Abstract

We report a novel and fast method for converting a digital, complex Fresnel hologram into a phase-only hologram. Briefly, the pixels in the complex hologram are scanned sequentially in a row by row manner. The odd and even rows are scanned from opposite directions, constituting to a bidirectional error diffusion process. The magnitude of each visited pixel is forced to be a constant value, while preserving the exact phase value. The resulting error is diffused to the neighboring pixels that have not been visited before. The resulting novel phase-only hologram is called the bidirectional error diffusion (BERD) hologram. The reconstructed image from the BERD hologram exhibits high fidelity as compared with those obtained with the original complex hologram.

© 2013 Optical Society of America

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  1. J. Weng, T. Shimobaba, N. Okada, H. Nakayama, M. Oikawa, N. Masuda, and T. Ito, “Generation of real-time large computer generated hologram using wavefront recording method,” Opt. Express20(4), 4018–4023 (2012).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. M. Makowski, A. Siemion, I. Ducin, K. Kakarenko, M. Sypek, A. Siemion, J. Suszek, D. Wojnowski, Z. Jaroszewicz, and A. Kolodziejczyk, “Complex light modulation for lensless image projection,” Chin. Opt. Lett. 9, 120008-1–120008-3 (2011).
  4. M.-L. Hsieh, M.-L. Chen, and C.-J. Cheng, “Improvement of the complex modulated characteristic of cascaded liquid crystal spatial light modulators by using a novel amplitude compensated technique,” Opt. Eng.46(7), 070501 (2007).
    [CrossRef]
  5. R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt.A5, S189–S194 (2003).
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    [CrossRef] [PubMed]
  7. X. Li, Y. Wang, J. Liu, J. Jia, Y. Pan, and J. Xie, “Color holographic display using a phase-only spatial light modulator,” OSA Technical Digest, paper DTh2A.3 (2013).
  8. S. Reichelt, R. Häussler, G. Fütterer, N. Leister, H. Kato, N. Usukura, and Y. Kanbayashi, “Full-range, complex spatial light modulator for real-time holography,” Opt. Lett.37(11), 1955–1957 (2012).
    [CrossRef] [PubMed]
  9. 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. Express20(28), 29844–29853 (2012).
    [CrossRef] [PubMed]
  10. J.-P. Liu, W. Y. Hsieh, T.-C. Poon, and P. W. M. Tsang, “Complex Fresnel hologram display using a single SLM,” Appl. Opt.50(34), H128–H135 (2011).
    [CrossRef] [PubMed]
  11. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 237–246 (1972).
  12. J. Yeom, J. Hong, J. -H. Jung, K. Hong, J.-H. Park, and B. Lee, “Phase-only hologram generation based on integral imaging and its enhancement in depth resolution,” Chin. Opt. Lett., 9(12), 12009-1–12009-4 (2011).
  13. E. Buckley, “Holographic laser projection technology,” Proc. SID Symp., 1074–1078 (2008).
    [CrossRef]
  14. A. J. Cable, E. Buckley, P. Marsh, N. A. Lawrence, T. D. Wilkinson, and W. A. Crossland, “Real-time binary hologram generation for high-quality video projection applications,” SID International Symposium Digest of Technical Papers, 35,1431–1433 (2004).
    [CrossRef]
  15. E. Buckley, “Real-time error diffusion for signal-to-noise ratio improvement in a holographic projection system,” J. Disp. Tech.7(2), 70–76 (2011).
    [CrossRef]
  16. R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial grey scale,” Proc Soc. Info. Disp.17, 75–77 (1976).

2013 (1)

X. Li, Y. Wang, J. Liu, J. Jia, Y. Pan, and J. Xie, “Color holographic display using a phase-only spatial light modulator,” OSA Technical Digest, paper DTh2A.3 (2013).

2012 (3)

2011 (5)

M. Makowski, A. Siemion, I. Ducin, K. Kakarenko, M. Sypek, A. Siemion, J. Suszek, D. Wojnowski, Z. Jaroszewicz, and A. Kolodziejczyk, “Complex light modulation for lensless image projection,” Chin. Opt. Lett. 9, 120008-1–120008-3 (2011).

