Abstract

With the principle of ray-tracing and the reversibility of light propagation, a new method of single-step full parallax synthetic holographic stereogram printing based on effective perspective images’ segmentation and mosaicking (EPISM) is proposed. The perspective images of the scene are first sampled by a virtual camera and the exposing images, which are called synthetic effective perspective images, are achieved using the algorithm of effective perspective images’ segmentation and mosaicking according to the propagation law of light and the viewing frustum effect of human eyes. The hogels are exposed using the synthetic effective perspective images in sequence to form the whole holographic stereogram. The influence of modeling parameters on the reconstructed images are also analyzed, and experimental results have demonstrated that the full parallax holographic stereogram printing with the proposed method could provide good reconstructed images by single-step printing. Moreover, detailed experiments with different holographic element sizes, different scene reconstructed distances, and different imaging planes are also analyzed and implemented.

© 2017 Optical Society of America

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References

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2017 (1)

H. Kang, E. Stoykova, N. Berberova, J. Park, D. Nazarova, J. S. Park, Y. Kim, S. Hong, B. Ivanov, and N. Malinowski, “Three-dimensional imaging of cultural heritage artifacts with holographic printers,” Proc. SPIE 10226, 102261I (2017).
[Crossref]

2016 (6)

2014 (4)

A. V. Morozov, A. N. Putilin, S. S. Kopenkin, Y. P. Borodin, V. V. Druzhin, S. E. Dubynin, and G. B. Dubinin, “3D holographic printer: fast printing approach,” Opt. Express 22(3), 2193–2206 (2014).
[Crossref] [PubMed]

C. Pei, X. Yan, and X. Jiang, “Computer-generated phase-modulated full parallax holographic stereograms without conjugate images,” Opt. Eng. 53(10), 103105 (2014).
[Crossref]

H. I. Bjelkhagen and D. Brotherton-Ratcliffe, “Ultrarealistic imaging: the future of display holography,” Opt. Eng. 53(11), 112310 (2014).
[Crossref]

B. Lee, J. -H. Kim, K. Moon, I. -J. Kim, and J. Kim, “Holographic stereogram printing under the non-vibration environment,” Proc. SPIE 9117, 911704 (2014).
[Crossref]

2013 (3)

2012 (2)

F. Yang, Y. Murakami, and M. Yamaguchi, “Digital color management in full-color holographic three-dimensional printer,” Appl. Opt. 51(19), 4343–4352 (2012).
[Crossref] [PubMed]

T. Yamaguchi, O. Miyamoto, and H. Yoshikawa, “Volume hologram printer to record the wavefront of three-dimensional objects,” Opt. Eng. 51(7), 075802 (2012).
[Crossref]

2011 (2)

D. Brotherton-Ratcliffe, S. J. Zacharovas, R. J. Bakanas, J. Pileckas, A. Nikolskij, and J. Kuchin, “Digital holographic printing using pulsed RGB lasers,” Opt. Eng. 50(9), 091307 (2011).
[Crossref]

X. Rong, X. Yu, and C. Guan, “Multichannel holographic recording method for three-dimensional displays,” Appl. Opt. 50(7), B77–B80 (2011).
[Crossref] [PubMed]

2010 (1)

P. -A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. -Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010).
[Crossref] [PubMed]

2008 (3)

H. I. Bjelkhagen and E. Mirlis, “Color holography to produce highly realistic three-dimensional images,” Appl. Opt. 47(4), 123–133 (2008).
[Crossref]

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,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

S. Maruyama, Y. Ono, and M. Yamaguchi, “High-density recording of full-color full-parallax holographic stereogram,” Proc. SPIE 6912, 69120N (2008).
[Crossref]

2003 (1)

M. Takano, H. Shigeta, T. Nishihara, M. Yamaguchi, S. Takahashi, N. Ohyama, A. Kobayashi, and F. Iwata, “Full-color holographic 3D printer,” Proc. SPIE 5005, 126–136 (2003).
[Crossref]

1996 (1)

M. Yamaguchi, H. Endoh, T. Koyama, and N. Ohyama, “High-speed recording of full-parallax holographic stereograms by a parallel exposure system,” Opt. Eng. 35(6), 1556–1559 (1996).
[Crossref]

1994 (2)

M. Yamaguchi, H. Endoh, T. Honda, and N. Ohyama, “High-quality recording of a full-parallax holographic sterogram with a digital diffuser,” Opt. Lett. 19(2), 135–137 (1994).
[Crossref] [PubMed]

M. Yamaguchi, T. Honda, N. Ohyama, and J. Ishikawa, “Multidot recording of rainbow and multicolor holographic stereograms,” Opt. Commun. 110(5–6), 523–528 (1994).
[Crossref]

1992 (1)

1991 (1)

M. W. Halle, “The generalized holographic stereogram,” Proc. SPIE 1461, 142–155 (1991).
[Crossref]

1976 (1)

1970 (1)

1969 (1)

An, J.

