Abstract

We propose a novel optical method to display a complex Fresnel hologram using a single spatial light modulator (SLM). The method consists of a standard coherent image processing system with a sinusoidal grating at the Fourier plane. Two or three position-shifted amplitude holograms displayed at the input plane of the processing system can be coupled via the grating and will be precisely overlapped at the system’s output plane. As a result, we can synthesize a complex hologram that is free of the twin image and the zero-order light using a single SLM. Because the twin image is not removed via filtering, the full bandwidth of the SLM can be utilized for displaying on-axis holograms. In addition, the degree of freedom of the synthesized complex hologram display can be extended by involving more than three amplitude holograms.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).
  2. E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 1123–1130 (1962).
    [CrossRef]
  3. Y. Takaki and N. Okada, “Hologram generation by horizontal scanning of a high-speed spatial light modulator,” Appl. Opt. 48, 3255–3260 (2009).
    [CrossRef] [PubMed]
  4. Y. Takaki, M. Yokouchi, and N. Okada, “Improvement of grayscale representation of the horizontally scanning holographic display,” Opt. Express 18, 24926–24936 (2010).
    [CrossRef] [PubMed]
  5. R. B. A. Tanjung, X. Xu, X. Liang, S. Solanki, Y. Pan, F. Farbiz, B. Xu, and T.-C. Chong, “Digital holographic three-dimensional display of 50-Mpixel holograms using a two-axis scanning mirror device,” Opt. Eng. 49, 025801 (2010).
    [CrossRef]
  6. 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, 12372–12386(2008).
    [CrossRef] [PubMed]
  7. K. Choi, J. Kim, Y. Lim, and B. Lee, “Full parallax viewing-angle enhanced computer-generated holographic 3D display system using integral lens array,” Opt. Express 13, 10494–10502 (2005).
    [CrossRef] [PubMed]
  8. T. Mishina, F. Okano, and I. Yuyama, “Time-alternating method based on single-sideband holography with half-zone-plate processing for the enlargement of viewing zones,” Appl. Opt. 38, 3703–3713 (1999).
    [CrossRef]
  9. Y. Takaki and Y. Tanemoto, “Band-limited zone plates for single-sideband holography,” Appl. Opt. 48, H64–H70 (2009).
    [CrossRef] [PubMed]
  10. T.-C. Poon, T. Kim, G. Indebetouw, B. W. Schilling, M. H. Wu, K. Shinoda, and Y. Suzuki, “Twin-image elimination experiments for three-dimensional images in optical scanning holography,” Opt. Lett. 25, 215–217 (2000).
    [CrossRef]
  11. B. E. A. Saleh and K. Lu, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
    [CrossRef]
  12. J. A. Coy, M. Zaldarriaga, D. F. Grosz, and O. E. Martinez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
    [CrossRef]
  13. P. Birch, R. Young, C. Chatwin, M. Farsari, D. Budgett, and J. Richardson, “Fully complex optical modulation with an analogue ferroelectric liquid crystal spatial light modulator,” Opt. Commun. 175, 347–352 (2000).
    [CrossRef]
  14. 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, 7913–7927 (2005).
    [CrossRef] [PubMed]
  15. R. W. Cohn and M. Liang, “Pseudorandom phase-only encoding of real-time spatial light modulators,” Appl. Opt. 35, 2488–2498 (1996).
    [CrossRef] [PubMed]
  16. V. Arrizón, “Complex modulation with a twisted-nematic liquid-crystal spatial light modulator: double-pixel approach,” Opt. Lett. 28, 1359–1361 (2003).
    [CrossRef] [PubMed]
  17. V. Arrizón, “Optimum on-axis computer-generated hologram encoded into low-resolution phase-modulation devices,” Opt. Lett. 28, 2521–2523 (2003).
    [CrossRef] [PubMed]
  18. V. Arrizón, L. A. González, R. Ponce, and A. Serrano-Heredia, “Computer-generated holograms with optimum bandwidths obtained with twisted-nematic liquid-crystal displays,” Appl. Opt. 44, 1625–1634 (2005).
    [CrossRef] [PubMed]
  19. E. Buckley, A. Cable, N. Lawrence, and T. Wilkinson, “Viewing angle enhancement for two-and three-dimensional holographic displays with random superresolution phase masks,” Appl. Opt. 45, 7334–7341 (2006).
    [CrossRef] [PubMed]
  20. D. Mendlovic, G. Shabtay, U. Levi, Z. Zalevsky, and E. Marom, “Encoding technique for design of zero-order (on-axis) Fraunhofer computer-generated holograms,” Appl. Opt. 36, 8427–8434 (1997).
    [CrossRef]
  21. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
    [CrossRef]
  22. 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, 4567–4576 (1996).
    [CrossRef] [PubMed]
  23. R. Tudela, I. Labastida, E. Martín-Badosa, S. Vallmitjana, I. Juvells, and A. Carnicer, “A simple method for displaying Fresnel holograms on liquid crystal panels,” Opt. Commun. 214, 107–114 (2002).
    [CrossRef]
  24. 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, 070501 (2007).
    [CrossRef]
  25. 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. A 5, S189–S194 (2003).
    [CrossRef]
  26. T. Ra, M.-B. Estela, L. Ignasi, V. Santiago, and C. Artur, “Wavefront reconstruction by adding modulation capabilities of two liquid crystal devices,” Opt. Eng. 43, 2650–2657 (2004).
    [CrossRef]
  27. S.-G. Kim, B. Lee, and E.-S. Kim, “Removal of bias and the conjugate image in incoherent on-axis triangular holography and real-time reconstruction of the complex hologram,” Appl. Opt. 36, 4784–4791 (1997).
    [CrossRef] [PubMed]
  28. T.-C. Poon, Optical Scanning Holography with MATLAB (Springer, 2007).
    [CrossRef]
  29. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 2005).
  30. P. Tsang, T.-C. Poon, W. K. Cheung, and J.-P. Liu, “Computer generation of binary Fresnel holography,” Appl. Opt. 50, B88–B95 (2011).
    [CrossRef] [PubMed]

