Abstract

In this paper, we analyze the depth of field (DOF) of integral imaging displays based on wave optics. With considering the diffraction effect, we analyze the intensity distribution of light with multiple micro-lenses and derive a DOF calculation formula for integral imaging display system. We study the variations of DOF values with different system parameters. Experimental results are provided to verify the accuracy of the theoretical analysis. The analyses and experimental results presented in this paper could be beneficial for better understanding and designing of integral imaging displays.

© 2013 Optical Society of America

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2013 (4)

C. C. Ji, C. G. Luo, H. Deng, D. H. Li, and Q. H. Wang, “Tilted elemental image array generation method for moiré-reduced computer generated integral imaging display,” Opt. Express21(17), 19816–19824 (2013).
[CrossRef] [PubMed]

X. Xiao, B. Javidi, M. Martínez-Corral, and A. Stern, “Advances in three-dimensional integral imaging: sensing, display, and applications,” Appl. Opt.52(4), 546–560 (2013).
[CrossRef] [PubMed]

J. Y. Son, W. H. Son, S. K. Kim, K. H. Lee, and B. Javidi, “Three-dimensional imaging for creating real-world-like environments,” Proc. IEEE101(1), 190–205 (2013).
[CrossRef]

C. W. Chen, Y. P. Huang, P. Y. Hsieh, T. H. Jen, Y. C. Chang, Y. R. Su, M. Cho, X. Xiao, and B. Javidi, “Enlarged viewing angle of integral imaging system by liquid crystal prism,” Proc. SID Symp. Dig.44(1), 231–234 (2013).

2012 (6)

H. Navarro, J. C. Barreiro, G. Saavedra, M. Martínez-Corral, and B. Javidi, “High-resolution far-field integral-imaging camera by double snapshot,” Opt. Express20(2), 890–895 (2012).
[CrossRef] [PubMed]

C. G. Luo, C. C. Ji, F. N. Wang, Y. Z. Wang, and Q. H. Wang, “Crosstalk free integral imaging display with wide viewing angle using periodic black mask,” J. Disp. Technol.8(11), 634–638 (2012).
[CrossRef]

C. G. Luo, Q. H. Wang, H. Deng, X. X. Gong, L. Li, and F. N. Wang, “Depth calculation method of integral imaging based on Gaussian beam distribution model,” J. Disp. Technol.8(2), 112–116 (2012).
[CrossRef]

J. Nakamura, T. Takahashi, C. W. Chen, Y. P. Huang, and Y. Takaki, “Analysis of longitudinal viewing freedom of reduced-view super multi-view display and increased longitudinal viewing freedom using eye-tracking technique,” J. Soc. Inf. Disp.20(4), 228–234 (2012).
[CrossRef]

M. Cho and B. Javidi, “Optimization of 3D integral imaging system parameters,” J. Disp. Technol.8(6), 357–360 (2012).
[CrossRef]

D. Shin, M. Daneshpanah, and B. Javidi, “Generalization of three-dimensional N-ocular imaging systems under fixed resource constraints,” Opt. Lett.37(1), 19–21 (2012).
[CrossRef] [PubMed]

2011 (5)

2010 (2)

J. Arai, F. Okano, M. Kawakita, M. Okui, Y. Haino, M. Yoshimura, M. Furuya, and M. Sato, “Integral three-dimensional television using a 33-megapixel imaging system,” J. Disp. Technol.6(10), 422–430 (2010).
[CrossRef]

M. Cho and B. Javidi, “Three-dimensional visualization of objects in turbid water using integral imaging,” J. Disp. Technol.6(10), 544–547 (2010).
[CrossRef]

2009 (3)

2008 (2)

R. Yang, X. Huang, S. Li, and C. Jaynes, “Toward the light field display: Autostereoscopic rendering via a cluster of projectors,” IEEE Trans. Vis. Comput. Graph.14(1), 84–96 (2008).
[CrossRef] [PubMed]

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature451(7179), 694–698 (2008).
[CrossRef] [PubMed]

2007 (2)

2006 (4)

B. Javidi, S. H. Hong, and O. Matoba, “Multidimensional optical sensor and imaging system,” Appl. Opt.45(13), 2986–2994 (2006).
[CrossRef] [PubMed]

B. Javidi, I. Moon, and S. Yeom, “Three-dimensional identification of biological microorganism using integral imaging,” Opt. Express14(25), 12096–12108 (2006).
[CrossRef] [PubMed]

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE94(3), 490–501 (2006).
[CrossRef]

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE94(3), 591–607 (2006).
[CrossRef]

2005 (2)

R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, and B. Javidi, “Extended depth-of-field 3-D display and visualization by combination of amplitude-modulated microlenses and deconvolution tools,” J. Disp. Technol.1(2), 321–327 (2005).
[CrossRef]

S. W. Min, J. Kim, and B. Lee, “New characteristic equation of three-dimensional integral imaging system and its applications,” Jpn. J. Appl. Phys.44(2), L71–L74 (2005).
[CrossRef]