Bablumian, A.

P. -A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. -Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010).
[Crossref] [PubMed]

Bakanas, R. J.

D. Brotherton-Ratcliffe, S. J. Zacharovas, R. J. Bakanas, J. Pileckas, A. Nikolskij, and J. Kuchin, “Digital holographic printing using pulsed RGB lasers,” Opt. Eng. 50(9), 091307 (2011).
[Crossref]

Berberova, N.

H. Kang, E. Stoykova, N. Berberova, J. Park, D. Nazarova, J. S. Park, Y. Kim, S. Hong, B. Ivanov, and N. Malinowski, “Three-dimensional imaging of cultural heritage artifacts with holographic printers,” Proc. SPIE 10226, 102261I (2017).
[Crossref]

Berry, D. H.

Bjelkhagen, H. I.

H. I. Bjelkhagen and D. Brotherton-Ratcliffe, “Ultrarealistic imaging: the future of display holography,” Opt. Eng. 53(11), 112310 (2014).
[Crossref]

H. I. Bjelkhagen and E. Mirlis, “Color holography to produce highly realistic three-dimensional images,” Appl. Opt. 47(4), 123–133 (2008).
[Crossref]

Blanche, P. -A.

P. -A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. -Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010).
[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,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Borodin, Y. P.

Brotherton-Ratcliffe, D.

H. I. Bjelkhagen and D. Brotherton-Ratcliffe, “Ultrarealistic imaging: the future of display holography,” Opt. Eng. 53(11), 112310 (2014).
[Crossref]

D. Brotherton-Ratcliffe, S. J. Zacharovas, R. J. Bakanas, J. Pileckas, A. Nikolskij, and J. Kuchin, “Digital holographic printing using pulsed RGB lasers,” Opt. Eng. 50(9), 091307 (2011).
[Crossref]

D. Brotherton-Ratcliffe, “Large format digital colour holograms produced using RGB pulsed laser technology,” in, 7th International Symposium on Display Holography, H. I. Bjelkhagen, ed. (River Valley, 2006), 200–208.

Cao, L.

Chen, N.

Choi, C.

Christenson, C.

P. -A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. -Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010).
[Crossref] [PubMed]

Chung, U.-i.

Debitetto, D. J.

Druzhin, V. V.

Dubinin, G. B.

Dubynin, S. E.

Endoh, H.

M. Yamaguchi, H. Endoh, T. Koyama, and N. Ohyama, “High-speed recording of full-parallax holographic stereograms by a parallel exposure system,” Opt. Eng. 35(6), 1556–1559 (1996).
[Crossref]

M. Yamaguchi, H. Endoh, T. Honda, and N. Ohyama, “High-quality recording of a full-parallax holographic sterogram with a digital diffuser,” Opt. Lett. 19(2), 135–137 (1994).
[Crossref] [PubMed]

Flores, D.

P. -A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. -Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010).
[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,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Fukuzawa, K.

Gu, C.

Gu, T.

P. -A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. -Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010).
[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,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Guan, C.

Hahn, J.

Y. Im, W. Moon, J. Roh, H. Kim, and J. Hahn, “Direct laser writing of computer-generated hologram using pulse laser system,” in Digital Holography and Three-Dimensional Imaging, (Optical Society of America, 2014), paper JTu4A.27.

Halle, M. W.

M. W. Halle, “The generalized holographic stereogram,” Proc. SPIE 1461, 142–155 (1991).
[Crossref]

M. W. Halle, “The generalized holographic stereogram,” Ph. D. thesis, Massachusetts Institute of Technology (1993).

Hilaire, P. St

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,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Honda, T.

Hong, K.

Hong, S.

H. Kang, E. Stoykova, N. Berberova, J. Park, D. Nazarova, J. S. Park, Y. Kim, S. Hong, B. Ivanov, and N. Malinowski, “Three-dimensional imaging of cultural heritage artifacts with holographic printers,” Proc. SPIE 10226, 102261I (2017).
[Crossref]

H. Kang, E. Stoykova, H. Yoshikawa, S. Hong, and Y. Kim, “Comparison of system properties for wave-front holographic printers,” in Fringe 2013, W. Osten, ed. (Springer-Verlag, 2014), 851–854.
[Crossref]

Hsieh, W. -Y.

P. -A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. -Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010).
[Crossref] [PubMed]

Ichihashi, Y.

K. Wakunami, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, and K. Yamamoto, “Wavefront printing technique with overlapping approach toward high definition holographic image reconstruction,” Proc. SPIE 9867, 98670J (2016).

