Abstract

In the angular-spectrum method–based computer-generated hologram, the zero-padding method is used to convert circular convolution into linear convolution. However, it will increase the calculation time and memory usage significantly. Therefore, a fast and simple method is proposed to solve the issue of the numerical convolution in the process of hologram generation by using the intermediate angular-spectrum method in this paper. Through replacing numerical Fourier transform by optical Fourier transform in the hologram generation, the calculation speed is approximately 6 times faster than that of the zero-padding method. And due to the scaling factors introduced by the Fourier lens and without the cropping operation, the reconstruction quality of the proposed method is improved significantly compared with the zero-padding method. Moreover, the optical reconstruction system is more compact than the 4-$f$ filter system in the on-axis holographic reconstruction. Both numerical simulations and optical experiments have validated the effectiveness of the proposed method.

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

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  1. 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]
  2. J. Hong, Y. Kim, H.-J. Choi, J. Hahn, J.-H. Park, H. Kim, S.-W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues [Invited],” Appl. Opt. 50(34), H87–H115 (2011).
    [Crossref]
  3. L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The Kinoform: A New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13(2), 150–155 (1969).
    [Crossref]
  4. Y.-Z. Liu, J.-W. Dong, Y.-Y. Pu, B.-C. Chen, H.-X. He, and H.-Z. Wang, “High-speed full analytical holographic computations for true-life scenes,” Opt. Express 18(4), 3345–3351 (2010).
    [Crossref]
  5. H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3(5), 312–315 (1971).
    [Crossref]
  6. D. Palima and V. R. Daria, “Holographic projection of arbitrary light patterns with a suppressed zero-order beam,” Appl. Opt. 46(20), 4197–4201 (2007).
    [Crossref]
  7. P. Sun, S. Chang, S. Liu, X. Tao, C. Wang, and Z. Zheng, “Holographic near-eye display system based on double-convergence light gerchberg-saxton algorithm,” Opt. Express 26(8), 10140–10151 (2018).
    [Crossref]
  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]
  9. Y. Qi, C. Chang, and J. Xia, “Speckleless holographic display by complex modulation based on double-phase method,” Opt. Express 24(26), 30368–30378 (2016).
    [Crossref]
  10. C. Chen, J. Wang, D. Xiao, and Q.-H. Wang, “Fast method for ringing artifacts reduction in random phase-free kinoforms,” Appl. Opt. 58(5), A13–A20 (2019).
    [Crossref]
  11. J. Cho, S. Kim, S. Park, B. Lee, and H. Kim, “DC-free on-axis holographic display using a phase-only spatial light modulator,” Opt. Lett. 43(14), 3397–3400 (2018).
    [Crossref]
  12. M. Agour, E. Kolenovic, C. Falldorf, and C. von Kopylow, “Suppression of higher diffraction orders and intensity improvement of optically reconstructed holograms from a spatial light modulator,” J. Opt. A: Pure Appl. Opt. 11(10), 105405 (2009).
    [Crossref]
  13. 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]
  14. X. Wang, H. Zhang, L. Cao, and G. Jin, “Generalized single-sideband three-dimensional computer-generated holography,” Opt. Express 27(3), 2612–2620 (2019).
    [Crossref]
  15. M. E. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
    [Crossref]
  16. S.-C. Kim and E.-S. Kim, “Effective generation of digital holograms of three-dimensional objects using a novel look-up table method,” Appl. Opt. 47(19), D55–D62 (2008).
    [Crossref]
  17. T. Shimobaba, N. Masuda, and T. Ito, “Simple and fast calculation algorithm for computer-generated hologram with wavefront recording plane,” Opt. Lett. 34(20), 3133–3135 (2009).
    [Crossref]
  18. T. Sugie, T. Akamatsu, T. Nishitsuji, R. Hirayama, N. Masuda, H. Nakayama, Y. Ichihashi, A. Shiraki, M. Oikawa, N. Takada, Y. Endo, T. Kakue, T. Shimobaba, and T. Ito, “High-performance parallel computing for next-generation holographic imaging,” Nat. Electron. 1(4), 254–259 (2018).
    [Crossref]
  19. N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, “Computer generated holography using a graphics processing unit,” Opt. Express 14(2), 603–608 (2006).
    [Crossref]
  20. 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]
  21. J.-S. Chen and D. P. Chu, “Improved layer-based method for rapid hologram generation and real-time interactive holographic display applications,” Opt. Express 23(14), 18143–18155 (2015).
    [Crossref]
  22. 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]
  23. T. Shimobaba, T. Takahashi, Y. Yamamoto, T. Nishitsuji, A. Shiraki, N. Hoshikawa, T. Kakue, and T. Ito, “Efficient diffraction calculations using implicit convolution,” OSA Continuum 1(2), 642–650 (2018).
    [Crossref]
  24. 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]
  25. K. Matsushima and T. Shimobaba, “Band-Limited Angular Spectrum Method for Numerical Simulation of Free-Space Propagation in Far and Near Fields,” Opt. Express 17(22), 19662–19673 (2009).
    [Crossref]
  26. J.-P. Liu, “Controlling the aliasing by zero-padding in the digital calculation of the scalar diffraction,” J. Opt. Soc. Am. A 29(9), 1956–1964 (2012).
    [Crossref]
  27. J. Jia, J. Si, and D. Chu, “Fast two-step layer-based method for computer generated hologram using sub-sparse 2D fast Fourier transform,” Opt. Express 26(13), 17487–17497 (2018).
    [Crossref]
  28. X. Yu, T. Xiahui, Q. Y. xiong, P. Hao, and W. Wei, “Wide-window angular spectrum method for diffraction propagation in far and near field,” Opt. Lett. 37(23), 4943–4945 (2012).
    [Crossref]
  29. 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]
  30. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), chap. 2.2.
  31. M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, M. Sypek, and A. Kolodziejczyk, “Simple holographic projection in color,” Opt. Express 20(22), 25130–25136 (2012).
    [Crossref]
  32. M. Makowski, “Minimized speckle noise in lens-less holographic projection by pixel separation,” Opt. Express 21(24), 29205–29216 (2013).
    [Crossref]
  33. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
    [Crossref]