2004 (1)

H. Liao, N. Hata, S. Nakajima, M. Iwahara, I. Sakuma, and T. Dohi, “Surgical navigation by autostereoscopic image overlay of integral videography,” IEEE Trans. Inf. Technol. Biomed.8(2), 114–121 (2004).
[CrossRef] [PubMed]

2003 (2)

1999 (1)

F. Okano, J. Arai, H. Hoshino, and I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng.38(6), 1072–1077 (1999).
[CrossRef]

1998 (2)

1988 (1)

1978 (1)

Y. Igarashi, H. Murata, and M. Ueda, “3D display system using a computer generated integral photography,” Jpn. J. Appl. Phys.17(9), 1683–1684 (1978).
[CrossRef]

1968 (1)

C. B. Burckhardt, “Optimum parameters and resolution limitation of integral photography,” J. Opt. Soc. Am. A58(1), 71–74 (1968).
[CrossRef]

1931 (1)

H. E. Ives, “Optical properties of a Lippman lenticulated sheet,” J. Opt. Soc. Am. A21(3), 171–176 (1931).
[CrossRef]

1908 (1)

G. Lippmann, “La photographie integrale,” C. R. Acad. Sci.146, 446–451 (1908).

Aloni, D.

Arai, J.

J. Arai, F. Okano, M. Kawakita, M. Okui, Y. Haino, M. Yoshimura, M. Furuya, and M. Sato, “Integral three-dimensional television using a 33-megapixel imaging system,” J. Disp. Technol.6(10), 422–430 (2010).
[CrossRef]

F. Okano, J. Arai, and M. Kawakita, “Wave optical analysis of integral method for three-dimensional images,” Opt. Lett.32(4), 364–366 (2007).
[CrossRef] [PubMed]

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE94(3), 490–501 (2006).
[CrossRef]

J. Arai, H. Hoshino, M. Okui, and F. Okano, “Effects of focusing on the resolution characteristics of integral photography,” J. Opt. Soc. Am. A20(6), 996–1004 (2003).
[CrossRef] [PubMed]

F. Okano, J. Arai, H. Hoshino, and I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng.38(6), 1072–1077 (1999).
[CrossRef]

J. Arai, F. Okano, H. Hoshino, and I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional images,” Appl. Opt.37(11), 2034–2045 (1998).
[CrossRef] [PubMed]

Barreiro, J. C.

Blanche, P. A.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Burckhardt, C. B.

C. B. Burckhardt, “Optimum parameters and resolution limitation of integral photography,” J. Opt. Soc. Am. A58(1), 71–74 (1968).
[CrossRef]

Chang, Y. C.

C. W. Chen, Y. P. Huang, P. Y. Hsieh, T. H. Jen, Y. C. Chang, Y. R. Su, M. Cho, X. Xiao, and B. Javidi, “Enlarged viewing angle of integral imaging system by liquid crystal prism,” Proc. SID Symp. Dig.44(1), 231–234 (2013).

Chen, C. W.

C. W. Chen, Y. P. Huang, P. Y. Hsieh, T. H. Jen, Y. C. Chang, Y. R. Su, M. Cho, X. Xiao, and B. Javidi, “Enlarged viewing angle of integral imaging system by liquid crystal prism,” Proc. SID Symp. Dig.44(1), 231–234 (2013).

J. Nakamura, T. Takahashi, C. W. Chen, Y. P. Huang, and Y. Takaki, “Analysis of longitudinal viewing freedom of reduced-view super multi-view display and increased longitudinal viewing freedom using eye-tracking technique,” J. Soc. Inf. Disp.20(4), 228–234 (2012).
[CrossRef]

Cho, M.

C. W. Chen, Y. P. Huang, P. Y. Hsieh, T. H. Jen, Y. C. Chang, Y. R. Su, M. Cho, X. Xiao, and B. Javidi, “Enlarged viewing angle of integral imaging system by liquid crystal prism,” Proc. SID Symp. Dig.44(1), 231–234 (2013).

M. Cho and B. Javidi, “Optimization of 3D integral imaging system parameters,” J. Disp. Technol.8(6), 357–360 (2012).
[CrossRef]

M. Cho, M. Daneshpanah, I. Moon, and B. Javidi, “Three-dimensional optical sensing and visualization using integral imaging,” Proc. IEEE99(4), 556–575 (2011).
[CrossRef]

M. Cho and B. Javidi, “Three-dimensional visualization of objects in turbid water using integral imaging,” J. Disp. Technol.6(10), 544–547 (2010).
[CrossRef]

Daneshpanah, M.

D. Shin, M. Daneshpanah, and B. Javidi, “Generalization of three-dimensional N-ocular imaging systems under fixed resource constraints,” Opt. Lett.37(1), 19–21 (2012).
[CrossRef] [PubMed]

M. Cho, M. Daneshpanah, I. Moon, and B. Javidi, “Three-dimensional optical sensing and visualization using integral imaging,” Proc. IEEE99(4), 556–575 (2011).
[CrossRef]

Davies, N.