Im, Y.

Y. Im, W. Moon, J. Roh, H. Kim, and J. Hahn, “Direct laser writing of computer-generated hologram using pulse laser system,” in Digital Holography and Three-Dimensional Imaging, (Optical Society of America, 2014), paper JTu4A.27.

Ishikawa, J.

M. Yamaguchi, T. Honda, N. Ohyama, and J. Ishikawa, “Multidot recording of rainbow and multicolor holographic stereograms,” Opt. Commun. 110(5–6), 523–528 (1994).
[Crossref]

Ivanov, B.

H. Kang, E. Stoykova, N. Berberova, J. Park, D. Nazarova, J. S. Park, Y. Kim, S. Hong, B. Ivanov, and N. Malinowski, “Three-dimensional imaging of cultural heritage artifacts with holographic printers,” Proc. SPIE 10226, 102261I (2017).
[Crossref]

Iwata, F.

M. Takano, H. Shigeta, T. Nishihara, M. Yamaguchi, S. Takahashi, N. Ohyama, A. Kobayashi, and F. Iwata, “Full-color holographic 3D printer,” Proc. SPIE 5005, 126–136 (2003).
[Crossref]

Jiang, X.

C. Pei, X. Yan, and X. Jiang, “Computer-generated phase-modulated full parallax holographic stereograms without conjugate images,” Opt. Eng. 53(10), 103105 (2014).
[Crossref]

Jin, G.

Kang, H.

H. Kang, E. Stoykova, N. Berberova, J. Park, D. Nazarova, J. S. Park, Y. Kim, S. Hong, B. Ivanov, and N. Malinowski, “Three-dimensional imaging of cultural heritage artifacts with holographic printers,” Proc. SPIE 10226, 102261I (2017).
[Crossref]

H. Kang, E. Stoykova, and H. Yoshikawa, “Fast phase-added stereogram algorithm for generation of photorealistic 3D content,” Appl. Opt. 55(3), A135–A143 (2016).
[Crossref] [PubMed]

H. Kang, E. Stoykova, H. Yoshikawa, S. Hong, and Y. Kim, “Comparison of system properties for wave-front holographic printers,” in Fringe 2013, W. Osten, ed. (Springer-Verlag, 2014), 851–854.
[Crossref]

Kathaperumal, M.

P. -A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. -Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010).
[Crossref] [PubMed]

Kawabe, Y.

Kim, H.

Y. Im, W. Moon, J. Roh, H. Kim, and J. Hahn, “Direct laser writing of computer-generated hologram using pulse laser system,” in Digital Holography and Three-Dimensional Imaging, (Optical Society of America, 2014), paper JTu4A.27.

Kim, I. -J.

B. Lee, J. -H. Kim, K. Moon, I. -J. Kim, and J. Kim, “Holographic stereogram printing under the non-vibration environment,” Proc. SPIE 9117, 911704 (2014).
[Crossref]

Kim, J.

Kim, J. -H.

B. Lee, J. -H. Kim, K. Moon, I. -J. Kim, and J. Kim, “Holographic stereogram printing under the non-vibration environment,” Proc. SPIE 9117, 911704 (2014).
[Crossref]

Kim, S.

Kim, Y.

H. Kang, E. Stoykova, N. Berberova, J. Park, D. Nazarova, J. S. Park, Y. Kim, S. Hong, B. Ivanov, and N. Malinowski, “Three-dimensional imaging of cultural heritage artifacts with holographic printers,” Proc. SPIE 10226, 102261I (2017).
[Crossref]

H. Kang, E. Stoykova, H. Yoshikawa, S. Hong, and Y. Kim, “Comparison of system properties for wave-front holographic printers,” in Fringe 2013, W. Osten, ed. (Springer-Verlag, 2014), 851–854.
[Crossref]

Kinashi, K.

King, M. C.

Klug, M.

C. Newswanger and M. Klug, “Holograms for the masses,” in 9th International Symposium on Display Holography(ISDH), (IOP Publishing, 2013), 012082.

Kobayashi, A.

M. Takano, H. Shigeta, T. Nishihara, M. Yamaguchi, S. Takahashi, N. Ohyama, A. Kobayashi, and F. Iwata, “Full-color holographic 3D printer,” Proc. SPIE 5005, 126–136 (2003).
[Crossref]

Kopenkin, S. S.

Koyama, T.

M. Yamaguchi, H. Endoh, T. Koyama, and N. Ohyama, “High-speed recording of full-parallax holographic stereograms by a parallel exposure system,” Opt. Eng. 35(6), 1556–1559 (1996).
[Crossref]

Kuchin, J.

