Abstract

A new setup established to measure the light polarization state and the birefringent media parameters is proposed. The described setup consists of two pairs of the linear Wollaston compensators and circular compensators which form a set of two spatially modulated elliptical compensators. These compensators could be used separately as a spatial generator of polarization states and as an analyzer. Using them together allows us to establish a polariscopic setup in which the birefringent media parameters could be measured. When analyzing both the light polarization state and the birefringent media parameters the singular points in the output light intensity appear. The coordinates of these points depend linearly on the azimuth and ellipticity angles of the examined light or on the eigenvectors of the birefringent medium, while the measured light maximum value corresponds to the phase shift for the measurements of the birefringent medium parameters. Neither movable parts nor active elements are needed and no complicated analysis of output light should be made to calculate the desired quantities.

© 2008 Optical Society of America

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  1. D. H. Goldstein, "Mueller matrix dual-rotating retarder polarimeter," Appl. Opt. 31, 6676-6683 (1992).
    [CrossRef] [PubMed]
  2. J. L. Pezzaniti and R. A. Chipman, "Mueller matrix imaging polarimetry," Opt. Eng. 34, 1558-1568 (1995).
    [CrossRef]
  3. C. C. Montarou and T. K. Gaylord, "Two-wave-plate compensator for single-point retardation measurement," Appl. Opt. 43, 6580-6595 (2004).
    [CrossRef]
  4. P. A. Williams, A. H. Rose, and C. M. Wang, "Rotating-polarizer polarimeter for accurate retardance measurement," Appl. Opt. 36, 6466-6472 (1997).
    [CrossRef]
  5. N. N. Nagib, "Phase retardometer: a proposed device for measuring phase retardance," Appl. Opt. 39, 2078-2080 (2000).
    [CrossRef]
  6. S. Y. Berezhna, I. V. Berezhnyy, and M. Takashi, "Dynamic photometric imaging polarizer-sample-analyzer polarimeter: instrument for mapping birefringence and optical rotation," J. Opt. Soc. Am. A 18, 666-672 (2001).
    [CrossRef]
  7. P. Kurzynowski and W. A. Woźniak, "Phase retardation measurement in simple and reverse Senarmont compensators without calibrated quarter wave plates," Optik 113, 51-53 (2002).
    [CrossRef]
  8. P. Kurzynowski and W.A. Woźniak, "Simple method of the birefringent media properties determination," Opt. Commun. 259, 424-427 (2006).
    [CrossRef]
  9. L. H. Shyu, C. L. Chen, and D. C. Su, "Method for measuring the retardation of a wave plate," Appl. Opt. 32, 4228-4230(1993).
    [CrossRef] [PubMed]
  10. J. M. Bueno, "Polarimetry using liquid-crystal variable retarders: theory and calibration," J. Opt. A, Pure Appl. Opt. 2, 216-222 (2000).
    [CrossRef]
  11. Y. L. Lo and P. F. Hsu, "Birefringence measurements by an electro-optic modulator using a new heterodyne scheme," Opt. Eng. 41, 2764-2767 (2002).
    [CrossRef]
  12. B. E. Benkelfat, E. H. Horache, Q. Zou, and B. Vinouze, "An electro-optic modulation technique for direct and accurate measurement of birefringence," Opt. Commun. 221, 271-278 (2003).
    [CrossRef]
  13. B. Laude-Boulesteix, A. de Martino, B. Drevillon, and L. Schwartz, "Mueller polarimetric imaging system with liquid crystals," Appl. Opt. 43, 2824-2832 (2004).
    [CrossRef] [PubMed]
  14. Y. L. Lo, S. Y. Lee, and J. F. Lin, "Polariscope for simultaneous measurement of the principal axis and the phase retardation by use of two phase-locked extractions," Appl. Opt. 43, 6248-6254 (2004).
    [CrossRef] [PubMed]
  15. S. Drobczy�?ski and P. Kurzynowski, "Imaging polarimeter for linear birefringence measurements using a liquid crystal modulator," Opt. Eng. 47, 023603 (2008).
    [CrossRef]
  16. T. Sato, Y. Sasaki, N. Hashimoto, and S. Kawakami, "Novel scheme of ellipsometry utilizing parallel processing with arrayed photonic crystal," Photonics Nanostruct. Fundam. Appl. 2, 149-154 (2004).
    [CrossRef]
  17. T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, "Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plates elements," Appl. Opt. 46, 4963-4967 (2007).
    [CrossRef] [PubMed]
  18. M. Mujat, E. Baleine, and A. Dogariu, "Interferometric imaging polarimeter," J. Opt. Soc. Am. A 21, 2244-2249 (2004).
    [CrossRef]
  19. J. F. Lin and 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]
  20. Y. L. Lo, C. H. Lai, J. F. Lin, and P. F. Hsu, "Simultaneously absolute measurements in principal angle and phase retardation using new common-path heterodyne interferometer," Appl. Opt. 43, 2013-2022 (2004).
    [CrossRef] [PubMed]
  21. B. Wang and T. C. Oakberg, "A new instrument for measuring both the magnitude and angle of low level birefringence," Rev. Sci. Instrum. 70, 3847-3854 (1999).
    [CrossRef]
  22. M. Takeda, H. Ina, and H. Kobayashi, "Fourier transform method of fringe-pattern analysis for computer based topography and interferometry," J. Opt. Soc. Am. 72, 156-159 (1982).
    [CrossRef]
  23. B. Zuccarello and 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]
  24. K. Oka and T. Kaneko, "Compact complete imaging polarimeter using birefringent wedge prisms," Opt. Express 11, 1510-1519 (2003).
    [CrossRef] [PubMed]
  25. K. Oka and N. Saito, "Snapshot complete imaging polarimeter using Savart plates," Proc. SPIE 6295, 1-7 (2006).
  26. S. Drobczy�?ski, J. M. Bueno, P. Artal, and H. Kasprzak, "Transmission imaging polarimetry for linear birefringent medium using carrier fringe method," Appl. Opt. 45, 5489-5496 (2006).
    [CrossRef] [PubMed]
  27. C. C. Montarou and T. K. Gaylord, "Analysis and design of modified Wollaston prisms," Appl. Opt. 38, 6604-6616 (1999).
    [CrossRef]
  28. M. Soskin and M. V. Vasnetov, "Singular Optics," in Progress in Optics, (Elsevier, 2001), Vol. 42 Chap. 4.