2011

2010

Y. Takaki, M. Yokouchi, and N. Okada, “Improvement of grayscale representation of the horizontally scanning holographic display,” Opt. Express 18, 24926–24936 (2010).
[CrossRef] [PubMed]

R. B. A. Tanjung, X. Xu, X. Liang, S. Solanki, Y. Pan, F. Farbiz, B. Xu, and T.-C. Chong, “Digital holographic three-dimensional display of 50-Mpixel holograms using a two-axis scanning mirror device,” Opt. Eng. 49, 025801 (2010).
[CrossRef]

2009

2008

2007

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, 070501 (2007).
[CrossRef]

2006

2005

2004

T. Ra, M.-B. Estela, L. Ignasi, V. Santiago, and C. Artur, “Wavefront reconstruction by adding modulation capabilities of two liquid crystal devices,” Opt. Eng. 43, 2650–2657 (2004).
[CrossRef]

2003

2002

R. Tudela, I. Labastida, E. Martín-Badosa, S. Vallmitjana, I. Juvells, and A. Carnicer, “A simple method for displaying Fresnel holograms on liquid crystal panels,” Opt. Commun. 214, 107–114 (2002).
[CrossRef]

2000

P. Birch, R. Young, C. Chatwin, M. Farsari, D. Budgett, and J. Richardson, “Fully complex optical modulation with an analogue ferroelectric liquid crystal spatial light modulator,” Opt. Commun. 175, 347–352 (2000).
[CrossRef]

T.-C. Poon, T. Kim, G. Indebetouw, B. W. Schilling, M. H. Wu, K. Shinoda, and Y. Suzuki, “Twin-image elimination experiments for three-dimensional images in optical scanning holography,” Opt. Lett. 25, 215–217 (2000).
[CrossRef]

1999

1997

1996

1990

B. E. A. Saleh and K. Lu, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

1962

Arrizón, V.

Artur, C.

T. Ra, M.-B. Estela, L. Ignasi, V. Santiago, and C. Artur, “Wavefront reconstruction by adding modulation capabilities of two liquid crystal devices,” Opt. Eng. 43, 2650–2657 (2004).
[CrossRef]

Birch, P.

P. Birch, R. Young, C. Chatwin, M. Farsari, D. Budgett, and J. Richardson, “Fully complex optical modulation with an analogue ferroelectric liquid crystal spatial light modulator,” Opt. Commun. 175, 347–352 (2000).
[CrossRef]

Buckley, E.

Budgett, D.

P. Birch, R. Young, C. Chatwin, M. Farsari, D. Budgett, and J. Richardson, “Fully complex optical modulation with an analogue ferroelectric liquid crystal spatial light modulator,” Opt. Commun. 175, 347–352 (2000).
[CrossRef]

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

Cable, A.

