Abstract

Electro-holography has the problem of having a narrow visual field angle, because the resolution of a spatial light modulator is insufficient for displaying a fringe pattern. To solve this problem, this paper proposes a projector-type electro-holographic compact display that achieves a wide visual field angle by using the combination of an optical system and calculation algorithms. The results of experiments show that the visual field angle is three times larger than that of a normal electro-holographic display. In addition, it is demonstrated that the system has the ability to display 3D reconstructed images with binocular, full-color, high-resolution, and accurate depth presentation.

© 2019 Optical Society of America

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References

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  1. S. F. Johnston, Holographic Visions (Oxford university, 2006).
  2. L. H. Enloe, J. A. Murphy, and C. B. Rubinstein, “Hologram transmission via television,” Bell Syst. Tech. J. 45, 335–339 (1966).
    [Crossref]
  3. P. St-Hilaire, S. A. Benton, M. E. Lucente, and P. M. Hubel, “Color images with the MIT holographic video display,” Proc. SPIE 1667, 73–84 (1992).
    [Crossref]
  4. S. A. Benton and V. M. Bove, Holographic Imaging (Wiley, 2008).
  5. N. Hashimoto, K. Hoshino, and S. Morokawa, “Improved real-time holography system with LCDs,” Proc. SPIE 1667, 2–7 (1992).
    [Crossref]
  6. N. Fukaya, K. Maeno, K. Sato, and T. Honda, “Improved electroholographic display using liquid crystal devices to shorten the viewing distance with both-eye observation,” Opt. Eng. 35, 1545–1549 (1996).
    [Crossref]
  7. R. Häussler, S. Reichelt, N. Leister, E. Zschau, R. Missbach, and A. Schwerdtner, “Large real-time holographic displays: from prototypes to a consumer product,” Proc. SPIE 7237, 72370S (2009).
    [Crossref]
  8. K. Yamamoto, T. Mishina, R. Oi, T. Senoh, and T. Kurita, “Real-time color holography system for live scene using 4  k2  k video system,” Proc. SPIE 7619, 761906 (2010).
    [Crossref]
  9. T. Yoneyama, E. Murakami, Y. Oguro, H. Kubo, K. Yamaguchi, and Y. Sakamoto, “Holographic head-mounted display with correct accommodation and vergence stimuli,” Opt. Eng. 57, 061619 (2018).
    [Crossref]
  10. A. Georgiou and J. Kollin, “Holographic near-eye displays for virtual and augmented reality,” ACM Trans. Graphics 36, 85 (2017).
    [Crossref]
  11. K. Wakunami, P.-Y. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y.-P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7, 12954 (2016).
    [Crossref]
  12. T. Ichikawa, T. Yoneyama, and Y. Sakamoto, “CGH calculation with the ray tracing method for the Fourier transform optical system,” Opt. Express 21, 32019–32031 (2013).
    [Crossref]
  13. A. Gilles and P. Gioia, “Real-time layer-based computer-generated hologram calculation for the Fourier transform optical system,” Appl. Opt. 57, 8508–8517 (2018).
    [Crossref]
  14. B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13, 85 (1968).
    [Crossref]
  15. T. Ichikawa, K. Yamaguchi, and Y. Sakamoto, “Realistic expression for full-parallax computer-generated holograms with the ray-tracing method,” Appl. Opt. 52, A201–A209 (2013).
    [Crossref]
  16. T. Shimobaba, T. Ito, N. Masuda, Y. Ichihashi, and N. Takada, “Fast calculation of computer-generated hologram on amd hd5000 series GPU and opencl,” Opt. Express 18, 9955–9960 (2010).
    [Crossref]
  17. “CUDA toolkit documentation,” https://docs.nvidia.com/cuda/index.html .
  18. “NVIDIA optiX ray tracing engine NVIDIA developer,” https://developer.nvidia.com/optix .
  19. Y. Oguro, H. Kubo, and Y. Sakamoto, “Study on correction of field curvature in head mounted display using electro-holography,” in Proceeding of the 25th International Display Workshops (IDW’18) VHFp6/3D (2018), pp. 2–3.
  20. R. W. Meier, “Depth of focus and depth of field in holography,” J. Opt. Soc. Am. 55, 1693–1694 (1965).
    [Crossref]

2018 (2)

T. Yoneyama, E. Murakami, Y. Oguro, H. Kubo, K. Yamaguchi, and Y. Sakamoto, “Holographic head-mounted display with correct accommodation and vergence stimuli,” Opt. Eng. 57, 061619 (2018).
[Crossref]