2008

S. Drobczy�?ski and P. Kurzynowski, "Imaging polarimeter for linear birefringence measurements using a liquid crystal modulator," Opt. Eng. 47, 023603 (2008).
[CrossRef]

2007

2006

S. Drobczy�?ski, J. M. Bueno, P. Artal, and H. Kasprzak, "Transmission imaging polarimetry for linear birefringent medium using carrier fringe method," Appl. Opt. 45, 5489-5496 (2006).
[CrossRef] [PubMed]

P. Kurzynowski and W.A. Woźniak, "Simple method of the birefringent media properties determination," Opt. Commun. 259, 424-427 (2006).
[CrossRef]

J. F. Lin and 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]

K. Oka and N. Saito, "Snapshot complete imaging polarimeter using Savart plates," Proc. SPIE 6295, 1-7 (2006).

2004

2003

K. Oka and T. Kaneko, "Compact complete imaging polarimeter using birefringent wedge prisms," Opt. Express 11, 1510-1519 (2003).
[CrossRef] [PubMed]

B. E. Benkelfat, E. H. Horache, Q. Zou, and B. Vinouze, "An electro-optic modulation technique for direct and accurate measurement of birefringence," Opt. Commun. 221, 271-278 (2003).
[CrossRef]

2002

P. Kurzynowski and W. A. Woźniak, "Phase retardation measurement in simple and reverse Senarmont compensators without calibrated quarter wave plates," Optik 113, 51-53 (2002).
[CrossRef]

Y. L. Lo and P. F. Hsu, "Birefringence measurements by an electro-optic modulator using a new heterodyne scheme," Opt. Eng. 41, 2764-2767 (2002).
[CrossRef]

B. Zuccarello and 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]

2001

2000

N. N. Nagib, "Phase retardometer: a proposed device for measuring phase retardance," Appl. Opt. 39, 2078-2080 (2000).
[CrossRef]

J. M. Bueno, "Polarimetry using liquid-crystal variable retarders: theory and calibration," J. Opt. A, Pure Appl. Opt. 2, 216-222 (2000).
[CrossRef]

1999

C. C. Montarou and T. K. Gaylord, "Analysis and design of modified Wollaston prisms," Appl. Opt. 38, 6604-6616 (1999).
[CrossRef]

B. Wang and T. C. Oakberg, "A new instrument for measuring both the magnitude and angle of low level birefringence," Rev. Sci. Instrum. 70, 3847-3854 (1999).
[CrossRef]

1997

1995

J. L. Pezzaniti and R. A. Chipman, "Mueller matrix imaging polarimetry," Opt. Eng. 34, 1558-1568 (1995).
[CrossRef]

1993

1992

1982

Araki, T.

