Abstract

We report a novel and non-iterative method for the generation of phase-only Fourier hologram for image projection. Briefly, target image is first added with a special quadratic phase and then padded with zeros. A complex Fourier hologram is generated via the simple fast Fourier transform. Subsequently, the error diffusion algorithm is applied to convert the complex hologram into a phase-only hologram. The numerical, as well as the optical reconstructed images with the proposed method are of higher visual quality and contain less speckle noise compared to the original random phase method, which add the random phase to the target image and then preserve the phase component of the complex hologram. The influences of quadratic phase and zero-padding on the image quality are also discussed in detail.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
  2. W. Qu, H. Gu, and Q. Tan, “Holographic projection with higher image quality,” Opt. Express 24(17), 19179–19184 (2016).
    [Crossref] [PubMed]
  3. D. Mengu, E. Ulusoy, and H. Urey, “Non-iterative phase hologram computation for low speckle holographic image projection,” Opt. Express 24(5), 4462–4476 (2016).
    [Crossref]
  4. C. Chang, Y. Qi, J. Wu, J. Xia, and S. Nie, “Speckle reduced lensless holographic projection from phase-only computer-generated hologram,” Opt. Express 25(6), 6568–6580 (2017).
    [Crossref] [PubMed]
  5. P. W. M. Tsang and T.-C. Poon, “Review on the state-of-the-art technologies for acquisition and display of digital holograms,” IEEE Trans. Industr. Inform. 12(3), 886–901 (2016).
    [Crossref]
  6. E. Buckley, “Real-time error diffusion for signal-to-noise ratio improvement in a holographic projection system,” J. Disp. Technol. 7(2), 70–76 (2011).
    [Crossref]
  7. 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]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  13. 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]
  14. P. W. M. Tsang, Y. T. Chow, and T.-C. Poon, “Generation of Complementary sampled phase-only holograms,” Opt. Express 24(20), 23390–23395 (2016).
    [Crossref] [PubMed]
  15. 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]
  16. P. W. M. Tsang, A. S. M. Jiao, and T.-C. Poon, “Fast conversion of digital Fresnel hologram to phase-only hologram based on localized error diffusion and redistribution,” Opt. Express 22(5), 5060–5066 (2014).
    [Crossref] [PubMed]
  17. T. Shimobaba and T. Ito, “Random phase-free computer-generated hologram,” Opt. Express 23(7), 9549–9554 (2015).
    [Crossref] [PubMed]
  18. 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).
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  20. Source, http://www.tupian114.com/photo_1442783.html

2017 (2)

2016 (5)

2015 (6)

2014 (2)

2013 (1)

2011 (1)

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

2010 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “Practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–250 (1972).

Buckley, E.

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

E. Buckley, “Holographic projector using one lens,” Opt. Lett. 35(20), 3399–3401 (2010).
[Crossref] [PubMed]

Cao, L.

Chang, C.

Chen, J.

Cheng, S.

L. Wu, S. Cheng, and S. Tao, “Simultaneous shaping of amplitude and phase of light in the entire output plane with a phase-only hologram,” Sci. Rep. 5, 15426 (2015).
[Crossref] [PubMed]

Chow, Y. T.

Endo, Y.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “Practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–250 (1972).

Gu, H.

Hasegawa, S.

Hirayama, R.

Hiyama, D.

Ito, T.

Jiao, A. S. M.

Jin, G.

Kakue, T.

Kong, D.

Lei, W.

Masuda, N.

Mengu, D.

Nagahama, Y.

Nie, S.

Oikawa, M.

Poon, T.-C.

Qi, Y.

Qu, W.

Sano, M.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “Practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–250 (1972).

Shimobaba, T.

Sugie, T.

Tan, Q.

Tao, S.

L. Wu, S. Cheng, and S. Tao, “Simultaneous shaping of amplitude and phase of light in the entire output plane with a phase-only hologram,” Sci. Rep. 5, 15426 (2015).
[Crossref] [PubMed]

S. Tao and W. Yu, “Beam shaping of complex amplitude with separate constraints on the output beam,” Opt. Express 23(2), 1052–1062 (2015).
[Crossref] [PubMed]

Tsang, P. W. M.

Ulusoy, E.

Urey, H.

Wu, J.

Wu, L.

L. Wu, S. Cheng, and S. Tao, “Simultaneous shaping of amplitude and phase of light in the entire output plane with a phase-only hologram,” Sci. Rep. 5, 15426 (2015).
[Crossref] [PubMed]

Xia, J.

Yang, L.

Yang, Z.

Yu, W.

Zhang, H.

Zhao, Y.