Campos, J.

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. A 5, S189–S194 (2003).
[CrossRef]

R. Tudela, I. Labastida, E. Martín-Badosa, S. Vallmitjana, I. Juvells, and A. Carnicer, “A simple method for displaying Fresnel holograms on liquid crystal panels,” Opt. Commun. 214, 107–114 (2002).
[CrossRef]

Chatwin, C.

P. Birch, R. Young, C. Chatwin, M. Farsari, D. Budgett, and J. Richardson, “Fully complex optical modulation with an analogue ferroelectric liquid crystal spatial light modulator,” Opt. Commun. 175, 347–352 (2000).
[CrossRef]

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, 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, 070501 (2007).
[CrossRef]

Cheung, W. K.

Choi, K.

Chong, T.-C.

R. B. A. Tanjung, X. Xu, X. Liang, S. Solanki, Y. Pan, F. Farbiz, B. Xu, and T.-C. Chong, “Digital holographic three-dimensional display of 50-Mpixel holograms using a two-axis scanning mirror device,” Opt. Eng. 49, 025801 (2010).
[CrossRef]

Cohn, R. W.

Collier, R. J.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

Cottrell, D. M.

Coy, J. A.

J. A. Coy, M. Zaldarriaga, D. F. Grosz, and O. E. Martinez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
[CrossRef]

Davis, J. A.

Estela, M.-B.

T. Ra, M.-B. Estela, L. Ignasi, V. Santiago, and C. Artur, “Wavefront reconstruction by adding modulation capabilities of two liquid crystal devices,” Opt. Eng. 43, 2650–2657 (2004).
[CrossRef]

Farbiz, F.

R. B. A. Tanjung, X. Xu, X. Liang, S. Solanki, Y. Pan, F. Farbiz, B. Xu, and T.-C. Chong, “Digital holographic three-dimensional display of 50-Mpixel holograms using a two-axis scanning mirror device,” Opt. Eng. 49, 025801 (2010).
[CrossRef]

Farsari, M.

P. Birch, R. Young, C. Chatwin, M. Farsari, D. Budgett, and J. Richardson, “Fully complex optical modulation with an analogue ferroelectric liquid crystal spatial light modulator,” Opt. Commun. 175, 347–352 (2000).
[CrossRef]

González, L. A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 2005).

Grosz, D. F.

J. A. Coy, M. Zaldarriaga, D. F. Grosz, and O. E. Martinez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
[CrossRef]

Hahn, J.

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, 070501 (2007).
[CrossRef]

Ignasi, L.

T. Ra, M.-B. Estela, L. Ignasi, V. Santiago, and C. Artur, “Wavefront reconstruction by adding modulation capabilities of two liquid crystal devices,” Opt. Eng. 43, 2650–2657 (2004).
[CrossRef]

Indebetouw, G.

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. A 5, S189–S194 (2003).
[CrossRef]

R. Tudela, I. Labastida, E. Martín-Badosa, S. Vallmitjana, I. Juvells, and A. Carnicer, “A simple method for displaying Fresnel holograms on liquid crystal panels,” Opt. Commun. 214, 107–114 (2002).
[CrossRef]

Kim, E.-S.

Kim, H.

Kim, J.

Kim, S.-G.

Kim, 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. A 5, S189–S194 (2003).
[CrossRef]

R. Tudela, I. Labastida, E. Martín-Badosa, S. Vallmitjana, I. Juvells, and A. Carnicer, “A simple method for displaying Fresnel holograms on liquid crystal panels,” Opt. Commun. 214, 107–114 (2002).
[CrossRef]

Lawrence, N.

Lee, B.

Leith, E. N.

Levi, U.

Liang, M.

Liang, X.

R. B. A. Tanjung, X. Xu, X. Liang, S. Solanki, Y. Pan, F. Farbiz, B. Xu, and T.-C. Chong, “Digital holographic three-dimensional display of 50-Mpixel holograms using a two-axis scanning mirror device,” Opt. Eng. 49, 025801 (2010).
[CrossRef]

Lim, Y.

Lin, L. H.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

Liu, J.-P.

Lu, K.

B. E. A. Saleh and K. Lu, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

Marom, E.