D. Brotherton-Ratcliffe, S. J. Zacharovas, R. J. Bakanas, J. Pileckas, A. Nikolskij, and J. Kuchin, “Digital holographic printing using pulsed RGB lasers,” Opt. Eng. 50(9), 091307 (2011).
[Crossref]

Lee, B.

Lee, H. -S.

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,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Lin, W.

P. -A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. -Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010).
[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,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Lucente, M.

M. Lucente, “The first 20 years of holographic video - and the next 20,” in SMPTE 2nd Annual International Conference on Stereoscopic 3D for Media and Entertainment - Society of Motion Picture and Television Engineers(SMPTE), 2011.

Malinowski, N.

H. Kang, E. Stoykova, N. Berberova, J. Park, D. Nazarova, J. S. Park, Y. Kim, S. Hong, B. Ivanov, and N. Malinowski, “Three-dimensional imaging of cultural heritage artifacts with holographic printers,” Proc. SPIE 10226, 102261I (2017).
[Crossref]

Maruyama, S.

S. Maruyama, Y. Ono, and M. Yamaguchi, “High-density recording of full-color full-parallax holographic stereogram,” Proc. SPIE 6912, 69120N (2008).
[Crossref]

Mirlis, E.

H. I. Bjelkhagen and E. Mirlis, “Color holography to produce highly realistic three-dimensional images,” Appl. Opt. 47(4), 123–133 (2008).
[Crossref]

Miyamoto, O.

T. Yamaguchi, O. Miyamoto, and H. Yoshikawa, “Volume hologram printer to record the wavefront of three-dimensional objects,” Opt. Eng. 51(7), 075802 (2012).
[Crossref]

Moon, K.

B. Lee, J. -H. Kim, K. Moon, I. -J. Kim, and J. Kim, “Holographic stereogram printing under the non-vibration environment,” Proc. SPIE 9117, 911704 (2014).
[Crossref]

Moon, W.

Y. Im, W. Moon, J. Roh, H. Kim, and J. Hahn, “Direct laser writing of computer-generated hologram using pulse laser system,” in Digital Holography and Three-Dimensional Imaging, (Optical Society of America, 2014), paper JTu4A.27.

Morozov, A. V.

Murakami, Y.

Nazarova, D.

H. Kang, E. Stoykova, N. Berberova, J. Park, D. Nazarova, J. S. Park, Y. Kim, S. Hong, B. Ivanov, and N. Malinowski, “Three-dimensional imaging of cultural heritage artifacts with holographic printers,” Proc. SPIE 10226, 102261I (2017).
[Crossref]

Newswanger, C.

C. Newswanger and M. Klug, “Holograms for the masses,” in 9th International Symposium on Display Holography(ISDH), (IOP Publishing, 2013), 012082.

Nikolskij, A.

D. Brotherton-Ratcliffe, S. J. Zacharovas, R. J. Bakanas, J. Pileckas, A. Nikolskij, and J. Kuchin, “Digital holographic printing using pulsed RGB lasers,” Opt. Eng. 50(9), 091307 (2011).
[Crossref]

Nishihara, T.

M. Takano, H. Shigeta, T. Nishihara, M. Yamaguchi, S. Takahashi, N. Ohyama, A. Kobayashi, and F. Iwata, “Full-color holographic 3D printer,” Proc. SPIE 5005, 126–136 (2003).
[Crossref]

Noll, A. M.

Norwood, R. A.

P. -A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. -Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010).
[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,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Ohyama, N.

M. Takano, H. Shigeta, T. Nishihara, M. Yamaguchi, S. Takahashi, N. Ohyama, A. Kobayashi, and F. Iwata, “Full-color holographic 3D printer,” Proc. SPIE 5005, 126–136 (2003).
[Crossref]

M. Yamaguchi, H. Endoh, T. Koyama, and N. Ohyama, “High-speed recording of full-parallax holographic stereograms by a parallel exposure system,” Opt. Eng. 35(6), 1556–1559 (1996).
[Crossref]

M. Yamaguchi, T. Honda, N. Ohyama, and J. Ishikawa, “Multidot recording of rainbow and multicolor holographic stereograms,” Opt. Commun. 110(5–6), 523–528 (1994).
[Crossref]

M. Yamaguchi, H. Endoh, T. Honda, and N. Ohyama, “High-quality recording of a full-parallax holographic sterogram with a digital diffuser,” Opt. Lett. 19(2), 135–137 (1994).
[Crossref] [PubMed]

M. Yamaguchi, N. Ohyama, and T. Honda, “Holographic three-dimensional printer: new method,” Appl. Opt. 31(2), 217–222 (1992).
[Crossref] [PubMed]

Oi, R.

