Abstract

The conjugate image and zero-order beam have considerable influences on the optical reconstructions in computer-generated holographic display systems based on the amplitude spatial light modulators. We propose a generalized single-sideband method for suppressing the unwanted terms in computer-generated holography. Computer-generated holograms (CGHs) are calculated based on frequency filtering of the object wave, which redistributes the diffraction wave in spatial frequency domain for spectrum filtering during optical reconstruction. Numerical simulations and optical experiments demonstrate that the proposed method is generally effective for different kinds of CGH algorithms to reconstruct quality three-dimensional scenes that are free of conjugate image and zero-order beam.

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

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References

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  1. S. A. Benton and V. M. Bove, Holographic imaging (John Wiley & Sons, 2008).
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    [Crossref]
  3. F. Yaras, H. Kang, and L. Onural, “State of the Art in Holographic Displays: A Survey,” J. Disp. Technol. 6(10), 443–454 (2010).
    [Crossref]
  4. Y. Takaki and K. Fujii, “Viewing-zone scanning holographic display using a MEMS spatial light modulator,” Opt. Express 22(20), 24713–24721 (2014).
    [Crossref] [PubMed]
  5. T. Inoue and Y. Takaki, “Table screen 360-degree holographic display using circular viewing-zone scanning,” Opt. Express 23(5), 6533–6542 (2015).
    [Crossref] [PubMed]
  6. Y. Takaki, Y. Matsumoto, and T. Nakajima, “Color image generation for screen-scanning holographic display,” Opt. Express 23(21), 26986–26998 (2015).
    [Crossref] [PubMed]
  7. Y. Takaki, “Super multi-view and holographic displays using MEMS devices,” Displays 37, 19–24 (2015).
    [Crossref]
  8. Y. Takaki and M. Nakaoka, “Scalable screen-size enlargement by multi-channel viewing-zone scanning holography,” Opt. Express 24(16), 18772–18781 (2016).
    [Crossref] [PubMed]
  9. Y. Lim, K. Hong, H. Kim, H.-E. Kim, E.-Y. Chang, S. Lee, T. Kim, J. Nam, H.-G. Choo, J. Kim, and J. Hahn, “360-degree tabletop electronic holographic display,” Opt. Express 24(22), 24999–25009 (2016).
    [Crossref] [PubMed]
  10. J. Jia, J. Chen, J. Yao, and D. Chu, “A scalable diffraction-based scanning 3D colour video display as demonstrated by using tiled gratings and a vertical diffuser,” Sci. Rep. 7(1), 44656 (2017).
    [Crossref] [PubMed]
  11. Y. Sando, D. Barada, and T. Yatagai, “Full-color holographic 3D display with horizontal full viewing zone by spatiotemporal-division multiplexing,” Appl. Opt. 57(26), 7622–7626 (2018).
    [Crossref] [PubMed]
  12. J. Li, Q. Smithwick, and D. Chu, “Full bandwidth dynamic coarse integral holographic displays with large field of view using a large resonant scanner and a galvanometer scanner,” Opt. Express 26(13), 17459–17476 (2018).
    [Crossref] [PubMed]
  13. H. Zhang, J. Xie, J. Liu, and Y. Wang, “Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection,” Appl. Opt. 48(30), 5834–5841 (2009).
    [Crossref] [PubMed]
  14. D. Wang, C. Liu, L. Li, X. Zhou, and Q.-H. Wang, “Adjustable liquid aperture to eliminate undesirable light in holographic projection,” Opt. Express 24(3), 2098–2105 (2016).
    [Crossref] [PubMed]
  15. J. Burch, “A computer algorithm for the synthesis of spatial frequency filters,” Proc. IEEE 55(4), 599–601 (1967).
    [Crossref]