A. Gilles and P. Gioia, “Real-time layer-based computer-generated hologram calculation for the Fourier transform optical system,” Appl. Opt. 57, 8508–8517 (2018).
[Crossref]

2017 (1)

A. Georgiou and J. Kollin, “Holographic near-eye displays for virtual and augmented reality,” ACM Trans. Graphics 36, 85 (2017).
[Crossref]

2016 (1)

K. Wakunami, P.-Y. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y.-P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7, 12954 (2016).
[Crossref]

2013 (2)

2010 (2)

T. Shimobaba, T. Ito, N. Masuda, Y. Ichihashi, and N. Takada, “Fast calculation of computer-generated hologram on amd hd5000 series GPU and opencl,” Opt. Express 18, 9955–9960 (2010).
[Crossref]

K. Yamamoto, T. Mishina, R. Oi, T. Senoh, and T. Kurita, “Real-time color holography system for live scene using 4  k2  k video system,” Proc. SPIE 7619, 761906 (2010).
[Crossref]

2009 (1)

R. Häussler, S. Reichelt, N. Leister, E. Zschau, R. Missbach, and A. Schwerdtner, “Large real-time holographic displays: from prototypes to a consumer product,” Proc. SPIE 7237, 72370S (2009).
[Crossref]

1996 (1)

N. Fukaya, K. Maeno, K. Sato, and T. Honda, “Improved electroholographic display using liquid crystal devices to shorten the viewing distance with both-eye observation,” Opt. Eng. 35, 1545–1549 (1996).
[Crossref]

1992 (2)

P. St-Hilaire, S. A. Benton, M. E. Lucente, and P. M. Hubel, “Color images with the MIT holographic video display,” Proc. SPIE 1667, 73–84 (1992).
[Crossref]

N. Hashimoto, K. Hoshino, and S. Morokawa, “Improved real-time holography system with LCDs,” Proc. SPIE 1667, 2–7 (1992).
[Crossref]

1968 (1)

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13, 85 (1968).
[Crossref]

1966 (1)

L. H. Enloe, J. A. Murphy, and C. B. Rubinstein, “Hologram transmission via television,” Bell Syst. Tech. J. 45, 335–339 (1966).
[Crossref]

1965 (1)

Benton, S. A.

P. St-Hilaire, S. A. Benton, M. E. Lucente, and P. M. Hubel, “Color images with the MIT holographic video display,” Proc. SPIE 1667, 73–84 (1992).
[Crossref]

S. A. Benton and V. M. Bove, Holographic Imaging (Wiley, 2008).

Bove, V. M.

S. A. Benton and V. M. Bove, Holographic Imaging (Wiley, 2008).

Brown, B. R.

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13, 85 (1968).
[Crossref]

Enloe, L. H.

L. H. Enloe, J. A. Murphy, and C. B. Rubinstein, “Hologram transmission via television,” Bell Syst. Tech. J. 45, 335–339 (1966).
[Crossref]

Fukaya, N.

N. Fukaya, K. Maeno, K. Sato, and T. Honda, “Improved electroholographic display using liquid crystal devices to shorten the viewing distance with both-eye observation,” Opt. Eng. 35, 1545–1549 (1996).
[Crossref]

Georgiou, A.

A. Georgiou and J. Kollin, “Holographic near-eye displays for virtual and augmented reality,” ACM Trans. Graphics 36, 85 (2017).
[Crossref]

Gilles, A.

Gioia, P.

Hashimoto, N.

N. Hashimoto, K. Hoshino, and S. Morokawa, “Improved real-time holography system with LCDs,” Proc. SPIE 1667, 2–7 (1992).
[Crossref]

Häussler, R.

R. Häussler, S. Reichelt, N. Leister, E. Zschau, R. Missbach, and A. Schwerdtner, “Large real-time holographic displays: from prototypes to a consumer product,” Proc. SPIE 7237, 72370S (2009).
[Crossref]

Honda, T.

N. Fukaya, K. Maeno, K. Sato, and T. Honda, “Improved electroholographic display using liquid crystal devices to shorten the viewing distance with both-eye observation,” Opt. Eng. 35, 1545–1549 (1996).
[Crossref]

Hoshino, K.

N. Hashimoto, K. Hoshino, and S. Morokawa, “Improved real-time holography system with LCDs,” Proc. SPIE 1667, 2–7 (1992).
[Crossref]

Hsieh, P.-Y.

K. Wakunami, P.-Y. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y.-P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7, 12954 (2016).
[Crossref]

Huang, Y.-P.

K. Wakunami, P.-Y. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y.-P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7, 12954 (2016).
[Crossref]

Hubel, P. M.