Deng, H.

C. C. Ji, C. G. Luo, H. Deng, D. H. Li, and Q. H. Wang, “Tilted elemental image array generation method for moiré-reduced computer generated integral imaging display,” Opt. Express21(17), 19816–19824 (2013).
[CrossRef] [PubMed]

C. G. Luo, Q. H. Wang, H. Deng, X. X. Gong, L. Li, and F. N. Wang, “Depth calculation method of integral imaging based on Gaussian beam distribution model,” J. Disp. Technol.8(2), 112–116 (2012).
[CrossRef]

H. Deng, Q. H. Wang, Y. H. Tao, D. H. Li, and F. N. Wang, “Realization of undistorted and orthoscopic integral imaging without black zone in real and virtual fields,” J. Disp. Technol.7(5), 255–258 (2011).
[CrossRef]

Dohi, T.

H. Liao, N. Hata, S. Nakajima, M. Iwahara, I. Sakuma, and T. Dohi, “Surgical navigation by autostereoscopic image overlay of integral videography,” IEEE Trans. Inf. Technol. Biomed.8(2), 114–121 (2004).
[CrossRef] [PubMed]

Flores, D.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Furuya, M.

J. Arai, F. Okano, M. Kawakita, M. Okui, Y. Haino, M. Yoshimura, M. Furuya, and M. Sato, “Integral three-dimensional television using a 33-megapixel imaging system,” J. Disp. Technol.6(10), 422–430 (2010).
[CrossRef]

Gong, X. X.

C. G. Luo, Q. H. Wang, H. Deng, X. X. Gong, L. Li, and F. N. Wang, “Depth calculation method of integral imaging based on Gaussian beam distribution model,” J. Disp. Technol.8(2), 112–116 (2012).
[CrossRef]

Gu, T.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Haino, Y.

J. Arai, F. Okano, M. Kawakita, M. Okui, Y. Haino, M. Yoshimura, M. Furuya, and M. Sato, “Integral three-dimensional television using a 33-megapixel imaging system,” J. Disp. Technol.6(10), 422–430 (2010).
[CrossRef]

Hata, N.

H. Liao, N. Hata, S. Nakajima, M. Iwahara, I. Sakuma, and T. Dohi, “Surgical navigation by autostereoscopic image overlay of integral videography,” IEEE Trans. Inf. Technol. Biomed.8(2), 114–121 (2004).
[CrossRef] [PubMed]

Hong, K.

Hong, S. H.

Hoshino, H.

Hsieh, P. Y.

C. W. Chen, Y. P. Huang, P. Y. Hsieh, T. H. Jen, Y. C. Chang, Y. R. Su, M. Cho, X. Xiao, and B. Javidi, “Enlarged viewing angle of integral imaging system by liquid crystal prism,” Proc. SID Symp. Dig.44(1), 231–234 (2013).

Huang, X.

R. Yang, X. Huang, S. Li, and C. Jaynes, “Toward the light field display: Autostereoscopic rendering via a cluster of projectors,” IEEE Trans. Vis. Comput. Graph.14(1), 84–96 (2008).
[CrossRef] [PubMed]

Huang, Y. P.

C. W. Chen, Y. P. Huang, P. Y. Hsieh, T. H. Jen, Y. C. Chang, Y. R. Su, M. Cho, X. Xiao, and B. Javidi, “Enlarged viewing angle of integral imaging system by liquid crystal prism,” Proc. SID Symp. Dig.44(1), 231–234 (2013).

J. Nakamura, T. Takahashi, C. W. Chen, Y. P. Huang, and Y. Takaki, “Analysis of longitudinal viewing freedom of reduced-view super multi-view display and increased longitudinal viewing freedom using eye-tracking technique,” J. Soc. Inf. Disp.20(4), 228–234 (2012).
[CrossRef]

Igarashi, Y.

Y. Igarashi, H. Murata, and M. Ueda, “3D display system using a computer generated integral photography,” Jpn. J. Appl. Phys.17(9), 1683–1684 (1978).
[CrossRef]

Isono, H.

Ives, H. E.

H. E. Ives, “Optical properties of a Lippman lenticulated sheet,” J. Opt. Soc. Am. A21(3), 171–176 (1931).
[CrossRef]

Iwahara, M.

H. Liao, N. Hata, S. Nakajima, M. Iwahara, I. Sakuma, and T. Dohi, “Surgical navigation by autostereoscopic image overlay of integral videography,” IEEE Trans. Inf. Technol. Biomed.8(2), 114–121 (2004).
[CrossRef] [PubMed]

Jang, J. S.

Javidi, B.

J. Y. Son, W. H. Son, S. K. Kim, K. H. Lee, and B. Javidi, “Three-dimensional imaging for creating real-world-like environments,” Proc. IEEE101(1), 190–205 (2013).
[CrossRef]

C. W. Chen, Y. P. Huang, P. Y. Hsieh, T. H. Jen, Y. C. Chang, Y. R. Su, M. Cho, X. Xiao, and B. Javidi, “Enlarged viewing angle of integral imaging system by liquid crystal prism,” Proc. SID Symp. Dig.44(1), 231–234 (2013).

