ( θ 1 + θ 2 ϕ ) sin δ eq ] .
( E x E y ) = exp ( i σ ) T ( 1 0 ) ,
T = a 2 + b 2 ,
σ = β + arctan ( b a ) .
z m = ( m + 1 4 ) D ,
V = I MAX I MIN I MAX + I MIN = sin Δ φ .
V ( g ) = 2 T ( g ) 1 + T ( g ) sin Δ φ ( g ) .
T ( g ) = I 1 ( g ) I 1 ( g ) + I 2 ( g ) .

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