K. Wakunami, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, and K. Yamamoto, “Wavefront printing technique with overlapping approach toward high definition holographic image reconstruction,” Proc. SPIE 9867, 98670J (2016).

Ono, Y.

S. Maruyama, Y. Ono, and M. Yamaguchi, “High-density recording of full-color full-parallax holographic stereogram,” Proc. SPIE 6912, 69120N (2008).
[Crossref]

Park, J.

H. Kang, E. Stoykova, N. Berberova, J. Park, D. Nazarova, J. S. Park, Y. Kim, S. Hong, B. Ivanov, and N. Malinowski, “Three-dimensional imaging of cultural heritage artifacts with holographic printers,” Proc. SPIE 10226, 102261I (2017).
[Crossref]

Park, J. S.

H. Kang, E. Stoykova, N. Berberova, J. Park, D. Nazarova, J. S. Park, Y. Kim, S. Hong, B. Ivanov, and N. Malinowski, “Three-dimensional imaging of cultural heritage artifacts with holographic printers,” Proc. SPIE 10226, 102261I (2017).
[Crossref]

Park, S. -g.

Pei, C.

C. Pei, X. Yan, and X. Jiang, “Computer-generated phase-modulated full parallax holographic stereograms without conjugate images,” Opt. Eng. 53(10), 103105 (2014).
[Crossref]

Peyghambarian, N.

P. -A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. -Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010).
[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,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Pileckas, J.

D. Brotherton-Ratcliffe, S. J. Zacharovas, R. J. Bakanas, J. Pileckas, A. Nikolskij, and J. Kuchin, “Digital holographic printing using pulsed RGB lasers,” Opt. Eng. 50(9), 091307 (2011).
[Crossref]

Putilin, A. N.

Pyun, K.

Rachwal, B.

P. -A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. -Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010).
[Crossref] [PubMed]

Roh, J.

Y. Im, W. Moon, J. Roh, H. Kim, and J. Hahn, “Direct laser writing of computer-generated hologram using pulse laser system,” in Digital Holography and Three-Dimensional Imaging, (Optical Society of America, 2014), paper JTu4A.27.

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,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Rong, X.

Sasaki, H.

K. Wakunami, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, and K. Yamamoto, “Wavefront printing technique with overlapping approach toward high definition holographic image reconstruction,” Proc. SPIE 9867, 98670J (2016).

Senoh, T.

K. Wakunami, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, and K. Yamamoto, “Wavefront printing technique with overlapping approach toward high definition holographic image reconstruction,” Proc. SPIE 9867, 98670J (2016).

Shigeta, H.

M. Takano, H. Shigeta, T. Nishihara, M. Yamaguchi, S. Takahashi, N. Ohyama, A. Kobayashi, and F. Iwata, “Full-color holographic 3D printer,” Proc. SPIE 5005, 126–136 (2003).
[Crossref]

Siddiqui, O.

P. -A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. -Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010).
[Crossref] [PubMed]

Stoykova, E.

H. Kang, E. Stoykova, N. Berberova, J. Park, D. Nazarova, J. S. Park, Y. Kim, S. Hong, B. Ivanov, and N. Malinowski, “Three-dimensional imaging of cultural heritage artifacts with holographic printers,” Proc. SPIE 10226, 102261I (2017).
[Crossref]

H. Kang, E. Stoykova, and H. Yoshikawa, “Fast phase-added stereogram algorithm for generation of photorealistic 3D content,” Appl. Opt. 55(3), A135–A143 (2016).
[Crossref] [PubMed]

H. Kang, E. Stoykova, H. Yoshikawa, S. Hong, and Y. Kim, “Comparison of system properties for wave-front holographic printers,” in Fringe 2013, W. Osten, ed. (Springer-Verlag, 2014), 851–854.
[Crossref]

Tada, K.

Taira, K.

Takahashi, S.

M. Takano, H. Shigeta, T. Nishihara, M. Yamaguchi, S. Takahashi, N. Ohyama, A. Kobayashi, and F. Iwata, “Full-color holographic 3D printer,” Proc. SPIE 5005, 126–136 (2003).
[Crossref]

Takaki, Y.

Takano, M.

M. Takano, H. Shigeta, T. Nishihara, M. Yamaguchi, S. Takahashi, N. Ohyama, A. Kobayashi, and F. Iwata, “Full-color holographic 3D printer,” Proc. SPIE 5005, 126–136 (2003).
[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,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Thomas, J.

P. -A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. -Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010).
[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,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Tsutsumi, N.

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,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Utsugi, T.

Voorakaranam, R.

P. -A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. -Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010).
[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,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Wakunami, K.

K. Wakunami, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, and K. Yamamoto, “Wavefront printing technique with overlapping approach toward high definition holographic image reconstruction,” Proc. SPIE 9867, 98670J (2016).

