Abstract

We present some applications of the optical vortex birefringence compensator, based on the C polarization type singularities generated using two Wollaston compensators. The theory and experimental results of birefringent media properties measurements are presented. The possibility of the simultaneous measurement of both the azimuth angle and the phase retardance has been analyzed and experimentally verified.

© 2007 Optical Society of America

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References

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  1. M. Soskin, M. V. Vasnetov, “Singular optics,” in Progress in Optics (Elsevier, 2001), Vol. 42, Chap. 4.
  2. A. S. Desyatnikov, L. Tornel, Y. S. Kivshar, “Optical vortices and vortex solitons,” in Progress in Optics (Elsevier, 2005), Vol. 47, Chap. 5.
    [CrossRef]
  3. J. Masajada, A. Popiołek–Masajada, D. Wieliczka, “The interferometric system using optical vortices as a phase markers,” Opt. Commun. 207, 85–93 (2002).
    [CrossRef]
  4. A. Popiołek–Masajada, M. Borwińska, W. Frączek, “Testing a new method for small-angle rotation measurements with the optical vortex interferometer,” Meas. Sci. Technol. 17, 653–658 (2006).
    [CrossRef]
  5. M. Borwińska, A. Popiołek–Masajada, B. Dubik, “Reconstruction of the plane wave tilt and its orientation using optical vortex interferometer,” Opt. Eng. 46, 073604 (2007).
    [CrossRef]
  6. W. Wang, T. Yokozeki, R. Ishjima, A. Wada, Y. Miyamoto, M. Takeda, S. Hanson, “Optical vortex metrology for nanometric speckle displacement measurement,” Opt. Express 14, 120–127 (2006).
    [CrossRef] [PubMed]
  7. M. R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213, 201–221 (2002).
    [CrossRef]
  8. F. Flossman, U. T. Schwartz, M. Maier, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95, 253901 (2006).
  9. P. Kurzynowski, W. A. Woźniak, E. Frączek, “Optical vortices generation using Wollaston prism,” Appl. Opt. 45, 7898–7903 (2006).
    [CrossRef] [PubMed]
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  11. C. C. Montarou, T. K. Gaylord, “Two-wave-plate compensator for single-point retardation measurement,” Appl. Opt. 43, 6580–6595 (2004).
    [CrossRef]
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    [CrossRef]
  13. P. Gomez, C. Hernandez, “High-accuracy universal polarimeter measurement of optical activity and birefringence of α-quartz in the presence of multiple reflections,” J. Opt. Soc. Am. B 15, 1147–1154 (1998).
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  14. S. Drobczyński, J. M. Bueno, P. Artal, H. Kasprzak, “Transmission imaging polarimetry for a linear birefringent medium using a carrier fringe method,” Appl. Opt. 45, 5489–5496 (2006).
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  16. B. Zuccarello, G. Tripoli, “Photoelastic stress pattern analysis Fourier transform with carrier fringes: influence of quarter wave plate error,” Opt. Lasers Eng. 37, 401–416 (2002).
    [CrossRef]
  17. J.-F. Lin, Y.-L. Lo, “The new circular heterodyne interferometer with electro-optic modulation for measurement of the optical linear birefringence,” Opt. Commun. 260, 486–492 (2006).
    [CrossRef]
  18. M. Mujat, E. Baleine, A. Dogariu, “Interferometric imaging polarimeter,” J. Opt. Soc. Am. A 21, 2244–2249 (2004).
    [CrossRef]
  19. P. Kurzynowski, M. Borwińska, “Generation of the vortex type markers in a one wave setup,” Appl. Opt. 46, 676–679 (2007).
    [CrossRef] [PubMed]
  20. I. Freund, N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. A 50, 5164–5172 (1994).
    [CrossRef] [PubMed]
  21. A. Sieradzki, A. Cizman, R. Poprawski, V. Shuvaeva, M. Glazer, “Birefringence imaging of phase transition in ferroelastic Li2TiGeO5,” Phase Transit. 78, 351–356 (2005).
    [CrossRef]
  22. M. A. Geday, W. Kaminsky, J. G. Lewis, M. Glazer, “Images of absolute retardance L · Δn, using the rotating polarizer method,” J. Microsc. (Oxford) 198, 1–9 (2000).
    [CrossRef] [PubMed]
  23. J. Masajada, A. Popiołek–Masajada, E. Frączek, W. Frączek, “Vortex point localization problem in optical vortices interferometry,” Opt. Commun. 234, 23–28 (2004).
    [CrossRef]