P. St-Hilaire, S. A. Benton, M. E. Lucente, and P. M. Hubel, “Color images with the MIT holographic video display,” Proc. SPIE 1667, 73–84 (1992).
[Crossref]

Ichihashi, Y.

K. Wakunami, P.-Y. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y.-P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7, 12954 (2016).
[Crossref]

T. Shimobaba, T. Ito, N. Masuda, Y. Ichihashi, and N. Takada, “Fast calculation of computer-generated hologram on amd hd5000 series GPU and opencl,” Opt. Express 18, 9955–9960 (2010).
[Crossref]

Ichikawa, T.

Ito, T.

Johnston, S. F.

S. F. Johnston, Holographic Visions (Oxford university, 2006).

Kollin, J.

A. Georgiou and J. Kollin, “Holographic near-eye displays for virtual and augmented reality,” ACM Trans. Graphics 36, 85 (2017).
[Crossref]

Kubo, H.

T. Yoneyama, E. Murakami, Y. Oguro, H. Kubo, K. Yamaguchi, and Y. Sakamoto, “Holographic head-mounted display with correct accommodation and vergence stimuli,” Opt. Eng. 57, 061619 (2018).
[Crossref]

Y. Oguro, H. Kubo, and Y. Sakamoto, “Study on correction of field curvature in head mounted display using electro-holography,” in Proceeding of the 25th International Display Workshops (IDW’18) VHFp6/3D (2018), pp. 2–3.

Kurita, T.

K. Yamamoto, T. Mishina, R. Oi, T. Senoh, and T. Kurita, “Real-time color holography system for live scene using 4  k2  k video system,” Proc. SPIE 7619, 761906 (2010).
[Crossref]

Leister, N.

R. Häussler, S. Reichelt, N. Leister, E. Zschau, R. Missbach, and A. Schwerdtner, “Large real-time holographic displays: from prototypes to a consumer product,” Proc. SPIE 7237, 72370S (2009).
[Crossref]

Lohmann, A. W.

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13, 85 (1968).
[Crossref]

Lucente, M. E.

P. St-Hilaire, S. A. Benton, M. E. Lucente, and P. M. Hubel, “Color images with the MIT holographic video display,” Proc. SPIE 1667, 73–84 (1992).
[Crossref]

Maeno, K.

N. Fukaya, K. Maeno, K. Sato, and T. Honda, “Improved electroholographic display using liquid crystal devices to shorten the viewing distance with both-eye observation,” Opt. Eng. 35, 1545–1549 (1996).
[Crossref]

Masuda, N.

Meier, R. W.

Mishina, T.

K. Yamamoto, T. Mishina, R. Oi, T. Senoh, and T. Kurita, “Real-time color holography system for live scene using 4  k2  k video system,” Proc. SPIE 7619, 761906 (2010).
[Crossref]

Missbach, R.

R. Häussler, S. Reichelt, N. Leister, E. Zschau, R. Missbach, and A. Schwerdtner, “Large real-time holographic displays: from prototypes to a consumer product,” Proc. SPIE 7237, 72370S (2009).
[Crossref]

Morokawa, S.

N. Hashimoto, K. Hoshino, and S. Morokawa, “Improved real-time holography system with LCDs,” Proc. SPIE 1667, 2–7 (1992).
[Crossref]

Murakami, E.

T. Yoneyama, E. Murakami, Y. Oguro, H. Kubo, K. Yamaguchi, and Y. Sakamoto, “Holographic head-mounted display with correct accommodation and vergence stimuli,” Opt. Eng. 57, 061619 (2018).
[Crossref]

Murphy, J. A.

L. H. Enloe, J. A. Murphy, and C. B. Rubinstein, “Hologram transmission via television,” Bell Syst. Tech. J. 45, 335–339 (1966).
[Crossref]

Oguro, Y.

T. Yoneyama, E. Murakami, Y. Oguro, H. Kubo, K. Yamaguchi, and Y. Sakamoto, “Holographic head-mounted display with correct accommodation and vergence stimuli,” Opt. Eng. 57, 061619 (2018).
[Crossref]

Y. Oguro, H. Kubo, and Y. Sakamoto, “Study on correction of field curvature in head mounted display using electro-holography,” in Proceeding of the 25th International Display Workshops (IDW’18) VHFp6/3D (2018), pp. 2–3.

Oi, R.

K. Wakunami, P.-Y. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y.-P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7, 12954 (2016).
[Crossref]

K. Yamamoto, T. Mishina, R. Oi, T. Senoh, and T. Kurita, “Real-time color holography system for live scene using 4  k2  k video system,” Proc. SPIE 7619, 761906 (2010).
[Crossref]

Okui, M.