J. Yeom, J. Hong, J. -H. Jung, K. Hong, J.-H. Park, and B. Lee, “Phase-only hologram generation based on integral imaging and its enhancement in depth resolution,” Chin. Opt. Lett., 9(12), 12009-1–12009-4 (2011).

E. Buckley, “Real-time error diffusion for signal-to-noise ratio improvement in a holographic projection system,” J. Disp. Tech.7(2), 70–76 (2011).
[CrossRef]

P. Tsang, W. K. Cheung, T.-C. Poon, and C. Zhou, “Holographic video at 40 frames per second for 4-million object points,” Opt. Express19(16), 15205–15211 (2011).
[CrossRef] [PubMed]

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

2007 (1)

M.-L. Hsieh, M.-L. Chen, and C.-J. Cheng, “Improvement of the complex modulated characteristic of cascaded liquid crystal spatial light modulators by using a novel amplitude compensated technique,” Opt. Eng.46(7), 070501 (2007).
[CrossRef]

2003 (1)

R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt.A5, S189–S194 (2003).

1978 (1)

1976 (1)

R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial grey scale,” Proc Soc. Info. Disp.17, 75–77 (1976).

1972 (1)

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

Buckley, E.

E. Buckley, “Real-time error diffusion for signal-to-noise ratio improvement in a holographic projection system,” J. Disp. Tech.7(2), 70–76 (2011).
[CrossRef]

E. Buckley, “Holographic laser projection technology,” Proc. SID Symp., 1074–1078 (2008).
[CrossRef]

A. J. Cable, E. Buckley, P. Marsh, N. A. Lawrence, T. D. Wilkinson, and W. A. Crossland, “Real-time binary hologram generation for high-quality video projection applications,” SID International Symposium Digest of Technical Papers, 35,1431–1433 (2004).
[CrossRef]

Cable, A. J.

A. J. Cable, E. Buckley, P. Marsh, N. A. Lawrence, T. D. Wilkinson, and W. A. Crossland, “Real-time binary hologram generation for high-quality video projection applications,” SID International Symposium Digest of Technical Papers, 35,1431–1433 (2004).
[CrossRef]

Carnicer, A.

R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt.A5, S189–S194 (2003).

Chen, M.-L.

M.-L. Hsieh, M.-L. Chen, and C.-J. Cheng, “Improvement of the complex modulated characteristic of cascaded liquid crystal spatial light modulators by using a novel amplitude compensated technique,” Opt. Eng.46(7), 070501 (2007).
[CrossRef]

Cheng, C.-J.

M.-L. Hsieh, M.-L. Chen, and C.-J. Cheng, “Improvement of the complex modulated characteristic of cascaded liquid crystal spatial light modulators by using a novel amplitude compensated technique,” Opt. Eng.46(7), 070501 (2007).
[CrossRef]

Cheung, W. K.

Choi, S.

Crossland, W. A.

A. J. Cable, E. Buckley, P. Marsh, N. A. Lawrence, T. D. Wilkinson, and W. A. Crossland, “Real-time binary hologram generation for high-quality video projection applications,” SID International Symposium Digest of Technical Papers, 35,1431–1433 (2004).
[CrossRef]

Ducin, I.

M. Makowski, A. Siemion, I. Ducin, K. Kakarenko, M. Sypek, A. Siemion, J. Suszek, D. Wojnowski, Z. Jaroszewicz, and A. Kolodziejczyk, “Complex light modulation for lensless image projection,” Chin. Opt. Lett. 9, 120008-1–120008-3 (2011).

Floyd, R. W.

R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial grey scale,” Proc Soc. Info. Disp.17, 75–77 (1976).

Fütterer, G.

Gerchberg, R. W.

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

Häussler, R.

Hong, J.

J. Yeom, J. Hong, J. -H. Jung, K. Hong, J.-H. Park, and B. Lee, “Phase-only hologram generation based on integral imaging and its enhancement in depth resolution,” Chin. Opt. Lett., 9(12), 12009-1–12009-4 (2011).

Hong, K.

J. Yeom, J. Hong, J. -H. Jung, K. Hong, J.-H. Park, and B. Lee, “Phase-only hologram generation based on integral imaging and its enhancement in depth resolution,” Chin. Opt. Lett., 9(12), 12009-1–12009-4 (2011).

Hsieh, M.-L.

