Abstract

An improved method of complex amplitude modulation (CAM) is proposed for color holographic display with a wide viewing angle. Bandlimited random initial phase is introduced to the CAM method, which overcomes the drawbacks brought by a constant initial phase and maintains the advantages of CAM. Modifications in CAM for color display are also explained. Both simulation and experimental results verify that the proposed method can reconstruct color 3D scenes successfully without the time-consuming process for encoding the computer-generated holograms. Compared with the display via traditional CAM, the results exhibit that the proposed method can reconstruct color 3D scenes with a better viewing effect. Because of the display effect improvement and the high calculation speed, this method can be applied to high performance holographic display.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  38. J. Hahn, H. Kim, Y. Lim, G. Park, and B. Lee, “Wide viewing angle dynamic holographic stereogram with a curved array of spatial light modulators,” Opt. Express 16(16), 12372–12386 (2008).
    [Crossref] [PubMed]

2017 (2)

2016 (3)

2015 (4)

2014 (3)

2013 (3)

2012 (2)

2011 (1)

2010 (1)

2009 (1)

2008 (2)

2005 (1)

2004 (2)

V. Bagnoud and J. D. Zuegel, “Independent phase and amplitude control of a laser beam by use of a single-phase-only spatial light modulator,” Opt. Lett. 29(3), 295–297 (2004).
[Crossref] [PubMed]

K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE 5290, 90–97 (2004).
[Crossref]

2000 (1)

1999 (1)

1998 (1)

J.-B. Martens and L. Meesters, “Image dissimilarity,” Signal Process. 70(3), 155–176 (1998).
[Crossref]

1997 (1)

1996 (1)

1994 (1)

1991 (1)

1987 (1)

1986 (1)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[Crossref] [PubMed]

1978 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Akahori, H.

Allebach, J. P.

An, J.

Arrizón, V.

Asundi, A. K.

Bagnoud, V.

Bernet, S.

Birch, P. M.

Bräuer, R.

Bryngdahl, O.

Buckley, E.

Budgett, D.

Campos, J.

Cao, L.

Chang, C.

Chatwin, C.

Chen, J.

Chen, S.

Choi, S.

Cottrell, D. M.

Davis, J. A.

de Bougrenet de la Tocnaye, J. L.

Dong, B. Z.

Duan, J.

Duan, X.

Dupont, L.

Endo, Y.

Ersoy, O. K.

Fienup, J. R.

Fütterer, G.

Gao, H.

Gao, Q.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[Crossref] [PubMed]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Gu, B. Y.

Hahn, J.

Hasegawa, S.

Häussler, R.

Hirayama, R.

Hiyama, D.

Hsieh, W. Y.

Hu, B.

Hwang, C. Y.

Ito, T.

Javidi, B.

Jesacher, A.

Jia, J.

Jiang, W.

Jin, G.

Jung, M.

Kakue, T.

Kanbayashi, Y.

Kato, H.

Kim, H.

Kim, K. S.

Kim, S.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[Crossref] [PubMed]

Kondoh, A.

K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE 5290, 90–97 (2004).
[Crossref]

Kong, D.

Lee, B.

Lee, B. R.

Lee, H. S.

Lee, H.-S.

Lei, W.

Leister, N.

Li, X.

Lim, Y.

Liu, J.

Liu, J. P.

Makowski, M.

Martens, J.-B.

J.-B. Martens and L. Meesters, “Image dissimilarity,” Signal Process. 70(3), 155–176 (1998).
[Crossref]

Matsushima, K.

K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE 5290, 90–97 (2004).
[Crossref]

Maurer, C.

Meesters, L.

J.-B. Martens and L. Meesters, “Image dissimilarity,” Signal Process. 70(3), 155–176 (1998).
[Crossref]

Méndez, G.

Moon, W.

Moreno, I.

Nagahama, Y.

Neto, L. G.

Oh, C. H.

Oh, S.

Oikawa, M.

Pan, Y.

Park, G.

Poon, T. C.

Reichelt, S.

Ritsch-Marte, M.

Roberge, D.

Roh, J.

Sánchez-de-La-Llave, D.

Sano, M.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Schwaighofer, A.

Seldowitz, M. A.

Seo, W.

Sheng, Y.

Shimobaba, T.

Song, H.

Sugie, T.

Sun, Z.

Sung, G.

Sweeney, D. W.

Tan, W.

Tao, S.

Tsang, P.

Ungnapatanin, J.

Usukura, N.

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[Crossref] [PubMed]

Wang, Y.

Wang, Z.

Wojak, U.

Won, K.

Wu, S.

Wu, W.

Wyrowski, F.

Xia, J.

Xie, J.

Xue, G.

Yang, G. Z.

Yang, L.

Yang, Q.