K. Wakunami, P.-Y. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y.-P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7, 12954 (2016).
[Crossref]

Reichelt, S.

R. Häussler, S. Reichelt, N. Leister, E. Zschau, R. Missbach, and A. Schwerdtner, “Large real-time holographic displays: from prototypes to a consumer product,” Proc. SPIE 7237, 72370S (2009).
[Crossref]

Rubinstein, C. B.

L. H. Enloe, J. A. Murphy, and C. B. Rubinstein, “Hologram transmission via television,” Bell Syst. Tech. J. 45, 335–339 (1966).
[Crossref]

Sakamoto, Y.

T. Yoneyama, E. Murakami, Y. Oguro, H. Kubo, K. Yamaguchi, and Y. Sakamoto, “Holographic head-mounted display with correct accommodation and vergence stimuli,” Opt. Eng. 57, 061619 (2018).
[Crossref]

T. Ichikawa, T. Yoneyama, and Y. Sakamoto, “CGH calculation with the ray tracing method for the Fourier transform optical system,” Opt. Express 21, 32019–32031 (2013).
[Crossref]

T. Ichikawa, K. Yamaguchi, and Y. Sakamoto, “Realistic expression for full-parallax computer-generated holograms with the ray-tracing method,” Appl. Opt. 52, A201–A209 (2013).
[Crossref]

Y. Oguro, H. Kubo, and Y. Sakamoto, “Study on correction of field curvature in head mounted display using electro-holography,” in Proceeding of the 25th International Display Workshops (IDW’18) VHFp6/3D (2018), pp. 2–3.

Sasaki, H.

K. Wakunami, P.-Y. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y.-P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7, 12954 (2016).
[Crossref]

Sato, K.

N. Fukaya, K. Maeno, K. Sato, and T. Honda, “Improved electroholographic display using liquid crystal devices to shorten the viewing distance with both-eye observation,” Opt. Eng. 35, 1545–1549 (1996).
[Crossref]

Schwerdtner, A.

R. Häussler, S. Reichelt, N. Leister, E. Zschau, R. Missbach, and A. Schwerdtner, “Large real-time holographic displays: from prototypes to a consumer product,” Proc. SPIE 7237, 72370S (2009).
[Crossref]

Senoh, T.

K. Wakunami, P.-Y. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y.-P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7, 12954 (2016).
[Crossref]

K. Yamamoto, T. Mishina, R. Oi, T. Senoh, and T. Kurita, “Real-time color holography system for live scene using 4  k2  k video system,” Proc. SPIE 7619, 761906 (2010).
[Crossref]

Shimobaba, T.

St-Hilaire, P.

P. St-Hilaire, S. A. Benton, M. E. Lucente, and P. M. Hubel, “Color images with the MIT holographic video display,” Proc. SPIE 1667, 73–84 (1992).
[Crossref]

Takada, N.

Wakunami, K.

K. Wakunami, P.-Y. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y.-P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7, 12954 (2016).
[Crossref]

Yamaguchi, K.

T. Yoneyama, E. Murakami, Y. Oguro, H. Kubo, K. Yamaguchi, and Y. Sakamoto, “Holographic head-mounted display with correct accommodation and vergence stimuli,” Opt. Eng. 57, 061619 (2018).
[Crossref]

T. Ichikawa, K. Yamaguchi, and Y. Sakamoto, “Realistic expression for full-parallax computer-generated holograms with the ray-tracing method,” Appl. Opt. 52, A201–A209 (2013).
[Crossref]

Yamamoto, K.

K. Wakunami, P.-Y. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y.-P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7, 12954 (2016).
[Crossref]

K. Yamamoto, T. Mishina, R. Oi, T. Senoh, and T. Kurita, “Real-time color holography system for live scene using 4  k2  k video system,” Proc. SPIE 7619, 761906 (2010).
[Crossref]

Yoneyama, T.

T. Yoneyama, E. Murakami, Y. Oguro, H. Kubo, K. Yamaguchi, and Y. Sakamoto, “Holographic head-mounted display with correct accommodation and vergence stimuli,” Opt. Eng. 57, 061619 (2018).
[Crossref]

T. Ichikawa, T. Yoneyama, and Y. Sakamoto, “CGH calculation with the ray tracing method for the Fourier transform optical system,” Opt. Express 21, 32019–32031 (2013).
[Crossref]

Zschau, E.