2007 (2)

M. Borwińska, A. Popiołek–Masajada, B. Dubik, “Reconstruction of the plane wave tilt and its orientation using optical vortex interferometer,” Opt. Eng. 46, 073604 (2007).
[CrossRef]

P. Kurzynowski, M. Borwińska, “Generation of the vortex type markers in a one wave setup,” Appl. Opt. 46, 676–679 (2007).
[CrossRef] [PubMed]

2006 (5)

2005 (1)

A. Sieradzki, A. Cizman, R. Poprawski, V. Shuvaeva, M. Glazer, “Birefringence imaging of phase transition in ferroelastic Li2TiGeO5,” Phase Transit. 78, 351–356 (2005).
[CrossRef]

2004 (3)

2002 (3)

B. Zuccarello, G. Tripoli, “Photoelastic stress pattern analysis Fourier transform with carrier fringes: influence of quarter wave plate error,” Opt. Lasers Eng. 37, 401–416 (2002).
[CrossRef]

J. Masajada, A. Popiołek–Masajada, D. Wieliczka, “The interferometric system using optical vortices as a phase markers,” Opt. Commun. 207, 85–93 (2002).
[CrossRef]

M. R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213, 201–221 (2002).
[CrossRef]

2001 (1)

2000 (1)

M. A. Geday, W. Kaminsky, J. G. Lewis, M. Glazer, “Images of absolute retardance L · Δn, using the rotating polarizer method,” J. Microsc. (Oxford) 198, 1–9 (2000).
[CrossRef] [PubMed]

1998 (1)

1994 (1)

I. Freund, N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. A 50, 5164–5172 (1994).
[CrossRef] [PubMed]

1983 (1)

J. Kobayashi, Y. Uesu, “A new optical method and apparatus ‘HAUP’ for measuring simultaneously optical activity and birefringence of crystals. I. Principles and construction,” J. Appl. Crystallogr. 16, 204–211 (1983).
[CrossRef]

1982 (1)

Artal, P.

Baleine, E.

Berezhna, S. Y.

Berezhnyy, I. V.

Borwinska, M.

M. Borwińska, A. Popiołek–Masajada, B. Dubik, “Reconstruction of the plane wave tilt and its orientation using optical vortex interferometer,” Opt. Eng. 46, 073604 (2007).
[CrossRef]

P. Kurzynowski, M. Borwińska, “Generation of the vortex type markers in a one wave setup,” Appl. Opt. 46, 676–679 (2007).
[CrossRef] [PubMed]

A. Popiołek–Masajada, M. Borwińska, W. Frączek, “Testing a new method for small-angle rotation measurements with the optical vortex interferometer,” Meas. Sci. Technol. 17, 653–658 (2006).
[CrossRef]

Bueno, J. M.

Cizman, A.

A. Sieradzki, A. Cizman, R. Poprawski, V. Shuvaeva, M. Glazer, “Birefringence imaging of phase transition in ferroelastic Li2TiGeO5,” Phase Transit. 78, 351–356 (2005).
[CrossRef]

Dennis, M. R.

M. R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213, 201–221 (2002).
[CrossRef]

Desyatnikov, A. S.

A. S. Desyatnikov, L. Tornel, Y. S. Kivshar, “Optical vortices and vortex solitons,” in Progress in Optics (Elsevier, 2005), Vol. 47, Chap. 5.
[CrossRef]

Dogariu, A.

Drobczynski, S.

Dubik, B.

