Abstract

The Gerchberg–Saxton (GS) iteration algorithm is widely used for phase-only computer-generated holograms. However, as the GS algorithm was originally developed for single-plane holographic reconstruction, its reconstruction capability for multiple planes is limited. The additive cross-talk between different image planes results in image-quality degradation. In this study, we propose a dynamic compensatory GS algorithm, where the weighting factors of the amplitude-constraining function are dynamically adjusted during each iteration. Both simulation and experimental results prove significant improvement on average image quality of multiple planes.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2015 (2)

2014 (3)

2013 (2)

2011 (3)

2010 (2)

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. Reichelt, R. Häussler, G. Fütterer, and N. Leister, “Depth cues in human visual perception and their realization in 3D displays,” Proc. SPIE 7690(1), 76900B (2010).
[Crossref]

2009 (1)

J. Xia and H. Yin, “Three-dimensional light modulation using phase-only spatial light modulator,” Opt. Eng. 48(2), 020502 (2009).
[Crossref]

2008 (1)

2007 (2)

M. Makowski, M. Sypek, A. Kolodziejczyk, G. Mikuła, and J. Suszek, “Iterative design of multiplane holograms: experiments and applications,” Opt. Eng. 46(4), 045802 (2007).
[Crossref]

Y. Shi, G. Situ, and J. Zhang, “Multiple-image hiding in the Fresnel domain,” Opt. Lett. 32(13), 1914–1916 (2007).
[Crossref] [PubMed]

2006 (1)

J. Liu, A. Caley, and M. Taghizadeh, “Symmetrical iterative Fourier-transform algorithm using both phase and amplitude freedoms,” Opt. Commun. 267(2), 347–355 (2006).
[Crossref]

2005 (1)

M. Makowski, M. Sypek, A. Kolodziejczyk, and G. Mikuła, “Three-plane phase-only computer hologram generated with iterative Fresnel algorithm,” Opt. Eng. 44(12), 125805 (2005).
[Crossref]

2003 (1)

2002 (2)

M. Yang and J. Ding, “Area encoding for design of phase-only computer-generated holograms,” Opt. Commun. 203(1-2), 51–60 (2002).
[Crossref]

J. S. Liu and M. R. Taghizadeh, “Iterative algorithm for the design of diffractive phase elements for laser beam shaping,” Opt. Lett. 27(16), 1463–1465 (2002).
[Crossref] [PubMed]

1997 (1)

T. Haist, M. Schönleber, and H. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140(4-6), 299–308 (1997).
[Crossref]

1984 (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(2), 237–246 (1972).

1969 (1)

L. Lesem, P. Hirsch, and J. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Develop. 13(2), 150–155 (1969).
[Crossref]

Arai, D.

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]

Bartelt, H. O.

Bi, Y.

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]

Caley, A.

J. Liu, A. Caley, and M. Taghizadeh, “Symmetrical iterative Fourier-transform algorithm using both phase and amplitude freedoms,” Opt. Commun. 267(2), 347–355 (2006).
[Crossref]

Chang, C.

Chen, C. P.

X. Li, C. P. Chen, H. Y. Gao, Z. H. He, Y. Xiong, H. J. Li, W. Hu, Z. C. Ye, G. F. He, J. G. Lu, and Y. Su, “Video-Rate Holographic Display Using Azo-Dye-Doped Liquid Crystal,” J. Disp. Technol. 10(6), 438–443 (2014).
[Crossref]

Chen, J.

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]

Ding, J.

M. Yang and J. Ding, “Area encoding for design of phase-only computer-generated holograms,” Opt. Commun. 203(1-2), 51–60 (2002).
[Crossref]

Endo, Y.

Fan, C.

C. Ying, H. Pang, C. Fan, and W. Zhou, “New method for the design of a phase-only computer hologram for multiplane reconstruction,” Opt. Eng. 50(5), 055802 (2011).
[Crossref]

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]

Fütterer, G.

S. Reichelt, R. Häussler, G. Fütterer, and N. Leister, “Depth cues in human visual perception and their realization in 3D displays,” Proc. SPIE 7690(1), 76900B (2010).
[Crossref]

Gao, H. Y.

X. Li, C. P. Chen, H. Y. Gao, Z. H. He, Y. Xiong, H. J. Li, W. Hu, Z. C. Ye, G. F. He, J. G. Lu, and Y. Su, “Video-Rate Holographic Display Using Azo-Dye-Doped Liquid Crystal,” J. Disp. Technol. 10(6), 438–443 (2014).
[Crossref]

Garner, H.

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(2), 237–246 (1972).

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]

Haist, T.

T. Haist, M. Schönleber, and H. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140(4-6), 299–308 (1997).
[Crossref]

Han, J.

Häussler, R.