Artal, P.

Baleine, E.

Benkelfat, B. E.

B. E. Benkelfat, E. H. Horache, Q. Zou, and B. Vinouze, "An electro-optic modulation technique for direct and accurate measurement of birefringence," Opt. Commun. 221, 271-278 (2003).
[CrossRef]

Berezhna, S. Y.

Berezhnyy, I. V.

Bueno, J. M.

Chen, C. L.

Chipman, R. A.

J. L. Pezzaniti and R. A. Chipman, "Mueller matrix imaging polarimetry," Opt. Eng. 34, 1558-1568 (1995).
[CrossRef]

de Martino, A.

Dogariu, A.

Drevillon, B.

Drobczy??ski, S.

S. Drobczy�?ski and P. Kurzynowski, "Imaging polarimeter for linear birefringence measurements using a liquid crystal modulator," Opt. Eng. 47, 023603 (2008).
[CrossRef]

S. Drobczy�?ski, J. M. Bueno, P. Artal, and H. Kasprzak, "Transmission imaging polarimetry for linear birefringent medium using carrier fringe method," Appl. Opt. 45, 5489-5496 (2006).
[CrossRef] [PubMed]

Gaylord, T. K.

Goldstein, D. H.

Hashimoto, N.

T. Sato, Y. Sasaki, N. Hashimoto, and S. Kawakami, "Novel scheme of ellipsometry utilizing parallel processing with arrayed photonic crystal," Photonics Nanostruct. Fundam. Appl. 2, 149-154 (2004).
[CrossRef]

Horache, E. H.

B. E. Benkelfat, E. H. Horache, Q. Zou, and B. Vinouze, "An electro-optic modulation technique for direct and accurate measurement of birefringence," Opt. Commun. 221, 271-278 (2003).
[CrossRef]

Hsu, P. F.

Ina, H.

Kaneko, T.

Kasprzak, H.

Kawakami, S.

T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, "Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plates elements," Appl. Opt. 46, 4963-4967 (2007).
[CrossRef] [PubMed]

T. Sato, Y. Sasaki, N. Hashimoto, and S. Kawakami, "Novel scheme of ellipsometry utilizing parallel processing with arrayed photonic crystal," Photonics Nanostruct. Fundam. Appl. 2, 149-154 (2004).
[CrossRef]

Kobayashi, H.

Kurzynowski, P.

S. Drobczy�?ski and P. Kurzynowski, "Imaging polarimeter for linear birefringence measurements using a liquid crystal modulator," Opt. Eng. 47, 023603 (2008).
[CrossRef]

P. Kurzynowski and W.A. Woźniak, "Simple method of the birefringent media properties determination," Opt. Commun. 259, 424-427 (2006).
[CrossRef]

P. Kurzynowski and W. A. Woźniak, "Phase retardation measurement in simple and reverse Senarmont compensators without calibrated quarter wave plates," Optik 113, 51-53 (2002).
[CrossRef]

Lai, C. H.

Laude-Boulesteix, B.

Lee, S. Y.

Lin, J. F.

Lo, Y. L.

J. F. Lin and 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]

Y. L. Lo, C. H. Lai, J. F. Lin, and P. F. Hsu, "Simultaneously absolute measurements in principal angle and phase retardation using new common-path heterodyne interferometer," Appl. Opt. 43, 2013-2022 (2004).
[CrossRef] [PubMed]

Y. L. Lo, S. Y. Lee, and J. F. Lin, "Polariscope for simultaneous measurement of the principal axis and the phase retardation by use of two phase-locked extractions," Appl. Opt. 43, 6248-6254 (2004).
[CrossRef] [PubMed]

Y. L. Lo and P. F. Hsu, "Birefringence measurements by an electro-optic modulator using a new heterodyne scheme," Opt. Eng. 41, 2764-2767 (2002).
[CrossRef]

Montarou, C. C.

Mujat, M.

Nagib, N. N.

Oakberg, T. C.

B. Wang and T. C. Oakberg, "A new instrument for measuring both the magnitude and angle of low level birefringence," Rev. Sci. Instrum. 70, 3847-3854 (1999).
[CrossRef]

Oka, K.

K. Oka and N. Saito, "Snapshot complete imaging polarimeter using Savart plates," Proc. SPIE 6295, 1-7 (2006).

K. Oka and T. Kaneko, "Compact complete imaging polarimeter using birefringent wedge prisms," Opt. Express 11, 1510-1519 (2003).
[CrossRef] [PubMed]

Pezzaniti, J. L.