Wang, P.

P. -A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. -Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010).
[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,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Wang, Z.

Yamaguchi, M.

M. Yamaguchi, “Light-field and holographic three-dimensional displays [Invited],” J. Opt. Soc. Am. A 33, (12)2348–2364 (2016).
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T. Utsugi and M. Yamaguchi, “Reduction of the recorded speckle noise in holographic 3D printer,” Opt. Express 21(1), 662–674 (2013).
[Crossref] [PubMed]

F. Yang, Y. Murakami, and M. Yamaguchi, “Digital color management in full-color holographic three-dimensional printer,” Appl. Opt. 51(19), 4343–4352 (2012).
[Crossref] [PubMed]

S. Maruyama, Y. Ono, and M. Yamaguchi, “High-density recording of full-color full-parallax holographic stereogram,” Proc. SPIE 6912, 69120N (2008).
[Crossref]

M. Takano, H. Shigeta, T. Nishihara, M. Yamaguchi, S. Takahashi, N. Ohyama, A. Kobayashi, and F. Iwata, “Full-color holographic 3D printer,” Proc. SPIE 5005, 126–136 (2003).
[Crossref]

M. Yamaguchi, H. Endoh, T. Koyama, and N. Ohyama, “High-speed recording of full-parallax holographic stereograms by a parallel exposure system,” Opt. Eng. 35(6), 1556–1559 (1996).
[Crossref]

M. Yamaguchi, T. Honda, N. Ohyama, and J. Ishikawa, “Multidot recording of rainbow and multicolor holographic stereograms,” Opt. Commun. 110(5–6), 523–528 (1994).
[Crossref]

M. Yamaguchi, H. Endoh, T. Honda, and N. Ohyama, “High-quality recording of a full-parallax holographic sterogram with a digital diffuser,” Opt. Lett. 19(2), 135–137 (1994).
[Crossref] [PubMed]

M. Yamaguchi, N. Ohyama, and T. Honda, “Holographic three-dimensional printer: new method,” Appl. Opt. 31(2), 217–222 (1992).
[Crossref] [PubMed]

Yamaguchi, T.

H. Yoshikawa and T. Yamaguchi, “Review of Holographic Printers for Computer-Generated Holograms,” IEEE T. Ind. Inform. 12(4), 1584–1589 (2016).
[Crossref]

T. Yamaguchi, O. Miyamoto, and H. Yoshikawa, “Volume hologram printer to record the wavefront of three-dimensional objects,” Opt. Eng. 51(7), 075802 (2012).
[Crossref]

Yamamoto, K.

K. Wakunami, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, and K. Yamamoto, “Wavefront printing technique with overlapping approach toward high definition holographic image reconstruction,” Proc. SPIE 9867, 98670J (2016).

Yamamoto, M.

P. -A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. -Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010).
[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,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Yan, X.

C. Pei, X. Yan, and X. Jiang, “Computer-generated phase-modulated full parallax holographic stereograms without conjugate images,” Opt. Eng. 53(10), 103105 (2014).
[Crossref]

Yang, F.

Yatagai, T.

Yeom, J.

Yoshikawa, H.

H. Yoshikawa and T. Yamaguchi, “Review of Holographic Printers for Computer-Generated Holograms,” IEEE T. Ind. Inform. 12(4), 1584–1589 (2016).
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H. Kang, E. Stoykova, and H. Yoshikawa, “Fast phase-added stereogram algorithm for generation of photorealistic 3D content,” Appl. Opt. 55(3), A135–A143 (2016).
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T. Yamaguchi, O. Miyamoto, and H. Yoshikawa, “Volume hologram printer to record the wavefront of three-dimensional objects,” Opt. Eng. 51(7), 075802 (2012).
[Crossref]

H. Kang, E. Stoykova, H. Yoshikawa, S. Hong, and Y. Kim, “Comparison of system properties for wave-front holographic printers,” in Fringe 2013, W. Osten, ed. (Springer-Verlag, 2014), 851–854.
[Crossref]

Yu, X.

Zacharovas, S. J.

D. Brotherton-Ratcliffe, S. J. Zacharovas, R. J. Bakanas, J. Pileckas, A. Nikolskij, and J. Kuchin, “Digital holographic printing using pulsed RGB lasers,” Opt. Eng. 50(9), 091307 (2011).
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Zhang, H.