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. A 5, S189–S194 (2003).
[CrossRef]

R. Tudela, I. Labastida, E. Martín-Badosa, S. Vallmitjana, I. Juvells, and A. Carnicer, “A simple method for displaying Fresnel holograms on liquid crystal panels,” Opt. Commun. 214, 107–114 (2002).
[CrossRef]

Martinez, O. E.

J. A. Coy, M. Zaldarriaga, D. F. Grosz, and O. E. Martinez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
[CrossRef]

Méndez, G.

Mendlovic, D.

Mishina, T.

Moreno, I.

Neto, L. G.

Okada, N.

Okano, F.

Pan, Y.

R. B. A. Tanjung, X. Xu, X. Liang, S. Solanki, Y. Pan, F. Farbiz, B. Xu, and T.-C. Chong, “Digital holographic three-dimensional display of 50-Mpixel holograms using a two-axis scanning mirror device,” Opt. Eng. 49, 025801 (2010).
[CrossRef]

Park, G.

Ponce, R.

Poon, T.-C.

Ra, T.

T. Ra, M.-B. Estela, L. Ignasi, V. Santiago, and C. Artur, “Wavefront reconstruction by adding modulation capabilities of two liquid crystal devices,” Opt. Eng. 43, 2650–2657 (2004).
[CrossRef]

Richardson, J.

P. Birch, R. Young, C. Chatwin, M. Farsari, D. Budgett, and J. Richardson, “Fully complex optical modulation with an analogue ferroelectric liquid crystal spatial light modulator,” Opt. Commun. 175, 347–352 (2000).
[CrossRef]

Roberge, D.

Saleh, B. E. A.

B. E. A. Saleh and K. Lu, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

Sánchez-de-La-Llave, D.

Santiago, V.

T. Ra, M.-B. Estela, L. Ignasi, V. Santiago, and C. Artur, “Wavefront reconstruction by adding modulation capabilities of two liquid crystal devices,” Opt. Eng. 43, 2650–2657 (2004).
[CrossRef]

Schilling, B. W.

Serrano-Heredia, A.

Shabtay, G.

Sheng, Y.

Shinoda, K.

Solanki, S.

R. B. A. Tanjung, X. Xu, X. Liang, S. Solanki, Y. Pan, F. Farbiz, B. Xu, and T.-C. Chong, “Digital holographic three-dimensional display of 50-Mpixel holograms using a two-axis scanning mirror device,” Opt. Eng. 49, 025801 (2010).
[CrossRef]

Suzuki, Y.

Takaki, Y.

Tanemoto, Y.

Tanjung, R. B. A.

R. B. A. Tanjung, X. Xu, X. Liang, S. Solanki, Y. Pan, F. Farbiz, B. Xu, and T.-C. Chong, “Digital holographic three-dimensional display of 50-Mpixel holograms using a two-axis scanning mirror device,” Opt. Eng. 49, 025801 (2010).
[CrossRef]

Tsang, P.

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. A 5, S189–S194 (2003).
[CrossRef]

R. Tudela, I. Labastida, E. Martín-Badosa, S. Vallmitjana, I. Juvells, and A. Carnicer, “A simple method for displaying Fresnel holograms on liquid crystal panels,” Opt. Commun. 214, 107–114 (2002).
[CrossRef]

Upatnieks, J.

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. A 5, S189–S194 (2003).
[CrossRef]

R. Tudela, I. Labastida, E. Martín-Badosa, S. Vallmitjana, I. Juvells, and A. Carnicer, “A simple method for displaying Fresnel holograms on liquid crystal panels,” Opt. Commun. 214, 107–114 (2002).
[CrossRef]

Wilkinson, T.

Wu, M. H.

Xu, B.

R. B. A. Tanjung, X. Xu, X. Liang, S. Solanki, Y. Pan, F. Farbiz, B. Xu, and T.-C. Chong, “Digital holographic three-dimensional display of 50-Mpixel holograms using a two-axis scanning mirror device,” Opt. Eng. 49, 025801 (2010).
[CrossRef]

Xu, X.

R. B. A. Tanjung, X. Xu, X. Liang, S. Solanki, Y. Pan, F. Farbiz, B. Xu, and T.-C. Chong, “Digital holographic three-dimensional display of 50-Mpixel holograms using a two-axis scanning mirror device,” Opt. Eng. 49, 025801 (2010).
[CrossRef]

Yokouchi, M.

Young, R.