M. Borwińska, A. Popiołek–Masajada, B. Dubik, “Reconstruction of the plane wave tilt and its orientation using optical vortex interferometer,” Opt. Eng. 46, 073604 (2007).
[CrossRef]

Flossman, F.

F. Flossman, U. T. Schwartz, M. Maier, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95, 253901 (2006).

Fraczek, E.

P. Kurzynowski, W. A. Woźniak, E. Frączek, “Optical vortices generation using Wollaston prism,” Appl. Opt. 45, 7898–7903 (2006).
[CrossRef] [PubMed]

J. Masajada, A. Popiołek–Masajada, E. Frączek, W. Frączek, “Vortex point localization problem in optical vortices interferometry,” Opt. Commun. 234, 23–28 (2004).
[CrossRef]

Fraczek, W.

A. Popiołek–Masajada, M. Borwińska, W. Frączek, “Testing a new method for small-angle rotation measurements with the optical vortex interferometer,” Meas. Sci. Technol. 17, 653–658 (2006).
[CrossRef]

J. Masajada, A. Popiołek–Masajada, E. Frączek, W. Frączek, “Vortex point localization problem in optical vortices interferometry,” Opt. Commun. 234, 23–28 (2004).
[CrossRef]

Freund, I.

I. Freund, N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. A 50, 5164–5172 (1994).
[CrossRef] [PubMed]

Gaylord, T. K.

Geday, M. A.

M. A. Geday, W. Kaminsky, J. G. Lewis, M. Glazer, “Images of absolute retardance L · Δn, using the rotating polarizer method,” J. Microsc. (Oxford) 198, 1–9 (2000).
[CrossRef] [PubMed]

Glazer, M.

A. Sieradzki, A. Cizman, R. Poprawski, V. Shuvaeva, M. Glazer, “Birefringence imaging of phase transition in ferroelastic Li2TiGeO5,” Phase Transit. 78, 351–356 (2005).
[CrossRef]

M. A. Geday, W. Kaminsky, J. G. Lewis, M. Glazer, “Images of absolute retardance L · Δn, using the rotating polarizer method,” J. Microsc. (Oxford) 198, 1–9 (2000).
[CrossRef] [PubMed]

Gomez, P.

Hanson, S.

Hernandez, C.

Ina, H.

Ishjima, R.

Kaminsky, W.

M. A. Geday, W. Kaminsky, J. G. Lewis, M. Glazer, “Images of absolute retardance L · Δn, using the rotating polarizer method,” J. Microsc. (Oxford) 198, 1–9 (2000).
[CrossRef] [PubMed]

Kasprzak, H.

Kivshar, Y. S.

A. S. Desyatnikov, L. Tornel, Y. S. Kivshar, “Optical vortices and vortex solitons,” in Progress in Optics (Elsevier, 2005), Vol. 47, Chap. 5.
[CrossRef]

Kobayashi, H.

Kobayashi, J.

J. Kobayashi, Y. Uesu, “A new optical method and apparatus ‘HAUP’ for measuring simultaneously optical activity and birefringence of crystals. I. Principles and construction,” J. Appl. Crystallogr. 16, 204–211 (1983).
[CrossRef]

Kurzynowski, P.

Lewis, J. G.

M. A. Geday, W. Kaminsky, J. G. Lewis, M. Glazer, “Images of absolute retardance L · Δn, using the rotating polarizer method,” J. Microsc. (Oxford) 198, 1–9 (2000).
[CrossRef] [PubMed]

Lin, J.-F.

J.-F. Lin, Y.-L. Lo, “The new circular heterodyne interferometer with electro-optic modulation for measurement of the optical linear birefringence,” Opt. Commun. 260, 486–492 (2006).
[CrossRef]

Lo, Y.-L.

J.-F. Lin, Y.-L. Lo, “The new circular heterodyne interferometer with electro-optic modulation for measurement of the optical linear birefringence,” Opt. Commun. 260, 486–492 (2006).
[CrossRef]

Maier, M.