Appl. Opt. (9)

H. Kang, E. Stoykova, and H. Yoshikawa, “Fast phase-added stereogram algorithm for generation of photorealistic 3D content,” Appl. Opt. 55(3), A135–A143 (2016).
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L. Cao, Z. Wang, H. Zhang, G. Jin, and C. Gu, “Volume holographic printing using unconventional angular multiplexing for three-dimensional display,” Appl. Opt. 55(22), 6046–6051 (2016).
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D. J. Debitetto, “Holographic panoramic stereograms synthesized from white light recordings,” Appl. Opt. 8(8), 1740–1741 (1969).
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M. C. King, A. M. Noll, and D. H. Berry, “A new approach to computer-generated holography,” Appl. Opt. 9(2), 471–475 (1970).
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X. Rong, X. Yu, and C. Guan, “Multichannel holographic recording method for three-dimensional displays,” Appl. Opt. 50(7), B77–B80 (2011).
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H. I. Bjelkhagen and E. Mirlis, “Color holography to produce highly realistic three-dimensional images,” Appl. Opt. 47(4), 123–133 (2008).
[Crossref]

F. Yang, Y. Murakami, and M. Yamaguchi, “Digital color management in full-color holographic three-dimensional printer,” Appl. Opt. 51(19), 4343–4352 (2012).
[Crossref] [PubMed]

M. Yamaguchi, N. Ohyama, and T. Honda, “Holographic three-dimensional printer: new method,” Appl. Opt. 31(2), 217–222 (1992).
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T. Yatagai, “Stereoscopic approach to 3-D display using computer-generated holograms,” Appl. Opt. 15(11), 2722–2729 (1976).
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IEEE T. Ind. Inform. (1)

H. Yoshikawa and T. Yamaguchi, “Review of Holographic Printers for Computer-Generated Holograms,” IEEE T. Ind. Inform. 12(4), 1584–1589 (2016).
[Crossref]

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

Nature (2)

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,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

P. -A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. -Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010).
[Crossref] [PubMed]

Opt. Commun. (1)

M. Yamaguchi, T. Honda, N. Ohyama, and J. Ishikawa, “Multidot recording of rainbow and multicolor holographic stereograms,” Opt. Commun. 110(5–6), 523–528 (1994).
[Crossref]

Opt. Eng. (5)

D. Brotherton-Ratcliffe, S. J. Zacharovas, R. J. Bakanas, J. Pileckas, A. Nikolskij, and J. Kuchin, “Digital holographic printing using pulsed RGB lasers,” Opt. Eng. 50(9), 091307 (2011).
[Crossref]

H. I. Bjelkhagen and D. Brotherton-Ratcliffe, “Ultrarealistic imaging: the future of display holography,” Opt. Eng. 53(11), 112310 (2014).
[Crossref]

C. Pei, X. Yan, and X. Jiang, “Computer-generated phase-modulated full parallax holographic stereograms without conjugate images,” Opt. Eng. 53(10), 103105 (2014).
[Crossref]

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Supplementary Material (3)

NameDescription
» Visualization 1       optical reconstruction from different perspectives
» Visualization 2       the video of motion parallax when the hogel size is 1cm
» Visualization 3       the video of motion parallax when the hogel size is 0.5cm

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Figures (21)

Fig. 1
Fig. 1 The production and reconstruction of two-step method. (a)The production of master hologram. (b)The reconstruction of master hologram. (c)The reproduction of master hologram to transfer hologram. (d)The reconstruction of transfer hologram.
Fig. 2
Fig. 2 The transformation principle of perspective images in infinite viewpoint camera method.
Fig. 3
Fig. 3 Principle of the single-step Lippmann holographic stereogram method. (a) Calculation of an exposing image. (b) Optical setup of the method. (c) Reconstruction geometry for the holographic stereogram.
Fig. 4
Fig. 4 The primitive principle of the proposed method. (a) The extraction of effective perspective image segment corresponding to a single virtual hogel. (b) The synthetic effective perspective image mosaicked by effective images segments of multiple virtual hogels.
Fig. 5
Fig. 5 The principle of effective pixels mosaicking for the hogel(in planar view).
Fig. 6
Fig. 6 The determination of viewing angle.
Fig. 7
Fig. 7 The determination of the number of all the contributed hogels in virtual H1 plate.
Fig. 8
Fig. 8 The one-dimension capture geometry of the perspective images.
Fig. 9
Fig. 9 The corresponding relationship between the hogel in H2 plate and the effective contributed hogels in virtual H1 plate.
Fig. 10
Fig. 10 The diagram of precise algorithm in segmentation and mosaicking of perspective images. (a)The perspective view along the gazing direction. (b)The front view along the gazing direction.
Fig. 11
Fig. 11 The diagram for calculating the flipping of the image.
Fig. 12
Fig. 12 The numerical simulation of perspective images in different viewing positions. (a)The original perspective images. (b)The synthetic effective perspective images.
Fig. 13
Fig. 13 Optical setup of synthetic holographic stereogram printer system.
Fig. 14
Fig. 14 The schematic for reconstruction.
Fig. 15
Fig. 15 The photographs of optical reconstruction from different perspectives(L2 = 11.4 cm, l2 = 1 cm, also seen in Visualization 1).
Fig. 16
Fig. 16 The photographs in different focus depths. (a)The spatial position relation of rulers and holographic plate. (b)Focused on the right ruler. (c)Focused on the left ruler(L2 = 11.4 cm, l2 = 1 cm).
Fig. 17
Fig. 17 The diagram of synthetic effective perspective images scaling
Fig. 18
Fig. 18 The photographs in different focus depths. (a)Focused on the right ruler. (c)Focused on the left ruler(L2 = 8.4 cm, l2 = 0.5 cm).
Fig. 19
Fig. 19 The photographs in different focus depths. (a)Focused on the right ruler. (c)Focused on the left ruler(L2 = 6 cm, l2 = 0.5 cm).
Fig. 20
Fig. 20 The diagram of experimental model with playing cards.
Fig. 21
Fig. 21 The optically reconstructed images with different clearest imaging planes. The clearest imaging plane is (a)the front card, (b)the middle card and (c)the rear card while (d) is the original model.