  16. M. E. Lucente, “Optimization of hologram computation for real-time display,” in Practical Holography VI, (International Society for Optics and Photonics, 1992), 32–44.
  17. E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39(23), 4070–4075 (2000).
    [Crossref] [PubMed]
  18. E. N. Leith and J. Upatnieks, “Reconstructed Wavefronts and Communication Theory*,” J. Opt. Soc. Am. 52(10), 1123–1130 (1962).
    [Crossref]
  19. U. Schnars and W. P. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
    [Crossref]
  20. M. K. Kim, “Principles and techniques of digital holographic microscopy,” SPIE Rev. 1, 018005 (2010).
  21. K. Matsushima and S. Nakahara, “Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method,” Appl. Opt. 48(34), H54–H63 (2009).
    [Crossref] [PubMed]
  22. H. Zhang, Y. Zhao, L. Cao, and G. Jin, “Fully computed holographic stereogram based algorithm for computer-generated holograms with accurate depth cues,” Opt. Express 23(4), 3901–3913 (2015).
    [Crossref] [PubMed]
  23. A. Lohmann, “Optische Einseitenbandübertragung Angewandt auf das Gabor-Mikroskop,” Opt. Acta (Lond.) 3(2), 97–99 (1956).
    [Crossref]
  24. O. Bryngdahl and A. Lohmann, “Single-Sideband Holography*,” J. Opt. Soc. Am. 58(5), 620–624 (1968).
    [Crossref]
  25. R. W. Meier, “Twin-Image Elimination in Holography Using Single-Sideband Waves,” J. Opt. Soc. Am. 59(3), 358–359 (1969).
    [Crossref]
  26. 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(17), 3703–3713 (1999).
    [Crossref] [PubMed]
  27. Y. Takaki and Y. Tanemoto, “Band-limited zone plates for single-sideband holography,” Appl. Opt. 48(34), H64–H70 (2009).
    [Crossref] [PubMed]
  28. T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Viewing-zone-angle-expanded color electronic holography system using ultra-high-definition liquid crystal displays with undesirable light elimination,” J. Disp. Technol. 7(7), 382–390 (2011).
    [Crossref]
  29. T. Kurihara and Y. Takaki, “Shading of a computer-generated hologram by zone plate modulation,” Opt. Express 20(4), 3529–3540 (2012).
    [Crossref] [PubMed]
  30. Y. Takaki and Y. Hayashi, “Elimination of conjugate image for holograms using a resolution redistribution optical system,” Appl. Opt. 47(24), 4302–4308 (2008).
    [Crossref] [PubMed]
  31. N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, M. Oikawa, T. Kakue, N. Masuda, and T. Ito, “Band-limited double-step Fresnel diffraction and its application to computer-generated holograms,” Opt. Express 21(7), 9192–9197 (2013).
    [Crossref] [PubMed]
  32. Y. Zhao, L. Cao, H. Zhang, D. Kong, and G. Jin, “Accurate calculation of computer-generated holograms using angular-spectrum layer-oriented method,” Opt. Express 23(20), 25440–25449 (2015).
    [Crossref] [PubMed]
  33. H. Zhang, Q. Tan, and G. Jin, “Holographic display system of a three-dimensional image with distortion-free magnification and zero-order elimination,” Opt. Eng. 51, 075801 (2012).
  34. K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44(22), 4607–4614 (2005).
    [Crossref] [PubMed]
  35. T. Shimobaba and T. Ito, “Random phase-free computer-generated hologram,” Opt. Express 23(7), 9549–9554 (2015).
    [Crossref] [PubMed]

2018 (2)

2017 (1)

J. Jia, J. Chen, J. Yao, and D. Chu, “A scalable diffraction-based scanning 3D colour video display as demonstrated by using tiled gratings and a vertical diffuser,” Sci. Rep. 7(1), 44656 (2017).
[Crossref] [PubMed]

2016 (3)

2015 (6)

2014 (2)

2013 (1)

2012 (2)

H. Zhang, Q. Tan, and G. Jin, “Holographic display system of a three-dimensional image with distortion-free magnification and zero-order elimination,” Opt. Eng. 51, 075801 (2012).