F. Flossman, U. T. Schwartz, M. Maier, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95, 253901 (2006).

Masajada, J.

J. Masajada, A. Popiołek–Masajada, E. Frączek, W. Frączek, “Vortex point localization problem in optical vortices interferometry,” Opt. Commun. 234, 23–28 (2004).
[CrossRef]

J. Masajada, A. Popiołek–Masajada, D. Wieliczka, “The interferometric system using optical vortices as a phase markers,” Opt. Commun. 207, 85–93 (2002).
[CrossRef]

Miyamoto, Y.

Montarou, C. C.

Mujat, M.

Popiolek–Masajada, A.

M. Borwińska, A. Popiołek–Masajada, B. Dubik, “Reconstruction of the plane wave tilt and its orientation using optical vortex interferometer,” Opt. Eng. 46, 073604 (2007).
[CrossRef]

A. Popiołek–Masajada, M. Borwińska, W. Frączek, “Testing a new method for small-angle rotation measurements with the optical vortex interferometer,” Meas. Sci. Technol. 17, 653–658 (2006).
[CrossRef]

J. Masajada, A. Popiołek–Masajada, E. Frączek, W. Frączek, “Vortex point localization problem in optical vortices interferometry,” Opt. Commun. 234, 23–28 (2004).
[CrossRef]

J. Masajada, A. Popiołek–Masajada, D. Wieliczka, “The interferometric system using optical vortices as a phase markers,” Opt. Commun. 207, 85–93 (2002).
[CrossRef]

Poprawski, R.

A. Sieradzki, A. Cizman, R. Poprawski, V. Shuvaeva, M. Glazer, “Birefringence imaging of phase transition in ferroelastic Li2TiGeO5,” Phase Transit. 78, 351–356 (2005).
[CrossRef]

Schwartz, U. T.

F. Flossman, U. T. Schwartz, M. Maier, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95, 253901 (2006).

Shuvaeva, V.

A. Sieradzki, A. Cizman, R. Poprawski, V. Shuvaeva, M. Glazer, “Birefringence imaging of phase transition in ferroelastic Li2TiGeO5,” Phase Transit. 78, 351–356 (2005).
[CrossRef]

Shvartsman, N.

I. Freund, N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. A 50, 5164–5172 (1994).
[CrossRef] [PubMed]

Sieradzki, A.

A. Sieradzki, A. Cizman, R. Poprawski, V. Shuvaeva, M. Glazer, “Birefringence imaging of phase transition in ferroelastic Li2TiGeO5,” Phase Transit. 78, 351–356 (2005).
[CrossRef]

Soskin, M.

M. Soskin, M. V. Vasnetov, “Singular optics,” in Progress in Optics (Elsevier, 2001), Vol. 42, Chap. 4.

Takashi, M.

Takeda, M.

Tornel, L.

A. S. Desyatnikov, L. Tornel, Y. S. Kivshar, “Optical vortices and vortex solitons,” in Progress in Optics (Elsevier, 2005), Vol. 47, Chap. 5.
[CrossRef]

Tripoli, G.

B. Zuccarello, G. Tripoli, “Photoelastic stress pattern analysis Fourier transform with carrier fringes: influence of quarter wave plate error,” Opt. Lasers Eng. 37, 401–416 (2002).
[CrossRef]

Uesu, Y.

J. Kobayashi, Y. Uesu, “A new optical method and apparatus ‘HAUP’ for measuring simultaneously optical activity and birefringence of crystals. I. Principles and construction,” J. Appl. Crystallogr. 16, 204–211 (1983).
[CrossRef]

Vasnetov, M. V.

M. Soskin, M. V. Vasnetov, “Singular optics,” in Progress in Optics (Elsevier, 2001), Vol. 42, Chap. 4.

Wada, A.

Wang, W.

Wieliczka, D.

J. Masajada, A. Popiołek–Masajada, D. Wieliczka, “The interferometric system using optical vortices as a phase markers,” Opt. Commun. 207, 85–93 (2002).
[CrossRef]

Wozniak, W. A.