S. Reichelt, R. Häussler, G. Fütterer, and N. Leister, “Depth cues in human visual perception and their realization in 3D displays,” Proc. SPIE 7690(1), 76900B (2010).
[Crossref]

He, G. F.

X. Li, C. P. Chen, H. Y. Gao, Z. H. He, Y. Xiong, H. J. Li, W. Hu, Z. C. Ye, G. F. He, J. G. Lu, and Y. Su, “Video-Rate Holographic Display Using Azo-Dye-Doped Liquid Crystal,” J. Disp. Technol. 10(6), 438–443 (2014).
[Crossref]

He, Z. H.

X. Li, C. P. Chen, H. Y. Gao, Z. H. He, Y. Xiong, H. J. Li, W. Hu, Z. C. Ye, G. F. He, J. G. Lu, and Y. Su, “Video-Rate Holographic Display Using Azo-Dye-Doped Liquid Crystal,” J. Disp. Technol. 10(6), 438–443 (2014).
[Crossref]

Hirayama, R.

Hirsch, P.

L. Lesem, P. Hirsch, and J. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Develop. 13(2), 150–155 (1969).
[Crossref]

Hiyama, D.

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]

Hu, B.

Hu, W.

X. Li, C. P. Chen, H. Y. Gao, Z. H. He, Y. Xiong, H. J. Li, W. Hu, Z. C. Ye, G. F. He, J. G. Lu, and Y. Su, “Video-Rate Holographic Display Using Azo-Dye-Doped Liquid Crystal,” J. Disp. Technol. 10(6), 438–443 (2014).
[Crossref]

Huebschman, M.

Ito, T.

Jia, J.

Jordan, J.

L. Lesem, P. Hirsch, and J. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Develop. 13(2), 150–155 (1969).
[Crossref]

Kakue, T.

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]

Kolodziejczyk, A.

M. Makowski, M. Sypek, A. Kolodziejczyk, G. Mikuła, and J. Suszek, “Iterative design of multiplane holograms: experiments and applications,” Opt. Eng. 46(4), 045802 (2007).
[Crossref]

M. Makowski, M. Sypek, A. Kolodziejczyk, and G. Mikuła, “Three-plane phase-only computer hologram generated with iterative Fresnel algorithm,” Opt. Eng. 44(12), 125805 (2005).
[Crossref]

Lei, W.

Leister, N.

S. Reichelt, R. Häussler, G. Fütterer, and N. Leister, “Depth cues in human visual perception and their realization in 3D displays,” Proc. SPIE 7690(1), 76900B (2010).
[Crossref]

Lesem, L.

L. Lesem, P. Hirsch, and J. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Develop. 13(2), 150–155 (1969).
[Crossref]

Li, F.

Li, H. J.

X. Li, C. P. Chen, H. Y. Gao, Z. H. He, Y. Xiong, H. J. Li, W. Hu, Z. C. Ye, G. F. He, J. G. Lu, and Y. Su, “Video-Rate Holographic Display Using Azo-Dye-Doped Liquid Crystal,” J. Disp. Technol. 10(6), 438–443 (2014).
[Crossref]

Li, X.

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]

Liu, J.

Liu, J. S.

Lu, J. G.

X. Li, C. P. Chen, H. Y. Gao, Z. H. He, Y. Xiong, H. J. Li, W. Hu, Z. C. Ye, G. F. He, J. G. Lu, and Y. Su, “Video-Rate Holographic Display Using Azo-Dye-Doped Liquid Crystal,” J. Disp. Technol. 10(6), 438–443 (2014).
[Crossref]

Makowski, M.

M. Makowski, M. Sypek, A. Kolodziejczyk, G. Mikuła, and J. Suszek, “Iterative design of multiplane holograms: experiments and applications,” Opt. Eng. 46(4), 045802 (2007).
[Crossref]

M. Makowski, M. Sypek, A. Kolodziejczyk, and G. Mikuła, “Three-plane phase-only computer hologram generated with iterative Fresnel algorithm,” Opt. Eng. 44(12), 125805 (2005).
[Crossref]

Mikula, G.

M. Makowski, M. Sypek, A. Kolodziejczyk, G. Mikuła, and J. Suszek, “Iterative design of multiplane holograms: experiments and applications,” Opt. Eng. 46(4), 045802 (2007).
[Crossref]

M. Makowski, M. Sypek, A. Kolodziejczyk, and G. Mikuła, “Three-plane phase-only computer hologram generated with iterative Fresnel algorithm,” Opt. Eng. 44(12), 125805 (2005).
[Crossref]

Munjuluri, B.

Murano, K.

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]

Pan, Y.

Pang, H.

C. Ying, H. Pang, C. Fan, and W. Zhou, “New method for the design of a phase-only computer hologram for multiplane reconstruction,” Opt. Eng. 50(5), 055802 (2011).
[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]

Qi, Y.

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]

Reichelt, S.

