Abstract

A non-iterative algorithm is proposed to generate phase holograms with optimized phase modulation. A quadratic initial phase with continuous distributed spectrum is utilized to iteratively optimize the phase modulation in the reconstruction plane, which can be used as an optimized phase distribution for arbitrary target images. The phase hologram can be calculated directly according to the modulated wave field distribution in the reconstruction plane. Fast generation of the phase holograms can be achieved by this non-iterative implementation, and the avoidance of the random phase modulation helps to suppress the speckle noise. Numerical and optical experiments have demonstrated that the proposed method can efficiently generate phase holograms with quality reconstructions.

© 2020 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 (Wiley, 2007).
  2. Y. Pan, Y. Wang, J. Liu, X. Li, and J. Jia, “Fast polygon-based method for calculating computer-generated holograms in three-dimensional display,” Appl. Opt. 52(1), A290–A299 (2013).
    [Crossref]
  3. 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]
  4. W. Qu, H. Gu, and Q. Tan, “Holographic projection with higher image quality,” Opt. Express 24(17), 19179–19184 (2016).
    [Crossref]
  5. A. Jesacher, C. Maurer, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Near-perfect hologram reconstruction with a spatial light modulator,” Opt. Express 16(4), 2597–2603 (2008).
    [Crossref]
  6. 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(12), 1–3 (2011).
    [Crossref]
  7. Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light: Sci. Appl. 3(1), e135 (2014).
    [Crossref]
  8. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  9. J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19(3), 193297 (1980).
    [Crossref]
  10. A. V. Kuzmenko, “Weighting iterative Fourier transform algorithm of the kinoform synthesis,” Opt. Lett. 33(10), 1147–1149 (2008).
    [Crossref]
  11. W. Hsu and S. Lin, “Iterative pixelwise approach applied to computer-generated holograms and diffractive optical element,” Appl. Opt. 57(1), A189–A196 (2018).
    [Crossref]
  12. R. Bräuer, F. Wyrowski, and O. Bryngdahl, “Diffusers in digital holography,” J. Opt. Soc. Am. A 8(3), 572–578 (1991).
    [Crossref]
  13. F. Wyrowski and O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5(7), 1058–1065 (1988).
    [Crossref]
  14. C. K. Hsueh and A. A. Sawchuk, “Computer-generated double-phase holograms,” Appl. Opt. 17(24), 3874–3883 (1978).
    [Crossref]
  15. O. Mendoza-Yero, G. Mínguez-Vega, and J. Lancis, “Encoding complex fields by using a phase-only optical element,” Opt. Lett. 39(7), 1740–1743 (2014).
    [Crossref]
  16. R. Eschbach and Z. G. Fan, “Complex-valued error diffusion for off-axis computer-generated holograms,” Appl. Opt. 32(17), 3130–3136 (1993).
    [Crossref]
  17. 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]
  18. A. Velez-Zea, J. F. Barrera-Ramirez, and R. Torroba, “Optimized random phase only holograms,” Opt. Lett. 43(15), 3558 (2018).
    [Crossref]
  19. P. Tsang, Y. T. Chow, and T.-C. Poon, “Generation of patterned-phase only holograms (PPOHs),” Opt. Express 25(8), 9088–9093 (2017).
    [Crossref]
  20. A. Velez-Zea and R. Torroba, “Optimized random phase tiles for non-iterative hologram generation,” Appl. Opt. 58(32), 9013–9019 (2019).
    [Crossref]
  21. T. Zhao, J. Liu, J. Duan, X. Li, and Y. Wang, “Image quality enhancement via gradient-limited random phase addition in holographic display,” Opt. Commun. 442, 84–89 (2019).
    [Crossref]
  22. T. Shimobaba and T. Ito, “Random phase-free computer-generated hologram,” Opt. Express 23(7), 9549–9554 (2015).
    [Crossref]
  23. Y. Nagahama, T. Shimobaba, T. Kakue, N. Masuda, and T. Ito, “Speeding up image quality improvement in random phase-free holograms using ringing artifact characteristics,” Appl. Opt. 56(13), F61–F66 (2017).
    [Crossref]
  24. 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]
  25. H. Pang, J. Wang, M. Zhang, A. Cao, L. Shi, and Q. Deng, “Non-iterative phase-only Fourier hologram generation with high image quality,” Opt. Express 25(13), 14323–14333 (2017).
    [Crossref]
  26. D. Fischer and S. Sinzinger, “Evaluation of quadratic phase hologram calculation algorithms in the Fourier regime,” Appl. Opt. 59(6), 1501–1506 (2020).
    [Crossref]
  27. A. Velez-Zea and R. Torroba, “Synthetic amplitude for improved reconstruction of noniterative phase holograms,” Appl. Opt. 58(22), 6144–6151 (2019).
    [Crossref]
  28. 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(7), 075801 (2012).
    [Crossref]