T. Kurihara and Y. Takaki, “Shading of a computer-generated hologram by zone plate modulation,” Opt. Express 20(4), 3529–3540 (2012).
[Crossref] [PubMed]

2011 (1)

T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Viewing-zone-angle-expanded color electronic holography system using ultra-high-definition liquid crystal displays with undesirable light elimination,” J. Disp. Technol. 7(7), 382–390 (2011).
[Crossref]

2010 (2)

F. Yaras, H. Kang, and L. Onural, “State of the Art in Holographic Displays: A Survey,” J. Disp. Technol. 6(10), 443–454 (2010).
[Crossref]

M. K. Kim, “Principles and techniques of digital holographic microscopy,” SPIE Rev. 1, 018005 (2010).

2009 (3)

2008 (1)

2005 (1)

2002 (1)

U. Schnars and W. P. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[Crossref]

2000 (1)

1999 (1)

1969 (1)

1968 (1)

1967 (1)

J. Burch, “A computer algorithm for the synthesis of spatial frequency filters,” Proc. IEEE 55(4), 599–601 (1967).
[Crossref]

1962 (1)

1956 (1)

A. Lohmann, “Optische Einseitenbandübertragung Angewandt auf das Gabor-Mikroskop,” Opt. Acta (Lond.) 3(2), 97–99 (1956).
[Crossref]

Barada, D.

Benton, S. A.

S. A. Benton and V. M. Bove, Holographic imaging (John Wiley & Sons, 2008).

Bove, V. M.

S. A. Benton and V. M. Bove, Holographic imaging (John Wiley & Sons, 2008).

Bryngdahl, O.

Burch, J.

J. Burch, “A computer algorithm for the synthesis of spatial frequency filters,” Proc. IEEE 55(4), 599–601 (1967).
[Crossref]

Cao, L.

Chang, E.-Y.

Chen, J.

J. Jia, J. Chen, J. Yao, and D. Chu, “A scalable diffraction-based scanning 3D colour video display as demonstrated by using tiled gratings and a vertical diffuser,” Sci. Rep. 7(1), 44656 (2017).
[Crossref] [PubMed]

Choo, H.-G.

Chu, D.

J. Li, Q. Smithwick, and D. Chu, “Full bandwidth dynamic coarse integral holographic displays with large field of view using a large resonant scanner and a galvanometer scanner,” Opt. Express 26(13), 17459–17476 (2018).
[Crossref] [PubMed]

J. Jia, J. Chen, J. Yao, and D. Chu, “A scalable diffraction-based scanning 3D colour video display as demonstrated by using tiled gratings and a vertical diffuser,” Sci. Rep. 7(1), 44656 (2017).
[Crossref] [PubMed]

Cuche, E.

Depeursinge, C.

Fujii, K.

Hahn, J.

Hayashi, Y.

Hong, K.

Ichihashi, Y.

Inoue, T.

Ito, T.

Jia, J.

J. Jia, J. Chen, J. Yao, and D. Chu, “A scalable diffraction-based scanning 3D colour video display as demonstrated by using tiled gratings and a vertical diffuser,” Sci. Rep. 7(1), 44656 (2017).
[Crossref] [PubMed]

Jin, G.

Jüptner, W. P.

U. Schnars and W. P. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[Crossref]

Kakue, T.

Kang, H.

F. Yaras, H. Kang, and L. Onural, “State of the Art in Holographic Displays: A Survey,” J. Disp. Technol. 6(10), 443–454 (2010).
[Crossref]

Kim, H.

Kim, H.-E.

Kim, J.

Kim, M. K.

M. K. Kim, “Principles and techniques of digital holographic microscopy,” SPIE Rev. 1, 018005 (2010).

Kim, T.

Kong, D.

Kurihara, T.

Kurita, T.