Appl. Opt. (2)

Chin. Opt. Lett. (1)

IEEE Trans. Industr. Inform. (1)

P. W. M. Tsang and T.-C. Poon, “Review on the state-of-the-art technologies for acquisition and display of digital holograms,” IEEE Trans. Industr. Inform. 12(3), 886–901 (2016).
[Crossref]

J. Disp. Technol. (1)

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

Opt. Express (11)

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]

P. W. M. Tsang, A. S. M. Jiao, and T.-C. Poon, “Fast conversion of digital Fresnel hologram to phase-only hologram based on localized error diffusion and redistribution,” Opt. Express 22(5), 5060–5066 (2014).
[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]

S. Tao and W. Yu, “Beam shaping of complex amplitude with separate constraints on the output beam,” Opt. Express 23(2), 1052–1062 (2015).
[Crossref] [PubMed]

T. Shimobaba and T. Ito, “Random phase-free computer-generated hologram,” Opt. Express 23(7), 9549–9554 (2015).
[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 Complementary sampled phase-only holograms,” Opt. Express 24(20), 23390–23395 (2016).
[Crossref] [PubMed]

C. Chang, Y. Qi, J. Wu, J. Xia, and S. Nie, “Speckle reduced lensless holographic projection from phase-only computer-generated hologram,” Opt. Express 25(6), 6568–6580 (2017).
[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. Mengu, E. Ulusoy, and H. Urey, “Non-iterative phase hologram computation for low speckle holographic image projection,” Opt. Express 24(5), 4462–4476 (2016).
[Crossref]

W. Qu, H. Gu, and Q. Tan, “Holographic projection with higher image quality,” Opt. Express 24(17), 19179–19184 (2016).
[Crossref] [PubMed]

Opt. Lett. (1)

Optik (Stuttg.) (1)

R. W. Gerchberg and W. O. Saxton, “Practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–250 (1972).

Sci. Rep. (1)

L. Wu, S. Cheng, and S. Tao, “Simultaneous shaping of amplitude and phase of light in the entire output plane with a phase-only hologram,” Sci. Rep. 5, 15426 (2015).
[Crossref] [PubMed]

Other (1)

Source, http://www.tupian114.com/photo_1442783.html

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Figures (12)

Fig. 1
Fig. 1 Proposed method for the generation of phase-only Fourier hologram.
Fig. 2
Fig. 2 The determination of quadratic phase.
Fig. 3
Fig. 3 (a)-(c) Test images “Orchid”, “Cameraman”, and “Peppers”.
Fig. 4
Fig. 4 (a) Generated hologram. (b) Reconstructed image with the proposed method. (c) Quadratic phase. (d) Phase distribution of the image in Fig. 4(b). (e) Comparison of the reconstructed phase and the original quadratic phase. (f) Reconstructed image with the original random-phase method.
Fig. 5
Fig. 5 Numerical reconstructed images of the phase-only Fourier hologram: (a)-(b) proposed method, (c)-(d) original random phase method.
Fig. 6
Fig. 6 Experimental setup for optical reconstruction of the hologram.
Fig. 7
Fig. 7 (a)-(c) Optical reconstructed images of the holograms generated by the random phase method.
Fig. 8
Fig. 8 (a)-(c) Optical reconstructed images of the holograms generated by the proposed method.
Fig. 9
Fig. 9 (a)-(d) Calculated spectrum of the image when different quadratic phases are added. (e)-(h) Numerical reconstructed images with different quadratic phase added in the design.
Fig. 10
Fig. 10 Calculated PSNR and diffraction efficiency of the reconstructed image when different quadratic phase is adopted.
Fig. 11
Fig. 11 Numerical reconstructed results when the target image is padded with different number of zeros.
Fig. 12
Fig. 12 Calculated PSNR and diffraction efficiency of the reconstructed image when different number of zeros is padded to the target image.

Tables (1)

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Table 1 The PSNR of the reconstructed images with two different methods.

Equations (11)

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φ ( m , n ) = a m 2 + b n 2 ,
O ( m , n ) = I ( m , n ) exp ( i φ ( m , n ) ) .
H ( u , v ) = F { O ( m , n ) } = F { I ( m , n ) × exp ( i φ ) } = F { I ( m , n ) } F { exp ( i φ ) } = h ( u , v ) p ( u , v )
H ( u , v + 1 ) H ( u , v + 1 ) + w 1 [ H ( u , v ) arg ( H ( u , v ) ) ] , H ( u + 1 , v 1 ) H ( u + 1 , v 1 ) + w 2 [ H ( u , v ) arg ( H ( u , v ) ) ] , H ( u + 1 , v ) H ( u + 1 , v ) + w 3 [ H ( u , v ) arg ( H ( u , v ) ) ] , H ( u + 1 , v + 1 ) H ( u + 1 , v + 1 ) + w 4 [ H ( u , v ) arg ( H ( u , v ) ) ] .
1 / l 1 + 1 / l 2 = 1 / f ,
S o : h = ( l 1 f ) : l 1 ,
S h : h = ( l 2 f ) : l 2 .
l 1 = S o + S h S h f .
f ( x , y ) = exp ( i π λ l 1 ( x 2 + y 2 ) ) = exp ( i π λ l 1 ( ( m d x ) 2 + ( n d y ) 2 ) ) ,
a = π λ l 1 d x 2 .
a = π d x 2 λ × S h S o + S h × 1 f = π λ × ( λ f M d x h ) 2 × M d x h λ f d x h + M d x h × 1 f = π M ( 1 + M d x h 2 λ f ) = π M ( 1 + S h S o ) .

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