X. Xiao, B. Javidi, M. Martínez-Corral, and A. Stern, “Advances in three-dimensional integral imaging: sensing, display, and applications,” Appl. Opt.52(4), 546–560 (2013).
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D. Shin, M. Daneshpanah, and B. Javidi, “Generalization of three-dimensional N-ocular imaging systems under fixed resource constraints,” Opt. Lett.37(1), 19–21 (2012).
[CrossRef] [PubMed]

M. Cho and B. Javidi, “Optimization of 3D integral imaging system parameters,” J. Disp. Technol.8(6), 357–360 (2012).
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H. Navarro, J. C. Barreiro, G. Saavedra, M. Martínez-Corral, and B. Javidi, “High-resolution far-field integral-imaging camera by double snapshot,” Opt. Express20(2), 890–895 (2012).
[CrossRef] [PubMed]

M. Cho, M. Daneshpanah, I. Moon, and B. Javidi, “Three-dimensional optical sensing and visualization using integral imaging,” Proc. IEEE99(4), 556–575 (2011).
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D. Aloni, A. Stern, and B. Javidi, “Three-dimensional photon counting integral imaging reconstruction using penalized maximum likelihood expectation maximization,” Opt. Express19(20), 19681–19687 (2011).
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M. Cho and B. Javidi, “Three-dimensional visualization of objects in turbid water using integral imaging,” J. Disp. Technol.6(10), 544–547 (2010).
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R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE97(6), 1067–1077 (2009).
[CrossRef]

R. Martínez-Cuenca, H. Navarro, G. Saavedra, B. Javidi, and M. Martinez-Corral, “Enhanced viewing-angle integral imaging by multiple-axis telecentric relay system,” Opt. Express15(24), 16255–16260 (2007).
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A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE94(3), 591–607 (2006).
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B. Javidi, S. H. Hong, and O. Matoba, “Multidimensional optical sensor and imaging system,” Appl. Opt.45(13), 2986–2994 (2006).
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B. Javidi, I. Moon, and S. Yeom, “Three-dimensional identification of biological microorganism using integral imaging,” Opt. Express14(25), 12096–12108 (2006).
[CrossRef] [PubMed]

R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, and B. Javidi, “Extended depth-of-field 3-D display and visualization by combination of amplitude-modulated microlenses and deconvolution tools,” J. Disp. Technol.1(2), 321–327 (2005).
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J. S. Jang and B. Javidi, “Large depth-of-focus time-multiplexed three-dimensional integral imaging by use of lenslets with nonuniform focal lengths and aperture sizes,” Opt. Lett.28(20), 1924–1926 (2003).
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Jaynes, C.

R. Yang, X. Huang, S. Li, and C. Jaynes, “Toward the light field display: Autostereoscopic rendering via a cluster of projectors,” IEEE Trans. Vis. Comput. Graph.14(1), 84–96 (2008).
[CrossRef] [PubMed]

Jen, T. H.

C. W. Chen, Y. P. Huang, P. Y. Hsieh, T. H. Jen, Y. C. Chang, Y. R. Su, M. Cho, X. Xiao, and B. Javidi, “Enlarged viewing angle of integral imaging system by liquid crystal prism,” Proc. SID Symp. Dig.44(1), 231–234 (2013).

Ji, C. C.

C. C. Ji, C. G. Luo, H. Deng, D. H. Li, and Q. H. Wang, “Tilted elemental image array generation method for moiré-reduced computer generated integral imaging display,” Opt. Express21(17), 19816–19824 (2013).
[CrossRef] [PubMed]

C. G. Luo, C. C. Ji, F. N. Wang, Y. Z. Wang, and Q. H. Wang, “Crosstalk free integral imaging display with wide viewing angle using periodic black mask,” J. Disp. Technol.8(11), 634–638 (2012).
[CrossRef]

Jung, J. H.

Kawakita, M.

J. Arai, F. Okano, M. Kawakita, M. Okui, Y. Haino, M. Yoshimura, M. Furuya, and M. Sato, “Integral three-dimensional television using a 33-megapixel imaging system,” J. Disp. Technol.6(10), 422–430 (2010).
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F. Okano, J. Arai, and M. Kawakita, “Wave optical analysis of integral method for three-dimensional images,” Opt. Lett.32(4), 364–366 (2007).
[CrossRef] [PubMed]

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S. W. Min, J. Kim, and B. Lee, “New characteristic equation of three-dimensional integral imaging system and its applications,” Jpn. J. Appl. Phys.44(2), L71–L74 (2005).
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Kim, S. K.

J. Y. Son, W. H. Son, S. K. Kim, K. H. Lee, and B. Javidi, “Three-dimensional imaging for creating real-world-like environments,” Proc. IEEE101(1), 190–205 (2013).
[CrossRef]

Kim, Y.