M.-L. Hsieh, M.-L. Chen, and C.-J. Cheng, “Improvement of the complex modulated characteristic of cascaded liquid crystal spatial light modulators by using a novel amplitude compensated technique,” Opt. Eng.46(7), 070501 (2007).
[CrossRef]

Hsieh, W. Y.

Hsueh, C. K.

Ito, T.

Jaroszewicz, Z.

M. Makowski, A. Siemion, I. Ducin, K. Kakarenko, M. Sypek, A. Siemion, J. Suszek, D. Wojnowski, Z. Jaroszewicz, and A. Kolodziejczyk, “Complex light modulation for lensless image projection,” Chin. Opt. Lett. 9, 120008-1–120008-3 (2011).

Jia, J.

X. Li, Y. Wang, J. Liu, J. Jia, Y. Pan, and J. Xie, “Color holographic display using a phase-only spatial light modulator,” OSA Technical Digest, paper DTh2A.3 (2013).

Jung, J. -H.

J. Yeom, J. Hong, J. -H. Jung, K. Hong, J.-H. Park, and B. Lee, “Phase-only hologram generation based on integral imaging and its enhancement in depth resolution,” Chin. Opt. Lett., 9(12), 12009-1–12009-4 (2011).

Juvells, I.

R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt.A5, S189–S194 (2003).

Kakarenko, K.

M. Makowski, A. Siemion, I. Ducin, K. Kakarenko, M. Sypek, A. Siemion, J. Suszek, D. Wojnowski, Z. Jaroszewicz, and A. Kolodziejczyk, “Complex light modulation for lensless image projection,” Chin. Opt. Lett. 9, 120008-1–120008-3 (2011).

Kanbayashi, Y.

Kato, H.

Kim, H.

Kolodziejczyk, A.

M. Makowski, A. Siemion, I. Ducin, K. Kakarenko, M. Sypek, A. Siemion, J. Suszek, D. Wojnowski, Z. Jaroszewicz, and A. Kolodziejczyk, “Complex light modulation for lensless image projection,” Chin. Opt. Lett. 9, 120008-1–120008-3 (2011).

Labastida, I.

R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt.A5, S189–S194 (2003).

Lawrence, N. A.

A. J. Cable, E. Buckley, P. Marsh, N. A. Lawrence, T. D. Wilkinson, and W. A. Crossland, “Real-time binary hologram generation for high-quality video projection applications,” SID International Symposium Digest of Technical Papers, 35,1431–1433 (2004).
[CrossRef]

Lee, B.

J. Yeom, J. Hong, J. -H. Jung, K. Hong, J.-H. Park, and B. Lee, “Phase-only hologram generation based on integral imaging and its enhancement in depth resolution,” Chin. Opt. Lett., 9(12), 12009-1–12009-4 (2011).

Lee, H. S.

Leister, N.

Li, X.

X. Li, Y. Wang, J. Liu, J. Jia, Y. Pan, and J. Xie, “Color holographic display using a phase-only spatial light modulator,” OSA Technical Digest, paper DTh2A.3 (2013).

Liu, J.

X. Li, Y. Wang, J. Liu, J. Jia, Y. Pan, and J. Xie, “Color holographic display using a phase-only spatial light modulator,” OSA Technical Digest, paper DTh2A.3 (2013).

Liu, J.-P.

Makowski, M.

M. Makowski, A. Siemion, I. Ducin, K. Kakarenko, M. Sypek, A. Siemion, J. Suszek, D. Wojnowski, Z. Jaroszewicz, and A. Kolodziejczyk, “Complex light modulation for lensless image projection,” Chin. Opt. Lett. 9, 120008-1–120008-3 (2011).

Marsh, P.

A. J. Cable, E. Buckley, P. Marsh, N. A. Lawrence, T. D. Wilkinson, and W. A. Crossland, “Real-time binary hologram generation for high-quality video projection applications,” SID International Symposium Digest of Technical Papers, 35,1431–1433 (2004).
[CrossRef]

Martín-Badosa, E.

R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt.A5, S189–S194 (2003).

Masuda, N.

Nakayama, H.

Oikawa, M.

Okada, N.

Pan, Y.

X. Li, Y. Wang, J. Liu, J. Jia, Y. Pan, and J. Xie, “Color holographic display using a phase-only spatial light modulator,” OSA Technical Digest, paper DTh2A.3 (2013).