S. Reichelt, R. Häussler, G. Fütterer, and N. Leister, “Depth cues in human visual perception and their realization in 3D displays,” Proc. SPIE 7690(1), 76900B (2010).
[Crossref]

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(2), 237–246 (1972).

Schönleber, M.

T. Haist, M. Schönleber, and H. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140(4-6), 299–308 (1997).
[Crossref]

Shi, Y.

Shimobaba, T.

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]

Situ, G.

Su, Y.

X. Li, C. P. Chen, H. Y. Gao, Z. H. He, Y. Xiong, H. J. Li, W. Hu, Z. C. Ye, G. F. He, J. G. Lu, and Y. Su, “Video-Rate Holographic Display Using Azo-Dye-Doped Liquid Crystal,” J. Disp. Technol. 10(6), 438–443 (2014).
[Crossref]

Sun, M.

Suszek, J.

M. Makowski, M. Sypek, A. Kolodziejczyk, G. Mikuła, and J. Suszek, “Iterative design of multiplane holograms: experiments and applications,” Opt. Eng. 46(4), 045802 (2007).
[Crossref]

Sypek, M.

M. Makowski, M. Sypek, A. Kolodziejczyk, G. Mikuła, and J. Suszek, “Iterative design of multiplane holograms: experiments and applications,” Opt. Eng. 46(4), 045802 (2007).
[Crossref]

M. Makowski, M. Sypek, A. Kolodziejczyk, and G. Mikuła, “Three-plane phase-only computer hologram generated with iterative Fresnel algorithm,” Opt. Eng. 44(12), 125805 (2005).
[Crossref]

Taghizadeh, M.

J. Liu, A. Caley, and M. Taghizadeh, “Symmetrical iterative Fourier-transform algorithm using both phase and amplitude freedoms,” Opt. Commun. 267(2), 347–355 (2006).
[Crossref]

Taghizadeh, M. R.

Takaki, Y.

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]

Tiziani, H.

T. Haist, M. Schönleber, and H. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140(4-6), 299–308 (1997).
[Crossref]

Voorakaranam, R.

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[Crossref]

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Figures (12)

Fig. 1
Fig. 1 Schematic diagram of the conventional GS algorithm.
Fig. 2
Fig. 2 (a) Flowchart of the DCGS method. (b) Schematic diagram of quality compensation.
Fig. 3
Fig. 3 Target image for all image planes.
Fig. 4
Fig. 4 Simulated images with the same content in different planes using (a) the GS algorithm, and (b) DCGS algorithm. Those images from left to right are corresponding to Plane 1, Plane 2… and Plane 8, respectively.
Fig. 5
Fig. 5 Simulated results of gray-level image using (a) the GS algorithm, and (b) DCGS algorithm. Those images from left to right are corresponding to Plane 1, Plane 2… and Plane 8, respectively.
Fig. 6
Fig. 6 Dynamic process about how the quality changes with the weighting factor.
Fig. 7
Fig. 7 Simulated images with different content in different planes, using (a) the GS algorithm, and (b) DCGS algorithm.
Fig. 8
Fig. 8 Reconstruction capacities of the GS, SGS and DCGS algorithms. (a) Average image quality of multiple plane reconstruction, and (b) difference between the minimum and the maximum C qualities.
Fig. 9
Fig. 9 Iteration processes for (a) binary images and (b) gray images, using the GS and DCGS algorithms. The gray level number is 256 in (b).
Fig. 10
Fig. 10 Experimental setup for reproducing the 3D images.
Fig. 11
Fig. 11 Experimentally reconstructed images using (a) the GS, and (b) DCGS algorithms, respectively. Those images from left to right are in Plane 1, Plane 2… and Plane 8, respectively.
Fig. 12
Fig. 12 Experimental reconstruction with different images in different planes, using (a) the GS, and (b) DCGS algorithms, respectively. Those images from left to right are in Plane 1, Plane 2… and Plane 4, respectively.

Equations (8)

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G i = g i exp ( j φ i ) = F r T z i λ ( H i ) ,
G i c o n s t r a i n t = t i exp ( j φ i ) ,
h i exp ( j ϕ i ) = I F r T z i λ ( G i c o n s t r a i n t ) ,
H i + 1 = h 0 exp ( j ϕ i ) ,
G i c o n s t r a i n t = [ α i g i + ( 1 α i ) t i ] exp ( j φ i ) .
C i = m l { [ ( t i ) m l t i ¯ ] [ ( g i ) m l g i ¯ ] } { m l [ ( t i ) m l t i ¯ ] 2 } { m l [ ( g i ) m l g i ¯ ] 2 } , t i ¯ = m l ( t i ) m l M × L , g i ¯ = m l ( g i ) m l M × L ,
α i k+1 = α i k + ( C i k C a v k ) 1000 ,
α i 0 = g i ( m , l ) t i ( m , l )

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