Abstract

Past research has demonstrated that a digital, complex Fresnel hologram can be converted into a phase-only hologram with the use of the bi-direction error diffusion (BERD) algorithm. However, the recursive nature error diffusion process is lengthy and increases monotonically with hologram size. In this paper, we propose a method to overcome this problem. Briefly, each row of a hologram is partitioned into short non-overlapping segments, and a localized error diffusion algorithm is applied to convert the pixels in each segment into phase only values. Subsequently, the error signal is redistributed with low-pass filtering. As the operation on each segment is independent of others, the conversion process can be conducted at high speed with the graphic processing unit. The hologram obtained with the proposed method, known as the Localized Error Diffusion and Redistribution (LERDR) hologram, is over two orders of magnitude faster than that obtained by BERD for a 2048×2048 hologram, exceeding the capability of generating quality phase-only holograms in video rate.

© 2014 Optical Society of America

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References

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  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 (2011).
  2. 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]
  3. 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).
  4. C. K. Hsueh and A. A. Sawchuk, “Computer-generated double-phase holograms,” Appl. Opt. 17(24), 3874–3883 (1978).
    [Crossref] [PubMed]
  5. X. Li, Y. Wang, J. Liu, J. Jia, Y. Pan, and J. Xie, “Color holographic display using a phase-only spatial light modulator” in Dig. Holo. and 3D Img., OSA Technical Digest, OSA, paper DTh2A.3 (2013).
  6. 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]
  7. 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]
  8. 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]
  9. 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).
  10. 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), 120009 (2011).
  11. E. Buckley, “Holographic laser projection technology” Proc. SID Symp., 1074–1078 (2008).
    [Crossref]
  12. 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]
  13. 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]
  14. R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial grey scale,” Proc Soc. Info. Disp. 17, 75–77 (1976).
  15. P. W. Tsang and T.-C. Poon, “Novel method for converting digital Fresnel hologram to phase-only hologram based on bidirectional error diffusion,” Opt. Express 21(20), 23680–23686 (2013).
    [Crossref] [PubMed]

2013 (1)

2012 (2)

2011 (4)

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]

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]

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

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.

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.

Hong, K.

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.

Jaroszewicz, Z.

Jung, J.-H.

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.

Kanbayashi, Y.

Kato, H.

Kim, H.

Kolodziejczyk, A.

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.

Lee, H. S.

Leister, N.

Liu, J.-P.

Makowski, M.

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).

Park, J.-H.

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).

Siemion, A.

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.

Sypek, M.

Tsang, P. W.

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).

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.

Won, K.

Yeom, J.

Appl. Opt. (2)

Chin. Opt. Lett. (2)

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 (2)

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).

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 (3)

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]

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

Supplementary Material (3)

» Media 1: JPG (795 KB)     
» Media 2: JPG (6110 KB)     
» Media 3: JPG (2496 KB)     

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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) Error diffusion from the current pixel to its neighborhood, scanned from right to left.

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Fig. 2
Fig. 2 (a) A segment of M pixels. (b) Error diffusion from a pixel within the first M-1 pixels of a segment, to its neighborhood. (c) Error diffusion from the last pixel in a segment.

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Fig. 3
Fig. 3 (Media 1) (a)-(c) Test images “CTU”, “Lena”, and “Peppers”.

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Fig. 4
Fig. 4 (Media 2) (a)-(c) Reconstructed images of the phase-only holograms derived from the LERD method

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Fig. 5
Fig. 5 (Media 3) (a)-(c) Reconstructed images of the phase-only holograms derived from our proposed LERDR method.

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Tables (1)

Tables Icon

Table 1 Quantitative comparison between the fidelity of the reconstructed images from the phase-only holograms derived from the LERD (Figs. 4(a)-4(c)), the LERDR (Figs. 5(a)-5(c)), and the BERD methods, with reference to the ones obtained from the original complex holograms. The reported values are PSNR values.

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Equations (11)

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| H p ( u , v ) | = 1 , a n d arg ( 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 + 1 , v j − 1 ) ← H ( u j + 1 , v j − 1 ) + w 5 E ( u j , v j ) ,
H ( u j + 1 , v j ) ← H ( u j + 1 , v j ) + w 6 E ( u j , v j ) ,
H ( u j + 1 , v j + 1 ) ← H ( u j + 1 , v j + 1 ) + w 7 E ( u j , v j ) ,
H L ( u , v ) = H p ( u , v ) ∗ G ( u , v ) ,
G ˜ ( ω u , ω v ) = { 1 ω x , ω y ≤ π / 4 0 o t h e r w i s e ,

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