Park, J.-H.

J. Yeom, J. Hong, J. -H. Jung, K. Hong, J.-H. Park, and B. Lee, “Phase-only hologram generation based on integral imaging and its enhancement in depth resolution,” Chin. Opt. Lett., 9(12), 12009-1–12009-4 (2011).

Poon, T.-C.

Reichelt, S.

Sawchuk, A. A.

Saxton, W. O.

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

Shimobaba, T.

Siemion, A.

M. Makowski, A. Siemion, I. Ducin, K. Kakarenko, M. Sypek, A. Siemion, J. Suszek, D. Wojnowski, Z. Jaroszewicz, and A. Kolodziejczyk, “Complex light modulation for lensless image projection,” Chin. Opt. Lett. 9, 120008-1–120008-3 (2011).

M. Makowski, A. Siemion, I. Ducin, K. Kakarenko, M. Sypek, A. Siemion, J. Suszek, D. Wojnowski, Z. Jaroszewicz, and A. Kolodziejczyk, “Complex light modulation for lensless image projection,” Chin. Opt. Lett. 9, 120008-1–120008-3 (2011).

Song, H.

Steinberg, L.

R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial grey scale,” Proc Soc. Info. Disp.17, 75–77 (1976).

Sung, G.

Suszek, J.

M. Makowski, A. Siemion, I. Ducin, K. Kakarenko, M. Sypek, A. Siemion, J. Suszek, D. Wojnowski, Z. Jaroszewicz, and A. Kolodziejczyk, “Complex light modulation for lensless image projection,” Chin. Opt. Lett. 9, 120008-1–120008-3 (2011).

Sypek, M.

M. Makowski, A. Siemion, I. Ducin, K. Kakarenko, M. Sypek, A. Siemion, J. Suszek, D. Wojnowski, Z. Jaroszewicz, and A. Kolodziejczyk, “Complex light modulation for lensless image projection,” Chin. Opt. Lett. 9, 120008-1–120008-3 (2011).

Tsang, P.

Tsang, P. W. M.

Tudela, R.

R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt.A5, S189–S194 (2003).

Usukura, N.

Vallmitjana, S.

R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt.A5, S189–S194 (2003).

Wang, Y.

X. Li, Y. Wang, J. Liu, J. Jia, Y. Pan, and J. Xie, “Color holographic display using a phase-only spatial light modulator,” OSA Technical Digest, paper DTh2A.3 (2013).

Weng, J.

Wilkinson, T. D.

A. J. Cable, E. Buckley, P. Marsh, N. A. Lawrence, T. D. Wilkinson, and W. A. Crossland, “Real-time binary hologram generation for high-quality video projection applications,” SID International Symposium Digest of Technical Papers, 35,1431–1433 (2004).
[CrossRef]

Wojnowski, D.

M. Makowski, A. Siemion, I. Ducin, K. Kakarenko, M. Sypek, A. Siemion, J. Suszek, D. Wojnowski, Z. Jaroszewicz, and A. Kolodziejczyk, “Complex light modulation for lensless image projection,” Chin. Opt. Lett. 9, 120008-1–120008-3 (2011).

Won, K.

Xie, J.

X. Li, Y. Wang, J. Liu, J. Jia, Y. Pan, and J. Xie, “Color holographic display using a phase-only spatial light modulator,” OSA Technical Digest, paper DTh2A.3 (2013).

Yeom, J.

J. Yeom, J. Hong, J. -H. Jung, K. Hong, J.-H. Park, and B. Lee, “Phase-only hologram generation based on integral imaging and its enhancement in depth resolution,” Chin. Opt. Lett., 9(12), 12009-1–12009-4 (2011).

Zhou, C.

Appl. Opt. (2)

Color holographic display using a phase-only spatial light modulator (1)

X. Li, Y. Wang, J. Liu, J. Jia, Y. Pan, and J. Xie, “Color holographic display using a phase-only spatial light modulator,” OSA Technical Digest, paper DTh2A.3 (2013).

Complex light modulation for lensless image projection (1)

M. Makowski, A. Siemion, I. Ducin, K. Kakarenko, M. Sypek, A. Siemion, J. Suszek, D. Wojnowski, Z. Jaroszewicz, and A. Kolodziejczyk, “Complex light modulation for lensless image projection,” Chin. Opt. Lett. 9, 120008-1–120008-3 (2011).

