Abstract

If an image is uniformly down-sampled into a sparse form and converted into a hologram, the phase component alone will be adequate to reconstruct the image. However, the appearance of the reconstructed image is degraded with numerous empty holes. In this paper, we present a low complexity and non-iterative solution to this problem. Briefly, two phase-only holograms are generated for an image, each based on a different down-sampling lattice. Subsequently, the holograms are displayed alternately at high frame rate. The reconstructed images of the 2 holograms will appear to be a single, densely sampled image with enhance visual quality.

© 2016 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).
    [Crossref]
  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. 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]
  5. 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]
  6. M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, and A. Kowalczyk, “Performance of the 4k phase-only spatial light modulator in image projection by computer-generated holography,” Photonics Lett. Pol. 8, 1 (2016).
  7. 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]
  8. 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 (2011).
  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 (1972).
  10. J.-P. Liu, S. Y. Wang, P. W. M. Tsang, and T.-C. Poon, “Nonlinearity compensation and complex-to-phase conversion of complex incoherent digital holograms for optical reconstruction,” Opt. Express 24(13), 14582–14588 (2016).
    [Crossref] [PubMed]
  11. 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]
  12. P. W. M. Tsang and T.-C. Poon, “Data-embedded-error-diffusion hologram,” Chin. Opt. Lett. 12, 060017 (2014).
    [Crossref]
  13. P. W. M. 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]
  14. 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]
  15. T. Kozacki and M. Chlipala, “Color holographic display with white light LED source and single phase only SLM,” Opt. Express 24(3), 2189–2199 (2016).
    [Crossref] [PubMed]
  16. I. Naydenova, Advanced Holography – Metrology and Imaging (InTech, 2011), Chap. 13.
  17. M. Makowski, “Minimized speckle noise in lens-less holographic projection by pixel separation,” Opt. Express 21(24), 29205–29216 (2013).
    [Crossref] [PubMed]
  18. P. W. M. Tsang, Y.-T. Chow, and T.-C. Poon, “Generation of phase-only Fresnel hologram based on down-sampling,” Opt. Express 22(21), 25208–25214 (2014).
    [Crossref] [PubMed]
  19. P. W. M. Tsang, Y.-T. Chow, and T.-C. Poon, “Enhancement on the generation of sampled phase-only holograms,” Chin. Opt. Lett. 13, 060901 (2015).
    [Crossref]

2016 (3)

2015 (3)

2014 (2)

2013 (3)

2012 (1)

2011 (3)

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).

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 (1972).

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).

Chang, C.

Chen, J.

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]

Chlipala, M.

Choi, S.

Chow, Y.-T.

Ducin, I.

M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, and A. Kowalczyk, “Performance of the 4k phase-only spatial light modulator in image projection by computer-generated holography,” Photonics Lett. Pol. 8, 1 (2016).

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).
[Crossref]

Endo, Y.

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 (1972).

Hasegawa, S.

Hirayama, R.

Hiyama, D.

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 (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 (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.

Ito, T.

Jaroszewicz, Z.

Jia, J.

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 (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, I. Ducin, K. Kakarenko, J. Suszek, and A. Kowalczyk, “Performance of the 4k phase-only spatial light modulator in image projection by computer-generated holography,” Photonics Lett. Pol. 8, 1 (2016).

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).
[Crossref]

Kakue, T.

Kim, H.

Kolodziejczyk, A.

Kowalczyk, A.

M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, and A. Kowalczyk, “Performance of the 4k phase-only spatial light modulator in image projection by computer-generated holography,” Photonics Lett. Pol. 8, 1 (2016).

Kozacki, T.

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).

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 (2011).

Lee, H. S.

Lei, W.

Li, X.

Liu, J.

Liu, J.-P.

Makowski, M.

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).

Nagahama, Y.

Oikawa, M.

Pan, Y.

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 (2011).

Poon, T.-C.

Sano, M.

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 (1972).

Shimobaba, T.

Siemion, A.

Song, H.

Sugie, T.

Sung, G.

Suszek, J.

M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, and A. Kowalczyk, “Performance of the 4k phase-only spatial light modulator in image projection by computer-generated holography,” Photonics Lett. Pol. 8, 1 (2016).

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).
[Crossref]

Sypek, M.

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).

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, S. Y.

Wang, Y.

Wojnowski, D.

Won, K.

Xia, J.

Yang, L.

Yang, Z.

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 (2011).

Appl. Opt. (2)

Chin. Opt. Lett. (4)

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 (8)

T. Kozacki and M. Chlipala, “Color holographic display with white light LED source and single phase only SLM,” Opt. Express 24(3), 2189–2199 (2016).
[Crossref] [PubMed]

J.-P. Liu, S. Y. Wang, P. W. M. Tsang, and T.-C. Poon, “Nonlinearity compensation and complex-to-phase conversion of complex incoherent digital holograms for optical reconstruction,” Opt. Express 24(13), 14582–14588 (2016).
[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]

P. W. M. Tsang, Y.-T. Chow, and T.-C. Poon, “Generation of phase-only Fresnel hologram based on down-sampling,” Opt. Express 22(21), 25208–25214 (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]

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]

P. W. M. 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]

M. Makowski, “Minimized speckle noise in lens-less holographic projection by pixel separation,” Opt. Express 21(24), 29205–29216 (2013).
[Crossref] [PubMed]

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 (1972).

Photonics Lett. Pol. (1)

M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, and A. Kowalczyk, “Performance of the 4k phase-only spatial light modulator in image projection by computer-generated holography,” Photonics Lett. Pol. 8, 1 (2016).

Other (1)

I. Naydenova, Advanced Holography – Metrology and Imaging (InTech, 2011), Chap. 13.

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Figures (6)

Fig. 1
Fig. 1 Generation of sampled phase-only hologram (SPOH).
Fig. 2
Fig. 2 A small section covering points of the down-sampling lattice.
Fig. 3
Fig. 3 Proposed complementary sampled phase-only hologram for display.
Fig. 4
Fig. 4 (a) A small section of the sampling lattice D2(x,y), (b) Union of the sampling lattices in Figs. 2 and 4(a).
Fig. 5
Fig. 5 (a) Test image “Lena”, (b) Optical setup for displaying the hologram.
Fig. 6
Fig. 6 (a) (b) Optical reconstructed images of the CSPOH derived from the test image down-sampled with D 1 ( x , y ) , and D 2 ( x , y ) , respectively, (c) Optical reconstructed image of the CSPOHs derived from the test image down-sampled with D 1 ( x , y ) and D 2 ( x , y ) , merged with POV, (d) Numerical reconstructed image of a complex-value hologram, generated from the test image that is down-sampled with the union of the down-sampling lattices D 1 ( x , y ) and D 2 ( x , y ) .

Equations (4)

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

I D ( x , y ) = I ( x , y ) if D ( x , y ) = 1 , and 0 otherwise,
H ( u , v ) = x = 0 X 1 y = 0 Y 1 [ I D ( x , y ) exp ( i 2 π w u ; v ; x ; y / λ ) ] / w u ; v ; x ; y ,
| H p ( u , v ) | = 1 , and arg ( H p ( u , v ) ) = arg ( H ( u , v ) ) .
D 2 ( x , y ) = D 1 ( x Δ , y Δ ) .

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