Kim, Y. H.

Lee, B.

Lee, K. H.

J. Y. Son, W. H. Son, S. K. Kim, K. H. Lee, and B. Javidi, “Three-dimensional imaging for creating real-world-like environments,” Proc. IEEE101(1), 190–205 (2013).
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Li, D. H.

C. C. Ji, C. G. Luo, H. Deng, D. H. Li, and Q. H. Wang, “Tilted elemental image array generation method for moiré-reduced computer generated integral imaging display,” Opt. Express21(17), 19816–19824 (2013).
[CrossRef] [PubMed]

H. Deng, Q. H. Wang, Y. H. Tao, D. H. Li, and F. N. Wang, “Realization of undistorted and orthoscopic integral imaging without black zone in real and virtual fields,” J. Disp. Technol.7(5), 255–258 (2011).
[CrossRef]

Li, G.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Li, L.

C. G. Luo, Q. H. Wang, H. Deng, X. X. Gong, L. Li, and F. N. Wang, “Depth calculation method of integral imaging based on Gaussian beam distribution model,” J. Disp. Technol.8(2), 112–116 (2012).
[CrossRef]

Li, S.

R. Yang, X. Huang, S. Li, and C. Jaynes, “Toward the light field display: Autostereoscopic rendering via a cluster of projectors,” IEEE Trans. Vis. Comput. Graph.14(1), 84–96 (2008).
[CrossRef] [PubMed]

Liao, H.

H. Liao, N. Hata, S. Nakajima, M. Iwahara, I. Sakuma, and T. Dohi, “Surgical navigation by autostereoscopic image overlay of integral videography,” IEEE Trans. Inf. Technol. Biomed.8(2), 114–121 (2004).
[CrossRef] [PubMed]

Lin, W.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Lippmann, G.

G. Lippmann, “La photographie integrale,” C. R. Acad. Sci.146, 446–451 (1908).

Luo, C. G.

C. C. Ji, C. G. Luo, H. Deng, D. H. Li, and Q. H. Wang, “Tilted elemental image array generation method for moiré-reduced computer generated integral imaging display,” Opt. Express21(17), 19816–19824 (2013).
[CrossRef] [PubMed]

C. G. Luo, C. C. Ji, F. N. Wang, Y. Z. Wang, and Q. H. Wang, “Crosstalk free integral imaging display with wide viewing angle using periodic black mask,” J. Disp. Technol.8(11), 634–638 (2012).
[CrossRef]

C. G. Luo, Q. H. Wang, H. Deng, X. X. Gong, L. Li, and F. N. Wang, “Depth calculation method of integral imaging based on Gaussian beam distribution model,” J. Disp. Technol.8(2), 112–116 (2012).
[CrossRef]

Martinez-Corral, M.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE97(6), 1067–1077 (2009).
[CrossRef]

R. Martínez-Cuenca, H. Navarro, G. Saavedra, B. Javidi, and M. Martinez-Corral, “Enhanced viewing-angle integral imaging by multiple-axis telecentric relay system,” Opt. Express15(24), 16255–16260 (2007).
[CrossRef] [PubMed]

Martínez-Corral, M.

Martinez-Cuenca, R.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE97(6), 1067–1077 (2009).
[CrossRef]

Martínez-Cuenca, R.

R. Martínez-Cuenca, H. Navarro, G. Saavedra, B. Javidi, and M. Martinez-Corral, “Enhanced viewing-angle integral imaging by multiple-axis telecentric relay system,” Opt. Express15(24), 16255–16260 (2007).
[CrossRef] [PubMed]

R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, and B. Javidi, “Extended depth-of-field 3-D display and visualization by combination of amplitude-modulated microlenses and deconvolution tools,” J. Disp. Technol.1(2), 321–327 (2005).
[CrossRef]

Matoba, O.

McCormick, M.

Min, S. W.

G. Park, J. H. Jung, K. Hong, Y. Kim, Y. H. Kim, S. W. Min, and B. Lee, “Multi-viewer tracking integral imaging system and its viewing zone analysis,” Opt. Express17(20), 17895–17908 (2009).
[CrossRef] [PubMed]

S. W. Min, J. Kim, and B. Lee, “New characteristic equation of three-dimensional integral imaging system and its applications,” Jpn. J. Appl. Phys.44(2), L71–L74 (2005).
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T. Mishina, “3D television system based on integral photography,” in Picture Coding Symposium (PCS) (Nagoya, Japan, 2010), p. 20.
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Mitani, K.

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE94(3), 490–501 (2006).
[CrossRef]

Moon, I.

M. Cho, M. Daneshpanah, I. Moon, and B. Javidi, “Three-dimensional optical sensing and visualization using integral imaging,” Proc. IEEE99(4), 556–575 (2011).
[CrossRef]

B. Javidi, I. Moon, and S. Yeom, “Three-dimensional identification of biological microorganism using integral imaging,” Opt. Express14(25), 12096–12108 (2006).
[CrossRef] [PubMed]

Murata, H.