R. Häussler, S. Reichelt, N. Leister, E. Zschau, R. Missbach, and A. Schwerdtner, “Large real-time holographic displays: from prototypes to a consumer product,” Proc. SPIE 7237, 72370S (2009).
[Crossref]

ACM Trans. Graphics (1)

A. Georgiou and J. Kollin, “Holographic near-eye displays for virtual and augmented reality,” ACM Trans. Graphics 36, 85 (2017).
[Crossref]

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

L. H. Enloe, J. A. Murphy, and C. B. Rubinstein, “Hologram transmission via television,” Bell Syst. Tech. J. 45, 335–339 (1966).
[Crossref]

IBM J. Res. Dev. (1)

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13, 85 (1968).
[Crossref]

J. Opt. Soc. Am. (1)

Nat. Commun. (1)

K. Wakunami, P.-Y. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y.-P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7, 12954 (2016).
[Crossref]

Opt. Eng. (2)

N. Fukaya, K. Maeno, K. Sato, and T. Honda, “Improved electroholographic display using liquid crystal devices to shorten the viewing distance with both-eye observation,” Opt. Eng. 35, 1545–1549 (1996).
[Crossref]

T. Yoneyama, E. Murakami, Y. Oguro, H. Kubo, K. Yamaguchi, and Y. Sakamoto, “Holographic head-mounted display with correct accommodation and vergence stimuli,” Opt. Eng. 57, 061619 (2018).
[Crossref]

Opt. Express (2)

Proc. SPIE (4)

R. Häussler, S. Reichelt, N. Leister, E. Zschau, R. Missbach, and A. Schwerdtner, “Large real-time holographic displays: from prototypes to a consumer product,” Proc. SPIE 7237, 72370S (2009).
[Crossref]

K. Yamamoto, T. Mishina, R. Oi, T. Senoh, and T. Kurita, “Real-time color holography system for live scene using 4  k2  k video system,” Proc. SPIE 7619, 761906 (2010).
[Crossref]

P. St-Hilaire, S. A. Benton, M. E. Lucente, and P. M. Hubel, “Color images with the MIT holographic video display,” Proc. SPIE 1667, 73–84 (1992).
[Crossref]

N. Hashimoto, K. Hoshino, and S. Morokawa, “Improved real-time holography system with LCDs,” Proc. SPIE 1667, 2–7 (1992).
[Crossref]

Other (5)

S. F. Johnston, Holographic Visions (Oxford university, 2006).

S. A. Benton and V. M. Bove, Holographic Imaging (Wiley, 2008).

“CUDA toolkit documentation,” https://docs.nvidia.com/cuda/index.html .

“NVIDIA optiX ray tracing engine NVIDIA developer,” https://developer.nvidia.com/optix .

Y. Oguro, H. Kubo, and Y. Sakamoto, “Study on correction of field curvature in head mounted display using electro-holography,” in Proceeding of the 25th International Display Workshops (IDW’18) VHFp6/3D (2018), pp. 2–3.

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Figures (14)

Fig. 1.
Fig. 1. Configuration of our proposed projector-type electro-holographic display.
Fig. 2.
Fig. 2. Optical schematic geometry of the single-eye system.
Fig. 3.
Fig. 3. Calculation algorithm for CGH with ray-tracing method.
Fig. 4.
Fig. 4. Single-eye optical system: configuration.
Fig. 5.
Fig. 5. Binocular stereovision system: photo.
Fig. 6.
Fig. 6. Single-eye optical system: photo.
Fig. 7.
Fig. 7. Visual field angles.
Fig. 8.
Fig. 8. Object arrangement.
Fig. 9.
Fig. 9. Parallax verification: (a) view from left eye; (b) view from right eye.
Fig. 10.
Fig. 10. Depth chart.
Fig. 11.
Fig. 11. Depth verification.
Fig. 12.
Fig. 12. Depth images.
Fig. 13.
Fig. 13. Resolution chart.
Fig. 14.
Fig. 14. Resolution verification.

Tables (1)

Tables Icon

Table 1. Optical Parameters

Equations (7)

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

θ = sin 1 ( λ 2 p ) .
θ f = tan 1 ( S 2 f 1 ) ,
v z = 2 f 1 tan ( θ ) .
z 1 = f 1 z 0 f 1 + z 0 , x 1 = x 0 z 0 z 1 , z 2 = f 2 ( d 2 z 1 ) f 2 + ( d 2 z 1 ) , x 2 = x 1 z 1 z 2 , z 3 = f 3 ( d 3 z 2 ) f 3 + ( d 3 z 2 ) , x 3 = x 2 z 2 z 3 ,
H m ( x , y ) = i = 1 N m I i r i exp { j ( 2 π λ + ϕ i ) } ,
r i = ( x i x ) 2 + ( y i y ) 2 + z i 2 .
I i = k a I a + k d I d ( N L ) + k s I s ( R V ) β .

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