Yang, Z.

Yoon, Y.

Young, R.

Yu, W.

Yu, Y.

Yzuel, M. J.

Zeng, Z.

Zhang, B.

Zhang, H.

Zhang, R.

Zhang, Z.

Zhao, Q.

Zhao, T.

Zhao, Y.

Zheng, H.

Zhuang, J. Y.

Zuegel, J. D.

Appl. Opt. (15)

J. L. de Bougrenet de la Tocnaye and L. Dupont, “Complex amplitude modulation by use of liquid-crystal spatial light modulators,” Appl. Opt. 36(8), 1730–1741 (1997).
[Crossref] [PubMed]

H. Zhang, J. Xie, J. Liu, and Y. Wang, “Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection,” Appl. Opt. 48(30), 5834–5841 (2009).
[Crossref] [PubMed]

G. Z. Yang, B. Z. Dong, B. Y. Gu, J. Y. Zhuang, and O. K. Ersoy, “Gerchberg-Saxton and Yang-Gu algorithms for phase retrieval in a nonunitary transform system: a comparison,” Appl. Opt. 33(2), 209–218 (1994).
[Crossref] [PubMed]

H. Akahori, “Spectrum leveling by an iterative algorithm with a dummy area for synthesizing the kinoform,” Appl. Opt. 25(5), 802–811 (1986).
[Crossref] [PubMed]

M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26(14), 2788–2798 (1987).
[Crossref] [PubMed]

L. G. Neto, D. Roberge, and Y. Sheng, “Full-range, continuous, complex modulation by the use of two coupled-mode liquid-crystal televisions,” Appl. Opt. 35(23), 4567–4576 (1996).
[Crossref] [PubMed]

C. Chang, J. Xia, L. Yang, W. Lei, Z. Yang, and J. Chen, “Speckle-suppressed phase-only holographic three-dimensional display based on double-constraint Gerchberg-Saxton algorithm,” Appl. Opt. 54(23), 6994–7001 (2015).
[Crossref] [PubMed]

D. Kong, L. Cao, G. Jin, and B. Javidi, “Three-dimensional scene encryption and display based on computer-generated holograms,” Appl. Opt. 55(29), 8296–8300 (2016).
[Crossref] [PubMed]

J. P. Liu, W. Y. Hsieh, T. C. Poon, and P. Tsang, “Complex Fresnel hologram display using a single SLM,” Appl. Opt. 50(34), H128–H135 (2011).
[Crossref] [PubMed]

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38(23), 5004–5013 (1999).
[Crossref] [PubMed]

H. Kim, C. Y. Hwang, K. S. Kim, J. Roh, W. Moon, S. Kim, B. R. Lee, S. Oh, and J. Hahn, “Anamorphic optical transformation of an amplitude spatial light modulator to a complex spatial light modulator with square pixels,” Appl. Opt. 53(27), G139–G146 (2014).
[Crossref] [PubMed]

J. Jia, Y. Wang, J. Liu, X. Li, Y. Pan, Z. Sun, B. Zhang, Q. Zhao, and W. Jiang, “Reducing the memory usage for effective computer-generated hologram calculation using compressed look-up table in full-color holographic display,” Appl. Opt. 52(7), 1404–1412 (2013).
[Crossref] [PubMed]

Y. Pan, Y. Wang, J. Liu, X. Li, and J. Jia, “Fast polygon-based method for calculating computer-generated holograms in three-dimensional display,” Appl. Opt. 52(1), A290–A299 (2013).
[Crossref] [PubMed]

Z. Zhang, S. Chen, H. Zheng, Z. Zeng, H. Gao, Y. Yu, and A. K. Asundi, “Full-color holographic 3D display using slice-based fractional Fourier transform combined with free-space Fresnel diffraction,” Appl. Opt. 56(20), 5668–5675 (2017).
[Crossref] [PubMed]

T. Zhao, J. Liu, X. Duan, Q. Gao, J. Duan, X. Li, Y. Wang, W. Wu, and R. Zhang, “Multi-region phase calibration of liquid crystal SLM for holographic display,” Appl. Opt. 56(22), 6168–6174 (2017).
[Crossref] [PubMed]

Chin. Opt. Lett. (2)

Opt. Express (10)

Y. Zhao, L. Cao, H. Zhang, D. Kong, and G. Jin, “Accurate calculation of computer-generated holograms using angular-spectrum layer-oriented method,” Opt. Express 23(20), 25440–25449 (2015).
[Crossref] [PubMed]

T. Shimobaba, T. Kakue, Y. Endo, R. Hirayama, D. Hiyama, S. Hasegawa, Y. Nagahama, M. Sano, M. Oikawa, T. Sugie, and T. Ito, “Random phase-free kinoform for large objects,” Opt. Express 23(13), 17269–17274 (2015).
[Crossref] [PubMed]