Y. Igarashi, H. Murata, and M. Ueda, “3D display system using a computer generated integral photography,” Jpn. J. Appl. Phys.17(9), 1683–1684 (1978).
[CrossRef]

Nakajima, S.

H. Liao, N. Hata, S. Nakajima, M. Iwahara, I. Sakuma, and T. Dohi, “Surgical navigation by autostereoscopic image overlay of integral videography,” IEEE Trans. Inf. Technol. Biomed.8(2), 114–121 (2004).
[CrossRef] [PubMed]

Nakamura, J.

J. Nakamura, T. Takahashi, C. W. Chen, Y. P. Huang, and Y. Takaki, “Analysis of longitudinal viewing freedom of reduced-view super multi-view display and increased longitudinal viewing freedom using eye-tracking technique,” J. Soc. Inf. Disp.20(4), 228–234 (2012).
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Y. Takaki, K. Tanaka, and J. Nakamura, “Super multi-view display with a lower resolution flat-panel display,” Opt. Express19(5), 4129–4139 (2011).
[CrossRef] [PubMed]

Navarro, H.

Norwood, R. A.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Okano, F.

J. Arai, F. Okano, M. Kawakita, M. Okui, Y. Haino, M. Yoshimura, M. Furuya, and M. Sato, “Integral three-dimensional television using a 33-megapixel imaging system,” J. Disp. Technol.6(10), 422–430 (2010).
[CrossRef]

F. Okano, J. Arai, and M. Kawakita, “Wave optical analysis of integral method for three-dimensional images,” Opt. Lett.32(4), 364–366 (2007).
[CrossRef] [PubMed]

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE94(3), 490–501 (2006).
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J. Arai, H. Hoshino, M. Okui, and F. Okano, “Effects of focusing on the resolution characteristics of integral photography,” J. Opt. Soc. Am. A20(6), 996–1004 (2003).
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J. Arai, F. Okano, H. Hoshino, and I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional images,” Appl. Opt.37(11), 2034–2045 (1998).
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Okui, M.

J. Arai, F. Okano, M. Kawakita, M. Okui, Y. Haino, M. Yoshimura, M. Furuya, and M. Sato, “Integral three-dimensional television using a 33-megapixel imaging system,” J. Disp. Technol.6(10), 422–430 (2010).
[CrossRef]

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE94(3), 490–501 (2006).
[CrossRef]

J. Arai, H. Hoshino, M. Okui, and F. Okano, “Effects of focusing on the resolution characteristics of integral photography,” J. Opt. Soc. Am. A20(6), 996–1004 (2003).
[CrossRef] [PubMed]

Onural, L.

Park, G.

Park, J. H.

Peyghambarian, N.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Rokutanda, S.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Saavedra, G.

H. Navarro, J. C. Barreiro, G. Saavedra, M. Martínez-Corral, and B. Javidi, “High-resolution far-field integral-imaging camera by double snapshot,” Opt. Express20(2), 890–895 (2012).
[CrossRef] [PubMed]

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE97(6), 1067–1077 (2009).
[CrossRef]

R. Martínez-Cuenca, H. Navarro, G. Saavedra, B. Javidi, and M. Martinez-Corral, “Enhanced viewing-angle integral imaging by multiple-axis telecentric relay system,” Opt. Express15(24), 16255–16260 (2007).
[CrossRef] [PubMed]

R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, and B. Javidi, “Extended depth-of-field 3-D display and visualization by combination of amplitude-modulated microlenses and deconvolution tools,” J. Disp. Technol.1(2), 321–327 (2005).
[CrossRef]

Sakuma, I.

H. Liao, N. Hata, S. Nakajima, M. Iwahara, I. Sakuma, and T. Dohi, “Surgical navigation by autostereoscopic image overlay of integral videography,” IEEE Trans. Inf. Technol. Biomed.8(2), 114–121 (2004).
[CrossRef] [PubMed]

Sato, M.

J. Arai, F. Okano, M. Kawakita, M. Okui, Y. Haino, M. Yoshimura, M. Furuya, and M. Sato, “Integral three-dimensional television using a 33-megapixel imaging system,” J. Disp. Technol.6(10), 422–430 (2010).
[CrossRef]

Shin, D.

Son, J. Y.

J. Y. Son, W. H. Son, S. K. Kim, K. H. Lee, and B. Javidi, “Three-dimensional imaging for creating real-world-like environments,” Proc. IEEE101(1), 190–205 (2013).
[CrossRef]

Son, W. H.

J. Y. Son, W. H. Son, S. K. Kim, K. H. Lee, and B. Javidi, “Three-dimensional imaging for creating real-world-like environments,” Proc. IEEE101(1), 190–205 (2013).
[CrossRef]

St Hilaire, P.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Stern, A.

Su, Y. R.