T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Viewing-zone-angle-expanded color electronic holography system using ultra-high-definition liquid crystal displays with undesirable light elimination,” J. Disp. Technol. 7(7), 382–390 (2011).
[Crossref]

Lee, S.

Leith, E. N.

Li, J.

Li, L.

Lim, Y.

Liu, C.

Liu, J.

Lohmann, A.

O. Bryngdahl and A. Lohmann, “Single-Sideband Holography*,” J. Opt. Soc. Am. 58(5), 620–624 (1968).
[Crossref]

A. Lohmann, “Optische Einseitenbandübertragung Angewandt auf das Gabor-Mikroskop,” Opt. Acta (Lond.) 3(2), 97–99 (1956).
[Crossref]

Marquet, P.

Masuda, N.

Matsumoto, Y.

Matsushima, K.

Meier, R. W.

Mishina, T.

T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Viewing-zone-angle-expanded color electronic holography system using ultra-high-definition liquid crystal displays with undesirable light elimination,” J. Disp. Technol. 7(7), 382–390 (2011).
[Crossref]

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(17), 3703–3713 (1999).
[Crossref] [PubMed]

Nakahara, S.

Nakajima, T.

Nakaoka, M.

Nam, J.

Oi, R.

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, M. Oikawa, T. Kakue, N. Masuda, and T. Ito, “Band-limited double-step Fresnel diffraction and its application to computer-generated holograms,” Opt. Express 21(7), 9192–9197 (2013).
[Crossref] [PubMed]

T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Viewing-zone-angle-expanded color electronic holography system using ultra-high-definition liquid crystal displays with undesirable light elimination,” J. Disp. Technol. 7(7), 382–390 (2011).
[Crossref]

Oikawa, M.

Okada, N.

Okano, F.

Onural, L.

F. Yaras, H. Kang, and L. Onural, “State of the Art in Holographic Displays: A Survey,” J. Disp. Technol. 6(10), 443–454 (2010).
[Crossref]

Sando, Y.

Schnars, U.

U. Schnars and W. P. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[Crossref]

Senoh, T.

T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Viewing-zone-angle-expanded color electronic holography system using ultra-high-definition liquid crystal displays with undesirable light elimination,” J. Disp. Technol. 7(7), 382–390 (2011).
[Crossref]

Shimobaba, T.

Smithwick, Q.

Takaki, Y.

Tan, Q.

H. Zhang, Q. Tan, and G. Jin, “Holographic display system of a three-dimensional image with distortion-free magnification and zero-order elimination,” Opt. Eng. 51, 075801 (2012).

Tanemoto, Y.

Upatnieks, J.

Wang, D.

Wang, Q.-H.

Wang, Y.

Xie, J.

Yamamoto, K.

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, M. Oikawa, T. Kakue, N. Masuda, and T. Ito, “Band-limited double-step Fresnel diffraction and its application to computer-generated holograms,” Opt. Express 21(7), 9192–9197 (2013).
[Crossref] [PubMed]

T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Viewing-zone-angle-expanded color electronic holography system using ultra-high-definition liquid crystal displays with undesirable light elimination,” J. Disp. Technol. 7(7), 382–390 (2011).
[Crossref]

Yao, J.

J. Jia, J. Chen, J. Yao, and D. Chu, “A scalable diffraction-based scanning 3D colour video display as demonstrated by using tiled gratings and a vertical diffuser,” Sci. Rep. 7(1), 44656 (2017).
[Crossref] [PubMed]

Yaras, F.

F. Yaras, H. Kang, and L. Onural, “State of the Art in Holographic Displays: A Survey,” J. Disp. Technol. 6(10), 443–454 (2010).
[Crossref]

Yatagai, T.

Yuyama, I.

Zhang, H.

Zhao, Y.

Zhou, X.