S. Choi, J. Roh, H. Song, G. Sung, J. An, W. Seo, K. Won, J. Ungnapatanin, M. Jung, Y. Yoon, H. S. Lee, C. H. Oh, J. Hahn, and H. Kim, “Modulation efficiency of double-phase hologram complex light modulation macro-pixels,” Opt. Express 22(18), 21460–21470 (2014).
[Crossref] [PubMed]

H. Song, G. Sung, S. Choi, K. Won, H.-S. Lee, and H. Kim, “Optimal synthesis of double-phase computer generated holograms using a phase-only spatial light modulator with grating filter,” Opt. Express 20(28), 29844–29853 (2012).
[Crossref] [PubMed]

A. Jesacher, C. Maurer, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Near-perfect hologram reconstruction with a spatial light modulator,” Opt. Express 16(4), 2597–2603 (2008).
[Crossref] [PubMed]

S. Tao and W. Yu, “Beam shaping of complex amplitude with separate constraints on the output beam,” Opt. Express 23(2), 1052–1062 (2015).
[Crossref] [PubMed]

V. Arrizón, G. Méndez, and D. Sánchez-de-La-Llave, “Accurate encoding of arbitrary complex fields with amplitude-only liquid crystal spatial light modulators,” Opt. Express 13(20), 7913–7927 (2005).
[Crossref] [PubMed]

X. Li, J. Liu, J. Jia, Y. Pan, and Y. Wang, “3D dynamic holographic display by modulating complex amplitude experimentally,” Opt. Express 21(18), 20577–20587 (2013).
[Crossref] [PubMed]

G. Xue, J. Liu, X. Li, J. Jia, Z. Zhang, B. Hu, and Y. Wang, “Multiplexing encoding method for full-color dynamic 3D holographic display,” Opt. Express 22(15), 18473–18482 (2014).
[Crossref] [PubMed]

J. Hahn, H. Kim, Y. Lim, G. Park, and B. Lee, “Wide viewing angle dynamic holographic stereogram with a curved array of spatial light modulators,” Opt. Express 16(16), 12372–12386 (2008).
[Crossref] [PubMed]

Opt. Lett. (6)

Optik (Stuttg.) (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Proc. SPIE (1)

K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE 5290, 90–97 (2004).
[Crossref]

Science (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[Crossref] [PubMed]

Signal Process. (1)

J.-B. Martens and L. Meesters, “Image dissimilarity,” Signal Process. 70(3), 155–176 (1998).
[Crossref]

Other (1)

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, 2005).

Supplementary Material (1)

NameDescription
» Visualization 1       Color dynamic holographic display

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Figures (5)

Fig. 1
Fig. 1 The simulation results of 2D scenes, where (a) is the original image, (b), (c) and (d) are reconstructed by method in [19], proposed method, and iteration method (G-S algorithm with 5 loops) respectively.
Fig. 2
Fig. 2 The simulation results of reconstructed 3D scenes by proposed method, where (a) is the scheme of target scene, (b) is focused on the plate of apples while (c) is focused on the chessboard.
Fig. 3
Fig. 3 The schematic of optical experiment. S1, S2 and S3 are shutters, HWP represent half wave plates, Pl are polarizers, BS are beam splitters, Ob is the objective, PH means pin hole, L1, L2 and L3 are lenses, and Ap is an aperture. Objective, pin hole and the collimating lens L1 constitute collimation system to extend the laser beams and collimate it as plane waves. A 4f filter system consist of Fourier lenses L2 and L3 and the aperture for filtering out unwanted orders. A digital camera is applied in the experiment to record the target scene at the view positions P1 and P2.
Fig. 4
Fig. 4 The optical experimental results by the CAM without/with bandlimited random initial phase, where (a), (b), (d) and (e) are captured at P1, while (c) and (f) are recorded at P2. (a), (c), (d) and (f) are focused on the front object, while (b) and (e) are on the rear one.
Fig. 5
Fig. 5 Dynamic display by proposed method (Visualization 1), (a) and (b) are the extracted frames.

Equations (4)

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Φ( x,y )=exp{ jβ O 0 ( x,y )cos[ φ 0 ( x,y ) φ r ( x,y ) ] },
u 1 ( x,y )jβ O 0 ( x,y )exp[ j φ 0 ( x,y ) ].
D max = λ f 3a .
F= F Σ F Φ = F Σ ( u,v ) F Φ ( uξ,vζ )dξdζ = Δ Σv Δ Φv Δ Σv + Δ Φv Δ Σu Δ Φu Δ Σu + Δ Φu F Σ ( u,v ) F Φ ( uξ,vζ )dξdζ ,

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