C. W. Chen, Y. P. Huang, P. Y. Hsieh, T. H. Jen, Y. C. Chang, Y. R. Su, M. Cho, X. Xiao, and B. Javidi, “Enlarged viewing angle of integral imaging system by liquid crystal prism,” Proc. SID Symp. Dig.44(1), 231–234 (2013).

Takahashi, T.

J. Nakamura, T. Takahashi, C. W. Chen, Y. P. Huang, and Y. Takaki, “Analysis of longitudinal viewing freedom of reduced-view super multi-view display and increased longitudinal viewing freedom using eye-tracking technique,” J. Soc. Inf. Disp.20(4), 228–234 (2012).
[CrossRef]

Takaki, Y.

J. Nakamura, T. Takahashi, C. W. Chen, Y. P. Huang, and Y. Takaki, “Analysis of longitudinal viewing freedom of reduced-view super multi-view display and increased longitudinal viewing freedom using eye-tracking technique,” J. Soc. Inf. Disp.20(4), 228–234 (2012).
[CrossRef]

Y. Takaki, K. Tanaka, and J. Nakamura, “Super multi-view display with a lower resolution flat-panel display,” Opt. Express19(5), 4129–4139 (2011).
[CrossRef] [PubMed]

Tanaka, K.

Tao, Y. H.

H. Deng, Q. H. Wang, Y. H. Tao, D. H. Li, and F. N. Wang, “Realization of undistorted and orthoscopic integral imaging without black zone in real and virtual fields,” J. Disp. Technol.7(5), 255–258 (2011).
[CrossRef]

Tay, S.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Thomas, J.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Tunç, A. V.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Ueda, M.

Y. Igarashi, H. Murata, and M. Ueda, “3D display system using a computer generated integral photography,” Jpn. J. Appl. Phys.17(9), 1683–1684 (1978).
[CrossRef]

Voorakaranam, R.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Wang, F. N.

C. G. Luo, C. C. Ji, F. N. Wang, Y. Z. Wang, and Q. H. Wang, “Crosstalk free integral imaging display with wide viewing angle using periodic black mask,” J. Disp. Technol.8(11), 634–638 (2012).
[CrossRef]

C. G. Luo, Q. H. Wang, H. Deng, X. X. Gong, L. Li, and F. N. Wang, “Depth calculation method of integral imaging based on Gaussian beam distribution model,” J. Disp. Technol.8(2), 112–116 (2012).
[CrossRef]

H. Deng, Q. H. Wang, Y. H. Tao, D. H. Li, and F. N. Wang, “Realization of undistorted and orthoscopic integral imaging without black zone in real and virtual fields,” J. Disp. Technol.7(5), 255–258 (2011).
[CrossRef]

Wang, P.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Wang, Q. H.

C. C. Ji, C. G. Luo, H. Deng, D. H. Li, and Q. H. Wang, “Tilted elemental image array generation method for moiré-reduced computer generated integral imaging display,” Opt. Express21(17), 19816–19824 (2013).
[CrossRef] [PubMed]

C. G. Luo, C. C. Ji, F. N. Wang, Y. Z. Wang, and Q. H. Wang, “Crosstalk free integral imaging display with wide viewing angle using periodic black mask,” J. Disp. Technol.8(11), 634–638 (2012).
[CrossRef]

C. G. Luo, Q. H. Wang, H. Deng, X. X. Gong, L. Li, and F. N. Wang, “Depth calculation method of integral imaging based on Gaussian beam distribution model,” J. Disp. Technol.8(2), 112–116 (2012).
[CrossRef]

H. Deng, Q. H. Wang, Y. H. Tao, D. H. Li, and F. N. Wang, “Realization of undistorted and orthoscopic integral imaging without black zone in real and virtual fields,” J. Disp. Technol.7(5), 255–258 (2011).
[CrossRef]

Wang, Y. Z.

C. G. Luo, C. C. Ji, F. N. Wang, Y. Z. Wang, and Q. H. Wang, “Crosstalk free integral imaging display with wide viewing angle using periodic black mask,” J. Disp. Technol.8(11), 634–638 (2012).
[CrossRef]

Xiao, X.

C. W. Chen, Y. P. Huang, P. Y. Hsieh, T. H. Jen, Y. C. Chang, Y. R. Su, M. Cho, X. Xiao, and B. Javidi, “Enlarged viewing angle of integral imaging system by liquid crystal prism,” Proc. SID Symp. Dig.44(1), 231–234 (2013).

X. Xiao, B. Javidi, M. Martínez-Corral, and A. Stern, “Advances in three-dimensional integral imaging: sensing, display, and applications,” Appl. Opt.52(4), 546–560 (2013).
[CrossRef] [PubMed]

Yamamoto, M.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Yang, L.

Yang, R.

R. Yang, X. Huang, S. Li, and C. Jaynes, “Toward the light field display: Autostereoscopic rendering via a cluster of projectors,” IEEE Trans. Vis. Comput. Graph.14(1), 84–96 (2008).
[CrossRef] [PubMed]

Yeom, S.

Yöntem, A. Ö.

Yoshimura, M.