Appl. Opt. (8)

H. Zhang, J. Xie, J. Liu, and Y. Wang, “Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection,” Appl. Opt. 48(30), 5834–5841 (2009).
[Crossref] [PubMed]

E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39(23), 4070–4075 (2000).
[Crossref] [PubMed]

Y. Sando, D. Barada, and T. Yatagai, “Full-color holographic 3D display with horizontal full viewing zone by spatiotemporal-division multiplexing,” Appl. Opt. 57(26), 7622–7626 (2018).
[Crossref] [PubMed]

K. Matsushima and S. Nakahara, “Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method,” Appl. Opt. 48(34), H54–H63 (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(17), 3703–3713 (1999).
[Crossref] [PubMed]

Y. Takaki and Y. Tanemoto, “Band-limited zone plates for single-sideband holography,” Appl. Opt. 48(34), H64–H70 (2009).
[Crossref] [PubMed]

Y. Takaki and Y. Hayashi, “Elimination of conjugate image for holograms using a resolution redistribution optical system,” Appl. Opt. 47(24), 4302–4308 (2008).
[Crossref] [PubMed]

K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44(22), 4607–4614 (2005).
[Crossref] [PubMed]

Chin. Opt. Lett. (1)

Displays (1)

Y. Takaki, “Super multi-view and holographic displays using MEMS devices,” Displays 37, 19–24 (2015).
[Crossref]

J. Disp. Technol. (2)

F. Yaras, H. Kang, and L. Onural, “State of the Art in Holographic Displays: A Survey,” J. Disp. Technol. 6(10), 443–454 (2010).
[Crossref]

T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Viewing-zone-angle-expanded color electronic holography system using ultra-high-definition liquid crystal displays with undesirable light elimination,” J. Disp. Technol. 7(7), 382–390 (2011).
[Crossref]

J. Opt. Soc. Am. (3)

Meas. Sci. Technol. (1)

U. Schnars and W. P. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[Crossref]

Opt. Acta (Lond.) (1)

A. Lohmann, “Optische Einseitenbandübertragung Angewandt auf das Gabor-Mikroskop,” Opt. Acta (Lond.) 3(2), 97–99 (1956).
[Crossref]

Opt. Eng. (1)

H. Zhang, Q. Tan, and G. Jin, “Holographic display system of a three-dimensional image with distortion-free magnification and zero-order elimination,” Opt. Eng. 51, 075801 (2012).

Opt. Express (12)

H. Zhang, Y. Zhao, L. Cao, and G. Jin, “Fully computed holographic stereogram based algorithm for computer-generated holograms with accurate depth cues,” Opt. Express 23(4), 3901–3913 (2015).
[Crossref] [PubMed]

J. Li, Q. Smithwick, and D. Chu, “Full bandwidth dynamic coarse integral holographic displays with large field of view using a large resonant scanner and a galvanometer scanner,” Opt. Express 26(13), 17459–17476 (2018).
[Crossref] [PubMed]

T. Kurihara and Y. Takaki, “Shading of a computer-generated hologram by zone plate modulation,” Opt. Express 20(4), 3529–3540 (2012).
[Crossref] [PubMed]

T. Shimobaba and T. Ito, “Random phase-free computer-generated hologram,” Opt. Express 23(7), 9549–9554 (2015).
[Crossref] [PubMed]

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, M. Oikawa, T. Kakue, N. Masuda, and T. Ito, “Band-limited double-step Fresnel diffraction and its application to computer-generated holograms,” Opt. Express 21(7), 9192–9197 (2013).
[Crossref] [PubMed]

Y. Zhao, L. Cao, H. Zhang, D. Kong, and G. Jin, “Accurate calculation of computer-generated holograms using angular-spectrum layer-oriented method,” Opt. Express 23(20), 25440–25449 (2015).
[Crossref] [PubMed]

D. Wang, C. Liu, L. Li, X. Zhou, and Q.-H. Wang, “Adjustable liquid aperture to eliminate undesirable light in holographic projection,” Opt. Express 24(3), 2098–2105 (2016).
[Crossref] [PubMed]