Yokozeki, T.

Zuccarello, B.

B. Zuccarello, G. Tripoli, “Photoelastic stress pattern analysis Fourier transform with carrier fringes: influence of quarter wave plate error,” Opt. Lasers Eng. 37, 401–416 (2002).
[CrossRef]

Appl. Opt. (4)

J. Appl. Crystallogr. (1)

J. Kobayashi, Y. Uesu, “A new optical method and apparatus ‘HAUP’ for measuring simultaneously optical activity and birefringence of crystals. I. Principles and construction,” J. Appl. Crystallogr. 16, 204–211 (1983).
[CrossRef]

J. Microsc. (1)

M. A. Geday, W. Kaminsky, J. G. Lewis, M. Glazer, “Images of absolute retardance L · Δn, using the rotating polarizer method,” J. Microsc. (Oxford) 198, 1–9 (2000).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (1)

Meas. Sci. Technol. (1)

A. Popiołek–Masajada, M. Borwińska, W. Frączek, “Testing a new method for small-angle rotation measurements with the optical vortex interferometer,” Meas. Sci. Technol. 17, 653–658 (2006).
[CrossRef]

Opt. Commun. (4)

M. R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213, 201–221 (2002).
[CrossRef]

J. Masajada, A. Popiołek–Masajada, D. Wieliczka, “The interferometric system using optical vortices as a phase markers,” Opt. Commun. 207, 85–93 (2002).
[CrossRef]

J.-F. Lin, Y.-L. Lo, “The new circular heterodyne interferometer with electro-optic modulation for measurement of the optical linear birefringence,” Opt. Commun. 260, 486–492 (2006).
[CrossRef]

J. Masajada, A. Popiołek–Masajada, E. Frączek, W. Frączek, “Vortex point localization problem in optical vortices interferometry,” Opt. Commun. 234, 23–28 (2004).
[CrossRef]

Opt. Eng. (1)

M. Borwińska, A. Popiołek–Masajada, B. Dubik, “Reconstruction of the plane wave tilt and its orientation using optical vortex interferometer,” Opt. Eng. 46, 073604 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

B. Zuccarello, G. Tripoli, “Photoelastic stress pattern analysis Fourier transform with carrier fringes: influence of quarter wave plate error,” Opt. Lasers Eng. 37, 401–416 (2002).
[CrossRef]

Phase Transit. (1)

A. Sieradzki, A. Cizman, R. Poprawski, V. Shuvaeva, M. Glazer, “Birefringence imaging of phase transition in ferroelastic Li2TiGeO5,” Phase Transit. 78, 351–356 (2005).
[CrossRef]

Phys. Rev. A (1)

I. Freund, N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. A 50, 5164–5172 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

F. Flossman, U. T. Schwartz, M. Maier, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95, 253901 (2006).

Other (2)

M. Soskin, M. V. Vasnetov, “Singular optics,” in Progress in Optics (Elsevier, 2001), Vol. 42, Chap. 4.

A. S. Desyatnikov, L. Tornel, Y. S. Kivshar, “Optical vortices and vortex solitons,” in Progress in Optics (Elsevier, 2005), Vol. 47, Chap. 5.
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Interferometer setup: P, polarizer, W 1 , W 2 , Wollaston compensators, M, medium, A, analyzer, CCD, camera. Azimuthal orientation of the elements in the text.

Fig. 2
Fig. 2

Main axes ( δ 1 , δ 2 ) with orientations of the Wollaston compensators W 1 and W 2 in regard to the Cartesian system coordinates ( x , y ) . Fringes mark lines of a constant phase retardance introduced by the proper Wollaston compensator.

Fig. 3
Fig. 3

Generated numerical intensity (a) and phase (b) distributions for the OVBC setup. Optical vortices points have been marked. Elementary lattice cell and the charges of the apex vortex points have also been drawn.