J. Arai, F. Okano, M. Kawakita, M. Okui, Y. Haino, M. Yoshimura, M. Furuya, and M. Sato, “Integral three-dimensional television using a 33-megapixel imaging system,” J. Disp. Technol.6(10), 422–430 (2010).
[CrossRef]

Yuyama, I.

Appl. Opt. (5)

C. R. Acad. Sci. (1)

G. Lippmann, “La photographie integrale,” C. R. Acad. Sci.146, 446–451 (1908).

IEEE Trans. Inf. Technol. Biomed. (1)

H. Liao, N. Hata, S. Nakajima, M. Iwahara, I. Sakuma, and T. Dohi, “Surgical navigation by autostereoscopic image overlay of integral videography,” IEEE Trans. Inf. Technol. Biomed.8(2), 114–121 (2004).
[CrossRef] [PubMed]

IEEE Trans. Vis. Comput. Graph. (1)

R. Yang, X. Huang, S. Li, and C. Jaynes, “Toward the light field display: Autostereoscopic rendering via a cluster of projectors,” IEEE Trans. Vis. Comput. Graph.14(1), 84–96 (2008).
[CrossRef] [PubMed]

J. Disp. Technol. (7)

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Figures (7)

Fig. 1
Fig. 1

Number of correspondence pixels to reconstruct image point A in the RPII display.

Fig. 2
Fig. 2

Light intensity distribution of the RPII display.

Fig. 3
Fig. 3

Cross sections and meridian sections (y = 0) of the diffraction intensity patterns on different depth planes (a) z = 20.0mm and (b) z = 26.0mm. Here, f = 4.0mm, g = 5.0mm, p = 0.8mm, λ ¯ = 5 . 5 × 1 0 4 mm, and H × V = 5 × 5.

Fig. 4
Fig. 4

Analysis of DOF of the RPII display based on wave optics taking into account the minimum angular resolution of human eyes.

Fig. 5
Fig. 5

Schematic, not to scale, of the pickup process of RPII conducted in Autodesk 3ds Max 2012. Here, M × N = 110 × 110, f = 3.3mm, and p = 1.0mm.

Fig. 6
Fig. 6

(a) Obtained elemental image array, and (b) experimental setup of the RPII display setup. Here, M × N = 110 × 110, H × V = 9 × 9, f = 3.3mm, p = 1.0mm, g = 3.7mm, and the resolution of each elemental image is 40 × 40 pixels.

Fig. 7
Fig. 7

(a) Different perspectives of the reconstructed 3D image, (b) enlarged view of the center viewpoint, and (c) 2D image of the original 3D“florets” number 4 for reference.

Tables (6)

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Table 1 Parameters used in DOF calculation

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Table 3 Variation of DOFWave with different gap g

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Table 2 Variation of DOFWave with different focal length f

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Table 4 Variation of DOFWave with different MLA pitch p

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Table 5 Parameters used in the pickup and display experiments

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Table 6 DOF calculation results obtained from geometrical optics, Gaussian beam, and wave optics methods

Equations (13)

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DO F Geom =2 l 2 g×p p d ,
DO F Gauss = 2l 4tan ( α e /2 ) 2 d 2 p 2 g 2 +4 p d 2 tan ( α e /2 ) 2 l 4 p 2 l 2 p d 2 | 4tan ( α e /2 ) 2 l 2 gg p 2 | ,
w= f 2| gf | ,
H×V={ ( 2w+1 )×( 2w+1 ) ( 2w+1 )min( M,N ) M×( 2w+1 ) M( 2w+1 )N ( 2w+1 )×N N( 2w+1 )M M×N ( 2w+1 )max( M,N ),
( x mn D , y mn D )=( g f mp, g f np ),
P 00 ( x 0 , y 0 )=rect( x 0 p , y 0 p )={ 1 - p 2 x 0 p 2 ,- p 2 y 0 p 2 0 otherwise .
t mn ( x 0 , y 0 )= P 00 ( x 0 mp, y 0 np )exp{ j k 2f [ ( x 0 mp ) 2 + ( y 0 np ) 2 ] }.
I mn ( x,y;z )=| 1 λ ¯ 2 gz + exp{ j k 2g [ ( x 0 x mn D ) 2 + ( y 0 y mn D ) 2 ] } × t mn ( x 0 , y 0 ) ×exp{ j k 2z [ ( x x 0 ) 2 + ( y y 0 ) 2 ] }d x 0 d y 0 | 2 ,
I( x,y;z )= m=w,n=w m=w,n=w I mn ( x,y;z ) .
-r(z) r(z) I( x,0;z ) dx=0.84 - I( x,0;z ) dx.
x 2 a 2 ( zl ) 2 b 2 =1,
x=±tan( α e 2 )( zld ).
DO F Wave = 2 a 4 b 2 + a 2 b 4 tan ( α e /2 ) 2 + a 2 b 2 d 2 tan ( α e /2 ) 2 | a 2 b 2 tan ( α e /2 ) 2 | .

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