Y. Takaki and K. Fujii, “Viewing-zone scanning holographic display using a MEMS spatial light modulator,” Opt. Express 22(20), 24713–24721 (2014).
[Crossref] [PubMed]

T. Inoue and Y. Takaki, “Table screen 360-degree holographic display using circular viewing-zone scanning,” Opt. Express 23(5), 6533–6542 (2015).
[Crossref] [PubMed]

Y. Takaki, Y. Matsumoto, and T. Nakajima, “Color image generation for screen-scanning holographic display,” Opt. Express 23(21), 26986–26998 (2015).
[Crossref] [PubMed]

Y. Takaki and M. Nakaoka, “Scalable screen-size enlargement by multi-channel viewing-zone scanning holography,” Opt. Express 24(16), 18772–18781 (2016).
[Crossref] [PubMed]

Y. Lim, K. Hong, H. Kim, H.-E. Kim, E.-Y. Chang, S. Lee, T. Kim, J. Nam, H.-G. Choo, J. Kim, and J. Hahn, “360-degree tabletop electronic holographic display,” Opt. Express 24(22), 24999–25009 (2016).
[Crossref] [PubMed]

Proc. IEEE (1)

J. Burch, “A computer algorithm for the synthesis of spatial frequency filters,” Proc. IEEE 55(4), 599–601 (1967).
[Crossref]

Sci. Rep. (1)

J. Jia, J. Chen, J. Yao, and D. Chu, “A scalable diffraction-based scanning 3D colour video display as demonstrated by using tiled gratings and a vertical diffuser,” Sci. Rep. 7(1), 44656 (2017).
[Crossref] [PubMed]

SPIE Rev. (1)

M. K. Kim, “Principles and techniques of digital holographic microscopy,” SPIE Rev. 1, 018005 (2010).

Other (2)

M. E. Lucente, “Optimization of hologram computation for real-time display,” in Practical Holography VI, (International Society for Optics and Photonics, 1992), 32–44.

S. A. Benton and V. M. Bove, Holographic imaging (John Wiley & Sons, 2008).

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Figures (7)

Fig. 1
Fig. 1 Amplitude hologram in spatial and spatial frequency domains: (a) unfiltered CGH, and (b) filtered CGH.
Fig. 2
Fig. 2 The diagram of generalized single-sideband method for 3D CGH: (a) hologram generation, and (b) hologram reconstruction.
Fig. 3
Fig. 3 Optical setup of generalized single-sideband CGH reconstructions.
Fig. 4
Fig. 4 Numerical and optical reconstructions of the generalized single-sideband CGH: (a), (e) 3D model and CGH, (b), (f) reconstructions without filtering; (c), (g) reconstructions with zero-order filtering; (d), (h) reconstructions with single-sideband filtering.
Fig. 5
Fig. 5 Numerical and optical reconstructions of the generalized single-sideband CGH with different reconstruction depths.
Fig. 6
Fig. 6 Numerical simulations and experimental results of the generalized single-sideband method with different CGH algorithms: layer based method (left column), point based method (middle column), and polygon based method (right column).
Fig. 7
Fig. 7 Comparison of the reconstruction results: (a) spectrum and (b) reconstruction without random phase; (c) spectrum and (d) reconstruction with random phase.

Equations (9)

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

I=O O * +R R * +O R * + O * R
H=O R * + O * R+Δ
H=O+ O * +Δ .
F(H)=F(O)+F( O * )+δ= O f ( u,v )+ O f * ( u,v )+δ
S(u,v)={ 0 v0 1 v<0
O filtered = F 1 [F(O)S]
H= O filtered + O filtered * +Δ
F( H )=F( O filtered )+F( O filtered * )+δ
F( H )=F( O filtered )+F( O filtered * )+δ = O f ( u,v )S( u,v )+ O f * ( u,v ) S * ( u,v )+δ

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