J. L. Pezzaniti and R. A. Chipman, "Mueller matrix imaging polarimetry," Opt. Eng. 34, 1558-1568 (1995).
[CrossRef]

Rose, A. H.

Saito, N.

K. Oka and N. Saito, "Snapshot complete imaging polarimeter using Savart plates," Proc. SPIE 6295, 1-7 (2006).

Sasaki, Y.

T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, "Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plates elements," Appl. Opt. 46, 4963-4967 (2007).
[CrossRef] [PubMed]

T. Sato, Y. Sasaki, N. Hashimoto, and S. Kawakami, "Novel scheme of ellipsometry utilizing parallel processing with arrayed photonic crystal," Photonics Nanostruct. Fundam. Appl. 2, 149-154 (2004).
[CrossRef]

Sato, T.

T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, "Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plates elements," Appl. Opt. 46, 4963-4967 (2007).
[CrossRef] [PubMed]

T. Sato, Y. Sasaki, N. Hashimoto, and S. Kawakami, "Novel scheme of ellipsometry utilizing parallel processing with arrayed photonic crystal," Photonics Nanostruct. Fundam. Appl. 2, 149-154 (2004).
[CrossRef]

Schwartz, L.

Shyu, L. H.

Su, D. C.

Tadokoro, T.

Takashi, M.

Takeda, M.

Tripoli, G.

B. Zuccarello and 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]

Tsuru, T.

Vinouze, B.

B. E. Benkelfat, E. H. Horache, Q. Zou, and B. Vinouze, "An electro-optic modulation technique for direct and accurate measurement of birefringence," Opt. Commun. 221, 271-278 (2003).
[CrossRef]

Wang, B.

B. Wang and T. C. Oakberg, "A new instrument for measuring both the magnitude and angle of low level birefringence," Rev. Sci. Instrum. 70, 3847-3854 (1999).
[CrossRef]

Wang, C. M.

Williams, P. A.

Wozniak, W. A.

P. Kurzynowski and W. A. Woźniak, "Phase retardation measurement in simple and reverse Senarmont compensators without calibrated quarter wave plates," Optik 113, 51-53 (2002).
[CrossRef]

Wozniak, W.A.

P. Kurzynowski and W.A. Woźniak, "Simple method of the birefringent media properties determination," Opt. Commun. 259, 424-427 (2006).
[CrossRef]

Zou, Q.

B. E. Benkelfat, E. H. Horache, Q. Zou, and B. Vinouze, "An electro-optic modulation technique for direct and accurate measurement of birefringence," Opt. Commun. 221, 271-278 (2003).
[CrossRef]

Zuccarello, B.

B. Zuccarello and 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.

D. H. Goldstein, "Mueller matrix dual-rotating retarder polarimeter," Appl. Opt. 31, 6676-6683 (1992).
[CrossRef] [PubMed]

L. H. Shyu, C. L. Chen, and D. C. Su, "Method for measuring the retardation of a wave plate," Appl. Opt. 32, 4228-4230(1993).
[CrossRef] [PubMed]

P. A. Williams, A. H. Rose, and C. M. Wang, "Rotating-polarizer polarimeter for accurate retardance measurement," Appl. Opt. 36, 6466-6472 (1997).
[CrossRef]

C. C. Montarou and T. K. Gaylord, "Analysis and design of modified Wollaston prisms," Appl. Opt. 38, 6604-6616 (1999).
[CrossRef]

N. N. Nagib, "Phase retardometer: a proposed device for measuring phase retardance," Appl. Opt. 39, 2078-2080 (2000).
[CrossRef]

Y. L. Lo, C. H. Lai, J. F. Lin, and P. F. Hsu, "Simultaneously absolute measurements in principal angle and phase retardation using new common-path heterodyne interferometer," Appl. Opt. 43, 2013-2022 (2004).
[CrossRef] [PubMed]

B. Laude-Boulesteix, A. de Martino, B. Drevillon, and L. Schwartz, "Mueller polarimetric imaging system with liquid crystals," Appl. Opt. 43, 2824-2832 (2004).
[CrossRef] [PubMed]

Y. L. Lo, S. Y. Lee, and J. F. Lin, "Polariscope for simultaneous measurement of the principal axis and the phase retardation by use of two phase-locked extractions," Appl. Opt. 43, 6248-6254 (2004).
[CrossRef] [PubMed]

C. C. Montarou and T. K. Gaylord, "Two-wave-plate compensator for single-point retardation measurement," Appl. Opt. 43, 6580-6595 (2004).
[CrossRef]