2020 (1)

2019 (3)

2018 (2)

2017 (3)

2016 (1)

2015 (3)

2014 (2)

Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light: Sci. Appl. 3(1), e135 (2014).
[Crossref]

O. Mendoza-Yero, G. Mínguez-Vega, and J. Lancis, “Encoding complex fields by using a phase-only optical element,” Opt. Lett. 39(7), 1740–1743 (2014).
[Crossref]

2013 (2)

2012 (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(7), 075801 (2012).
[Crossref]

2011 (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(12), 1–3 (2011).
[Crossref]

2008 (2)

1993 (1)

1991 (1)

1988 (1)

1980 (1)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19(3), 193297 (1980).
[Crossref]

1978 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Barrera-Ramirez, J. F.

Benton, S. A.

S. A. Benton and V. M. Bove, Holographic Imaging (Wiley, 2007).

Bernet, S.

Bove, V. M.

S. A. Benton and V. M. Bove, Holographic Imaging (Wiley, 2007).

Bräuer, R.

Bryngdahl, O.

Cao, A.

Cao, L.

Chow, Y. T.

Chu, D.

Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light: Sci. Appl. 3(1), e135 (2014).
[Crossref]

Deng, Q.

Duan, J.

T. Zhao, J. Liu, J. Duan, X. Li, and Y. Wang, “Image quality enhancement via gradient-limited random phase addition in holographic display,” Opt. Commun. 442, 84–89 (2019).
[Crossref]

Ducin, I.

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(12), 1–3 (2011).
[Crossref]

Endo, Y.

Eschbach, R.

Fan, Z. G.

Fienup, J. R.

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19(3), 193297 (1980).
[Crossref]

Fischer, D.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Gu, H.

Hasegawa, S.

Hirayama, R.

Hiyama, D.

Hsu, W.

Hsueh, C. K.

Ito, T.

Jaroszewicz, Z.

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(12), 1–3 (2011).
[Crossref]

Jesacher, A.

Jia, J.

Jin, G.

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]

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(7), 075801 (2012).
[Crossref]

Kakarenko, K.

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(12), 1–3 (2011).
[Crossref]

Kakue, T.

Kolodziejczyk, A.

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(12), 1–3 (2011).
[Crossref]

Kuzmenko, A. V.

Lancis, J.

Li, X.

T. Zhao, J. Liu, J. Duan, X. Li, and Y. Wang, “Image quality enhancement via gradient-limited random phase addition in holographic display,” Opt. Commun. 442, 84–89 (2019).
[Crossref]

Y. Pan, Y. Wang, J. Liu, X. Li, and J. Jia, “Fast polygon-based method for calculating computer-generated holograms in three-dimensional display,” Appl. Opt. 52(1), A290–A299 (2013).
[Crossref]

Lin, S.

Liu, J.

T. Zhao, J. Liu, J. Duan, X. Li, and Y. Wang, “Image quality enhancement via gradient-limited random phase addition in holographic display,” Opt. Commun. 442, 84–89 (2019).
[Crossref]

Y. Pan, Y. Wang, J. Liu, X. Li, and J. Jia, “Fast polygon-based method for calculating computer-generated holograms in three-dimensional display,” Appl. Opt. 52(1), A290–A299 (2013).
[Crossref]

Makowski, M.

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(12), 1–3 (2011).
[Crossref]

Masuda, N.

Maurer, C.

Mendoza-Yero, O.

Mínguez-Vega, G.

Nagahama, Y.

Oikawa, M.

Pan, Y.

Pang, H.

Poon, T.-C.

Qu, W.

Ritsch-Marte, M.

Sano, M.

Sawchuk, A. A.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Schwaighofer, A.

Shi, L.

Shimobaba, T.

Siemion, A.

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(12), 1–3 (2011).
[Crossref]

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(12), 1–3 (2011).
[Crossref]

Sinzinger, S.

Sugie, T.

Suszek, J.

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(12), 1–3 (2011).
[Crossref]

Sypek, M.

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(12), 1–3 (2011).
[Crossref]

Tan, Q.

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

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(7), 075801 (2012).
[Crossref]

Torroba, R.

Tsang, P.

Tsang, P. W. M.

Velez-Zea, A.

Wang, J.

Wang, Y.