Fig. 4
Fig. 4

Vortex position changes due to the variable birefringent medium properties in coordinates of the Wollaston compensators main axes ( δ 1 , δ 2 ) . Solid lines refer to the variable phase retardances for chosen azimuth angles. Closed dotted curves correspond to variable azimuth angle. (b) Vortex position changes due to the variable birefringent medium properties in the detection plane for the same Wollaston compensators applied. Closed dotted curves correspond to variable azimuth angle, and the solid ones to the medium's variable phase retardance.

Fig. 5
Fig. 5

Exemplary intensity distribution detected in the OVBC system. Vortex points have been marked.

Fig. 6
Fig. 6

Change of the optical vortices positions due to variable phase retardances for the given azimuth angles of the probe: (a) 0°, (b) 12°, (c) 34°, (d) 57°. Points of the initial lattice (for γ = 0 ) have been marked.

Fig. 7
Fig. 7

Change of the optical vortices positions for different azimuth angles of the birefringent sample—the plane-parallel quarter-wave plate.

Fig. 8
Fig. 8

Intensity distributions for the half-wave plate for different azimuth angles: (a) 0°, (b) 22.5°, (c) 45°.

Fig. 9
Fig. 9

Intensity distributions for the half-wave plate of the azimuth angles (a) less than and (b) greater than 22.5°.

Fig. 10
Fig. 10

Change of the optical vortices positions for different azimuth angles of the birefringent sample—the wedged quarter-wave plate.

Fig. 11
Fig. 11

Two vortex lattices with and without the optical isotropic wedge.

Fig. 12
Fig. 12

Vortex positions as detected while rotating the wedge over 360°.

Equations (19)

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

I out ( δ 1 , δ 2 ; α , γ ) = cos 2   μ × cos 2 1 2 [ ( δ 1 + ψ 1 ) ( δ 2 + ψ 2 ) ] + sin 2   μ × sin 2 1 2 [ ( δ 1 + ψ 1 ) + ( δ 2 + ψ 2 ) ] ,
cos ψ 1 = 1 tan ( 2 α ) × cos ( 2 μ ) r ,
sin ψ 1 = sin ( 2 α ) × sin γ r ,
cos ψ 2 = 1 cot ( 2 α ) × cos ( 2 μ ) r ,
sin ψ 2 = cos ( 2 α ) × sin γ r ,
cos 2 μ = sin ( 4 α ) × sin 2 ( γ 2 ) ,
r = | sin ( 2 μ ) | .
I out = 0 { δ 1 = δ 1 + ψ 1 = π 2 + π × M δ 2 = δ 2 + ψ 2 = π 2 + π × ( M 2 N ) ,
I out ( x 0 , y 0 ; γ = 0 ) = 0 I out ( x 0 , y 0 ; γ 0 ) = sin 2 γ ,
Φ x y [ Φ x Φ y ] = 1 2 π [ 0 Λ 2 2 Λ 1 Λ 2 ] Ψ = 1 2 π [ ψ 2 Λ 2 ψ 2 Λ 2 2 ψ 1 Λ 1 ] ,
tan ( 2 α ) = sin ψ 1 sin ψ 2 ,
cos γ = sin 2 ψ 1 × cos ψ 1 sin 2 ψ 2 × cos ψ 2 sin 2 ψ 1 × cos ψ 2 sin 2 ψ 2 × cos ψ 1 .
Ψ = γ [ 0 1 ] ,
Ψ = γ [ 1 0 ] ,
Φ x y = γ 2 π Λ 2 [ 1 1 ] ,
Φ x y = γ 2 π Λ 1 [ 0 2 ] .
Δ Ψ j , j + 1 [ Δ ψ 1 ; j , j + 1 Δ ψ 2; j , j + 1 ] = Δ γ j , j + 1 [ sin ( 2 Δ α j , j + 1 ) cos ( 2 Δ α j , j + 1 ) ] ,
Δ γ j , j + 1 = | Δ Ψ j , j + 1 | ,
tan ( 2 Δ α j , j + 1 ) = Δ ψ 1 ; j , j + 1 Δ ψ 2; j , j + 1 .

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