P. Birch, R. Young, C. Chatwin, M. Farsari, D. Budgett, and J. Richardson, “Fully complex optical modulation with an analogue ferroelectric liquid crystal spatial light modulator,” Opt. Commun. 175, 347–352 (2000).
[CrossRef]

Yuyama, I.

Yzuel, M. J.

Zaldarriaga, M.

J. A. Coy, M. Zaldarriaga, D. F. Grosz, and O. E. Martinez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
[CrossRef]

Zalevsky, Z.

Appl. Opt.

Y. Takaki and N. Okada, “Hologram generation by horizontal scanning of a high-speed spatial light modulator,” Appl. Opt. 48, 3255–3260 (2009).
[CrossRef] [PubMed]

T. Mishina, F. Okano, and I. Yuyama, “Time-alternating method based on single-sideband holography with half-zone-plate processing for the enlargement of viewing zones,” Appl. Opt. 38, 3703–3713 (1999).
[CrossRef]

Y. Takaki and Y. Tanemoto, “Band-limited zone plates for single-sideband holography,” Appl. Opt. 48, H64–H70 (2009).
[CrossRef] [PubMed]

V. Arrizón, L. A. González, R. Ponce, and A. Serrano-Heredia, “Computer-generated holograms with optimum bandwidths obtained with twisted-nematic liquid-crystal displays,” Appl. Opt. 44, 1625–1634 (2005).
[CrossRef] [PubMed]

E. Buckley, A. Cable, N. Lawrence, and T. Wilkinson, “Viewing angle enhancement for two-and three-dimensional holographic displays with random superresolution phase masks,” Appl. Opt. 45, 7334–7341 (2006).
[CrossRef] [PubMed]

D. Mendlovic, G. Shabtay, U. Levi, Z. Zalevsky, and E. Marom, “Encoding technique for design of zero-order (on-axis) Fraunhofer computer-generated holograms,” Appl. Opt. 36, 8427–8434 (1997).
[CrossRef]

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

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, 4567–4576 (1996).
[CrossRef] [PubMed]

R. W. Cohn and M. Liang, “Pseudorandom phase-only encoding of real-time spatial light modulators,” Appl. Opt. 35, 2488–2498 (1996).
[CrossRef] [PubMed]

S.-G. Kim, B. Lee, and E.-S. Kim, “Removal of bias and the conjugate image in incoherent on-axis triangular holography and real-time reconstruction of the complex hologram,” Appl. Opt. 36, 4784–4791 (1997).
[CrossRef] [PubMed]

P. Tsang, T.-C. Poon, W. K. Cheung, and J.-P. Liu, “Computer generation of binary Fresnel holography,” Appl. Opt. 50, B88–B95 (2011).
[CrossRef] [PubMed]

J. Opt. 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. A 5, S189–S194 (2003).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

R. Tudela, I. Labastida, E. Martín-Badosa, S. Vallmitjana, I. Juvells, and A. Carnicer, “A simple method for displaying Fresnel holograms on liquid crystal panels,” Opt. Commun. 214, 107–114 (2002).
[CrossRef]

P. Birch, R. Young, C. Chatwin, M. Farsari, D. Budgett, and J. Richardson, “Fully complex optical modulation with an analogue ferroelectric liquid crystal spatial light modulator,” Opt. Commun. 175, 347–352 (2000).
[CrossRef]

Opt. Eng.

B. E. A. Saleh and K. Lu, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

J. A. Coy, M. Zaldarriaga, D. F. Grosz, and O. E. Martinez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
[CrossRef]

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, 070501 (2007).
[CrossRef]

R. B. A. Tanjung, X. Xu, X. Liang, S. Solanki, Y. Pan, F. Farbiz, B. Xu, and T.-C. Chong, “Digital holographic three-dimensional display of 50-Mpixel holograms using a two-axis scanning mirror device,” Opt. Eng. 49, 025801 (2010).
[CrossRef]

T. Ra, M.-B. Estela, L. Ignasi, V. Santiago, and C. Artur, “Wavefront reconstruction by adding modulation capabilities of two liquid crystal devices,” Opt. Eng. 43, 2650–2657 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Other

T.-C. Poon, Optical Scanning Holography with MATLAB (Springer, 2007).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 2005).

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Schematic setup of the proposed display system for displaying a complex hologram.

Fig. 2
Fig. 2

(a) Original object pattern, (b) the amplitude hologram H r , (c) intensity of the reconstructed optical field.