T. Zhao, J. Liu, J. Duan, X. Li, and Y. Wang, “Image quality enhancement via gradient-limited random phase addition in holographic display,” Opt. Commun. 442, 84–89 (2019).
[Crossref]

Y. Pan, Y. Wang, J. Liu, X. Li, and J. Jia, “Fast polygon-based method for calculating computer-generated holograms in three-dimensional display,” Appl. Opt. 52(1), A290–A299 (2013).
[Crossref]

Wojnowski, D.

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(12), 1–3 (2011).
[Crossref]

Wyrowski, F.

You, Z.

Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light: Sci. Appl. 3(1), e135 (2014).
[Crossref]

Zhang, H.

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]

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(7), 075801 (2012).
[Crossref]

Zhang, M.

Zhang, Z.

Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light: Sci. Appl. 3(1), e135 (2014).
[Crossref]

Zhao, T.

T. Zhao, J. Liu, J. Duan, X. Li, and Y. Wang, “Image quality enhancement via gradient-limited random phase addition in holographic display,” Opt. Commun. 442, 84–89 (2019).
[Crossref]

Zhao, Y.

Appl. Opt. (8)

Chin. Opt. Lett. (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(12), 1–3 (2011).
[Crossref]

J. Opt. Soc. Am. A (2)

Light: Sci. Appl. (1)

Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light: Sci. Appl. 3(1), e135 (2014).
[Crossref]

Opt. Commun. (1)

T. Zhao, J. Liu, J. Duan, X. Li, and Y. Wang, “Image quality enhancement via gradient-limited random phase addition in holographic display,” Opt. Commun. 442, 84–89 (2019).
[Crossref]

Opt. Eng. (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(7), 075801 (2012).
[Crossref]

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19(3), 193297 (1980).
[Crossref]

Opt. Express (8)

Opt. Lett. (3)

Optik (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Other (1)

S. A. Benton and V. M. Bove, Holographic Imaging (Wiley, 2007).

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Figures (12)

Fig. 1.
Fig. 1. Numerical simulations: (a) original image; (b) reconstructed image with constant phase; (c) reconstructed image with random phase.
Fig. 2.
Fig. 2. Block diagram of optimized quadratic phase generation.
Fig. 3.
Fig. 3. Flowchart of phase hologram generation.
Fig. 4.
Fig. 4. Spectrums of different quadratic phase distribution.
Fig. 5.
Fig. 5. Numerical simulations: (a) initial quadratic phase; optimized quadratic phase (b) under 20 iterations, (c) under 50 iterations, (d) under 100 iterations; (e) initial intensity of rectangular aperture; reconstructed intensity of rectangular aperture (f) under 20 iterations, (g) under 50 iterations, (h) under 100 iterations.
Fig. 6.
Fig. 6. Numerical reconstructions: reconstructed intensity with (a) RAP method, (b) GS algorithm, (c) unoptimized quadratic phase and (d) our proposed method; reconstructed phase distribution in the signal region with (e) RAP method, (f) GS algorithm, (g) unoptimized quadratic phase and (h) our proposed method.
Fig. 7.
Fig. 7. Numerical reconstructions with the RAP method (top), GS algorithm (middle) and our proposed method (bottom).
Fig. 8.
Fig. 8. Schematic of experimental setup.
Fig. 9.
Fig. 9. Optical reconstructions of (a) RAP method, (b) GS algorithm, (c) our proposed method.
Fig. 10.
Fig. 10. Optical reconstructions of the RAP method (top), the GS algorithm (middle) and our proposed method (bottom).
Fig. 11.
Fig. 11. Numerical results with different sampling numbers of the signal region: reconstructed intensity (a), (b), (c) and (d); corresponding reconstructed phase in the signal region (e), (f), (g) and (h).
Fig. 12.
Fig. 12. Numerical Reconstructions: (a) without feedback operation; (b) with feedback operation.

Equations (15)

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φ t ( m , n ) = a m 2 + b n 2 ,
| A con | = T | A k | ( | A t | / | A k | ) α k  +  ( 1 T ) | A k | ,
α k = α k 1 .
| A holo | = m = 1 M n = 1 N | A t | 2 M N ,
β = | A t | / ( | A r |  +  ε ) ,
A m = β | A t | exp ( φ o ) .
f m = 1 2 π φ t x = a m π d x ,
f M = a M 2 π d x ,
f M = S h 2 λ f ,
d x = λ f S h ,
a = π M ,
b = π N ,
PSNR = 20 l o g [ 255 RMSE ] ,
RMSE = 1 M N m = 1 M n = 1 N [ I t ( m , n ) I r ( m , n ) ] 2 ,
SSIM = ( 2 μ t μ r + c 1 ) ( 2 σ t , r + c 2 ) ( μ t 2 + μ r 2 + c 1 ) ( σ t 2 + σ r 2 + c 2 ) ,

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