S. Drobczy�?ski, J. M. Bueno, P. Artal, and H. Kasprzak, "Transmission imaging polarimetry for linear birefringent medium using carrier fringe method," Appl. Opt. 45, 5489-5496 (2006).
[CrossRef] [PubMed]

T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, "Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plates elements," Appl. Opt. 46, 4963-4967 (2007).
[CrossRef] [PubMed]

J. Opt. A, Pure Appl. Opt.

J. M. Bueno, "Polarimetry using liquid-crystal variable retarders: theory and calibration," J. Opt. A, Pure Appl. Opt. 2, 216-222 (2000).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

B. E. Benkelfat, E. H. Horache, Q. Zou, and B. Vinouze, "An electro-optic modulation technique for direct and accurate measurement of birefringence," Opt. Commun. 221, 271-278 (2003).
[CrossRef]

P. Kurzynowski and W.A. Woźniak, "Simple method of the birefringent media properties determination," Opt. Commun. 259, 424-427 (2006).
[CrossRef]

J. F. Lin and 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]

Opt. Eng.

S. Drobczy�?ski and P. Kurzynowski, "Imaging polarimeter for linear birefringence measurements using a liquid crystal modulator," Opt. Eng. 47, 023603 (2008).
[CrossRef]

Y. L. Lo and P. F. Hsu, "Birefringence measurements by an electro-optic modulator using a new heterodyne scheme," Opt. Eng. 41, 2764-2767 (2002).
[CrossRef]

J. L. Pezzaniti and R. A. Chipman, "Mueller matrix imaging polarimetry," Opt. Eng. 34, 1558-1568 (1995).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

B. Zuccarello and 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]

Optik

P. Kurzynowski and W. A. Woźniak, "Phase retardation measurement in simple and reverse Senarmont compensators without calibrated quarter wave plates," Optik 113, 51-53 (2002).
[CrossRef]

Photonics Nanostruct. Fundam. Appl.

T. Sato, Y. Sasaki, N. Hashimoto, and S. Kawakami, "Novel scheme of ellipsometry utilizing parallel processing with arrayed photonic crystal," Photonics Nanostruct. Fundam. Appl. 2, 149-154 (2004).
[CrossRef]

Proc. SPIE

K. Oka and N. Saito, "Snapshot complete imaging polarimeter using Savart plates," Proc. SPIE 6295, 1-7 (2006).

Rev. Sci. Instrum.

B. Wang and T. C. Oakberg, "A new instrument for measuring both the magnitude and angle of low level birefringence," Rev. Sci. Instrum. 70, 3847-3854 (1999).
[CrossRef]

Other

M. Soskin and M. V. Vasnetov, "Singular Optics," in Progress in Optics, (Elsevier, 2001), Vol. 42 Chap. 4.

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Figures (6)

Fig. 1.
Fig. 1.

Scheme of all polarization state spatial generator. P - linear polarizer, L - Wollaston compensator, C - circular wedge compensator.

Fig. 2.
Fig. 2.

Scheme of polarization state spatial analyzer. C - circular wedge compensator, L - Wollaston compensator, A - linear analyzer.

Fig. 3.
Fig. 3.

The output light intensity I distribution after the elliptical analyzer for constant azimuth angle α=-20° and variable ellipticity angles of the examined light: a) ϑ=0°,b) ϑ=15°, c) ϑ=35°, d) ϑ=45°. The points with the minimum light intensity are marked as white circles.

Fig. 4.
Fig. 4.

The phase distribution of the output light for the intensity distribution presented in Fig. 3(b).

Fig. 5.
Fig. 5.

Scheme of the spatial elliptical polariscope. PLC - all polarization state spatial generator, M - elliptically birefringent medium, CLA - polarization state spatial analyzer, CCD - CCD camera.

Fig. 6.
Fig. 6.

The output light intensity I (a) and phase (b) distributions for elliptically birefringent medium with the azimuth angle α=75° and the ellipticity angle ϑ=-30°. Points representing parameters of two medium eigenwaves (and where the output light intensity reaches the minimum) were marked as white circles, while the point where the output light intensity reaches the maximum value - as black circle.

Equations (7)

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

δ L ( x , y ) = 2 π Λ L · x
δ C ( x , y ) = 2 π Λ C · y
α = y Λ C · π + π 4
ϑ = x Λ L · π .
I = I 0 · T CLA · [ 1 + sin ( 2 α + δ C ) cos ( δ L ) cos ( 2 ϑ ) + sin ( δ L ) sin ( 2 ϑ ) ]
I ( x , y ) = 0 { x = ϑ π Λ L y = α π 4 π Λ C .
I max = C · sin 2 ( γ 2 )

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