Equations (26)

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θ = θ = 2 arctan l LCD 2 L 1 .
n hogel = π θ ( L 1 + L 2 ) 360 l 1 1 ,
N H 1 = 2 n hogel + [ l 2 × ( N H 2 1 ) + l 1 ] / l 1 ,
l A B = l B C = l C D = l D A = Z 0 Z 1 Z 0 l 1 .
P ( x P = z 1 z 0 z 0 ( x 0 2 n l 1 l 1 2 ) + x 0 , y P = z 1 z 0 z 0 ( y 0 2 m l 1 l 1 2 ) + y 0 , z P = z 1 ) .
x A = x P l LCD 2 = 2 n l 1 l 1 l LCD 2 .
x A = x P l A B 2 = z 1 z 0 ( x 0 n l 1 + l 1 ) + n l 1 l 1 ,
y A = y P l A B 2 = z 1 z 0 ( y 0 m l 1 + l 1 ) + m l 1 l 1 .
l x A A = | x A x A | = | z 1 z 0 ( x 0 n l 1 + l 1 ) l 1 2 + l LCD 2 | .
l y A A = | z 1 z 0 ( y 0 m l 1 + l 1 ) l 1 2 + l LCD 2 | .
A ( | z 1 z 0 ( x 0 n l 1 + l 1 ) l 1 2 + l LCD 2 | × N l LCD + 1 , | z 1 z 0 ( y 0 m l 1 + l 1 ) l 1 2 + l LCD 2 | × N l LCD + 1 ) ,
B ( | z 1 z 0 ( x 0 n l 1 + l 1 ) l 1 2 + l LCD 2 | × N l LCD + z 0 z 1 z 0 × N l 1 l LCD , | z 1 z 0 ( y 0 m l 1 + l 1 ) l 1 2 + l LCD 2 | × N l LCD + 1 ) ,
C ( | z 1 z 0 ( x 0 n l 1 + l 1 ) l 1 2 + l LCD 2 | × N l LCD + z 0 z 1 z 0 × N l 1 l LCD , | z 1 z 0 ( y 0 m l 1 + l 1 ) l 2 + l LCD 2 | × N l LCD + z 0 z 1 z 0 × N l 1 l LCD ) ,
D ( | z 1 z 0 ( x 0 n l 1 + l 1 ) l 1 2 + l LCD 2 | × N l LCD + 1 , | z 1 z 0 ( y 0 m l 1 + l 1 ) l 1 2 + l LCD 2 | × N l LCD + z 0 z 1 z 0 × N l 1 l LCD ) .
δ = L d l L + L d .
| δ | β ,
β = 1.22 λ L α .
1.22 λ L 2 l α + 1.22 λ L L d 1.22 λ L 2 l α 1.22 λ L .
Δ L = 1.22 λ L 2 l α 1.22 λ L + 1.22 λ L 2 l α 1.22 λ L .
Δ L 2.44 λ L 2 l α = { 2.44 λ L 2 l α , when a l 2.44 λ L 2 l 2 , when a > l .
l eff = L 2 L 1 + L 2 × l 1 .
N eff = l eff × N uni .
M = N eff × ( 2 n hogel + 1 ) .
M = N uni × ( 2 n hogel + 1 ) × l 1 × L 2 L 1 + L 2 .
2 L 1 × tan θ 2 + L H 1 l 1 > L O ,
L H 1 = 2 ( L 1 + L 2 ) × t a n θ 2 + L H 2 l 2 ,

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