J. Disp. Tech. (1)

E. Buckley, “Real-time error diffusion for signal-to-noise ratio improvement in a holographic projection system,” J. Disp. Tech.7(2), 70–76 (2011).
[CrossRef]

J. Opt. (1)

R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt.A5, S189–S194 (2003).

Opt. Eng. (1)

M.-L. Hsieh, M.-L. Chen, and C.-J. Cheng, “Improvement of the complex modulated characteristic of cascaded liquid crystal spatial light modulators by using a novel amplitude compensated technique,” Opt. Eng.46(7), 070501 (2007).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Optik (Stuttg.) (1)

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

Phase-only hologram generation based on integral imaging and its enhancement in depth resolution (1)

J. Yeom, J. Hong, J. -H. Jung, K. Hong, J.-H. Park, and B. Lee, “Phase-only hologram generation based on integral imaging and its enhancement in depth resolution,” Chin. Opt. Lett., 9(12), 12009-1–12009-4 (2011).

Proc Soc. Info. Disp. (1)

R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial grey scale,” Proc Soc. Info. Disp.17, 75–77 (1976).

Other (2)

E. Buckley, “Holographic laser projection technology,” Proc. SID Symp., 1074–1078 (2008).
[CrossRef]

A. J. Cable, E. Buckley, P. Marsh, N. A. Lawrence, T. D. Wilkinson, and W. A. Crossland, “Real-time binary hologram generation for high-quality video projection applications,” SID International Symposium Digest of Technical Papers, 35,1431–1433 (2004).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Horizontal and vertical axes of the co-ordinate system. (b) Diffusion of the error from the current pixel to its neighborhood, scanned from left to right. (c) An alternative representation of (a), showing the updating of a pixel from its neighborhood. (d) Diffusion of the error from the current pixel to its neighborhood, scanned from right to left.

Fig. 2
Fig. 2

(a)-(c) Test images “CITYU”, “Lena”, and “Mandrill”.

Fig. 3
Fig. 3

(a)-(c) Reconstructed images of the phase-only holograms derived from direct removal of the magnitude component of the complex holograms.

Fig. 4
Fig. 4

(a)-(c) Reconstructed images of the phase-only holograms derived from our proposed unidirectional error diffusion method.

Fig. 5
Fig. 5

(a)-(c) Reconstructed images of the BERD holograms (novel phase-only holograms derived from our proposed bidirectional error diffusion method).

Tables (1)

Tables Icon

Table 1 Quantitative comparison between the fidelity of the reconstructed images as shown in the Figs. 3(a)-3(c), 4(a)-4(c), and 5(a)-5(c) (with reference to the ones obtained from the original complex holograms in Figs. 2(a)-2(c)) from phase-only holograms derived from different means. The reported values are PSNR values.

Equations (12)

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

H( u,v )| 0u<X 0v<Y = x=0 X1 y=0 Y1 I( x,y )exp( i2π r x;y;u;v /λ ) r x;y;u;v ,
| H p ( u,v ) |=1, andarg( H p ( u,v ) )=arg( H( u,v ) ) .
E( u j , v j )=H( u j , v j ) H p ( u j , v j ).
H( u j , v j +1 )H( u j , v j +1 )+ w 1 E( u j , v j ) ,
H( u j +1, v j 1 )H( u j +1, v j 1 )+ w 2 E( u j , v j ) ,
H( u j +1, v j )H( u j +1, v j )+ w 3 E( u j , v j ) ,
H( u j +1, v j +1 )H( u j +1, v j +1 )+ w 4 E( u j , v j ) ,
H( u j , v j )H( u j , v j )+ w 1 E( u j , v j 1 )+ w 4 E( u j 1, v j 1 )+ w 3 E( u j 1, v j )+ w 2 E( u j 1, v j +1 ) ,
H( u j , v j 1 )H( u j , v j 1 )+ w 1 E( u j , v j ) ,
H( u j +1, v j +1 )H( u j +1, v j +1 )+ w 2 E( u j , v j ) ,
H( u j +1, v j )H( u j +1, v j )+ w 3 E( u j , v j ) ,
H( u j +1, v j 1 )H( u j +1, v j 1 )+ w 4 E( u j , v j ) .

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