Fig. 3
Fig. 3

Modulus of the (a) designed input pattern at SLM and the (b) optical field at the output plane. The central portion of the light, which is marked with a yellow square, is the synthesized complex hologram. (c) Intensity of the reconstructed image at the reconstruction plane.

Fig. 4
Fig. 4

Same as Fig. 3, but in (a) the designed input pattern at SLM contains three amplitude holograms.

Fig. 5
Fig. 5

(a) Binary hologram B r , (b) binary hologram B i , (c) image reconstructed using a single hologram B r , (d) image reconstructed using two binary holograms and the proposed system.

Fig. 6
Fig. 6

RMSE as a function of the reconstruction phase difference between two gray-tone holograms. The horizontal dashed line indicates the RMSE for a single gray-tone hologram.

Fig. 7
Fig. 7

RMSE as a function of the reconstruction phase difference between two binary holograms. The horizontal dashed line indicates the RMSE for a single binary hologram.

Fig. 8
Fig. 8

Photographs of the reconstructed images for (a) hologram B r and the (b) synthesized complex hologram. The original object pattern is the same as Fig. 2a.

Equations (15)

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

H = | O + R | 2 = | O | 2 + | R | 2 + O R * + O * R ,
H cp = O R *
H cp = | H cp | × e i Φ ,
H cp = Re { H cp } + i × Im { H cp } ,
H r = Re { H cp } + I 0 , H i = Im { H cp } + I 0 ,
u ( x 1 , y 1 ) = 1 i λ f 1 F { 1 × t ( x 0 , y 0 ) } f x = x 1 / λ f 1 f y = y 1 / λ f 1 = 1 i λ f 1 T ( f x , f y ) = 1 i λ f 1 T ( x 1 λ f 1 , y 1 λ f 1 ) ,
u 2 ( x 2 , y 2 ) = 1 i λ f 2 F { 1 i λ f 1 T ( x 1 λ f 1 , y 1 λ f 1 ) × [ 1 2 + m 2 cos ( 2 π x 1 Λ ) ] } f x = x 2 / λ f 2 f y = y 2 / λ f 2 ,
u 2 ( x 2 , y 2 ) = 1 M { 1 2 t ( x 2 M , y 2 M ) + m 4 t ( x 2 M + λ f 1 Λ , y 2 M ) + m 4 t ( x 2 M λ f 1 Λ , y 2 M ) } ,
t ( x 0 , y 0 ) = H r ( x 0 d , y 0 ) + H i ( x 0 + d , y 0 ) × e i π / 2 ,
u 2 ( x 2 , y 2 ) = 1 M { 1 2 [ H r ( x 2 M d , y 2 M ) + i × H i ( x 2 M + d , y 2 M ) ] + m 4 [ H r ( x 2 M d + λ f 1 Λ , y 2 M ) + i × H i ( x 2 M + d + λ f 1 Λ , y 2 M ) ] + m 4 [ H r ( x 2 M d λ f 1 Λ , y 2 M ) + i × H i ( x 2 M + d λ f 1 Λ , y 2 M ) ] } .
u 2 ( x 2 , y 2 ) = 1 M { m 4 [ H r ( x 2 M , y 2 M ) + i × H i ( x 2 M , y 2 M ) ] + 1 2 H r ( x 2 M d , y 2 M ) + i 2 × H i ( x 2 M + d , y 2 M ) + m 4 H r ( x 2 M 2 d , y 2 M ) + i m 4 × H i ( x 2 M + 2 d , y 2 M ) } ,
t ( x 0 , y 0 ) = H r ( x 0 d , y 0 ) + H i ( x 0 + d , y 0 ) × e i π / 2 + H d c ( x 0 , y 0 ) × e i 5 π / 4 ,
1 M { m 4 H r ( x 2 M , y 2 M ) + i m 4 H i ( x 2 M , y 2 M ) 1 2 × ( 1 2 + i 2 ) H dc ( x 2 M , y 2 M ) } = m 4 M [ H r ( x 2 M , y 2 M ) + i H i ( x 2 M , y 2 M ) ( 1 + i ) I 0 ] = m 4 M H cp ( x 2 M , y 2 M ) ,
H r = Re { O } + I 0 = Re { u h } + I 0 ,
B r = B 0 { Re { ( u · e i θ ) h } } , B i = B 0 { Im { ( u · e i θ ) h } } ,

Metrics