2019 (2)

2018 (5)

2016 (1)

2015 (3)

2013 (3)

2012 (4)

2011 (1)

2010 (2)

2009 (4)

2008 (1)

2007 (1)

2006 (1)

2004 (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref]

1993 (1)

M. E. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
[Crossref]

1971 (1)

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3(5), 312–315 (1971).
[Crossref]

1969 (1)

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The Kinoform: A New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13(2), 150–155 (1969).
[Crossref]

Agour, M.

M. Agour, E. Kolenovic, C. Falldorf, and C. von Kopylow, “Suppression of higher diffraction orders and intensity improvement of optically reconstructed holograms from a spatial light modulator,” J. Opt. A: Pure Appl. Opt. 11(10), 105405 (2009).
[Crossref]

Akamatsu, T.

T. Sugie, T. Akamatsu, T. Nishitsuji, R. Hirayama, N. Masuda, H. Nakayama, Y. Ichihashi, A. Shiraki, M. Oikawa, N. Takada, Y. Endo, T. Kakue, T. Shimobaba, and T. Ito, “High-performance parallel computing for next-generation holographic imaging,” Nat. Electron. 1(4), 254–259 (2018).
[Crossref]

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref]

Cao, L.

Chang, C.

Chang, S.

Chen, B.-C.

Chen, C.

Chen, J.-S.

Chen, N.

Cho, J.

Choi, H.-J.

Chu, D.

Chu, D. P.

Dammann, H.

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3(5), 312–315 (1971).
[Crossref]

Daria, V. R.

Dong, J.-W.

Ducin, I.

Endo, Y.

T. Sugie, T. Akamatsu, T. Nishitsuji, R. Hirayama, N. Masuda, H. Nakayama, Y. Ichihashi, A. Shiraki, M. Oikawa, N. Takada, Y. Endo, T. Kakue, T. Shimobaba, and T. Ito, “High-performance parallel computing for next-generation holographic imaging,” Nat. Electron. 1(4), 254–259 (2018).
[Crossref]

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]

Falldorf, C.

M. Agour, E. Kolenovic, C. Falldorf, and C. von Kopylow, “Suppression of higher diffraction orders and intensity improvement of optically reconstructed holograms from a spatial light modulator,” J. Opt. A: Pure Appl. Opt. 11(10), 105405 (2009).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), chap. 2.2.

Görtler, K.

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3(5), 312–315 (1971).
[Crossref]

Hahn, J.

Hao, P.

Hasegawa, S.

He, H.-X.

Hirayama, R.

T. Sugie, T. Akamatsu, T. Nishitsuji, R. Hirayama, N. Masuda, H. Nakayama, Y. Ichihashi, A. Shiraki, M. Oikawa, N. Takada, Y. Endo, T. Kakue, T. Shimobaba, and T. Ito, “High-performance parallel computing for next-generation holographic imaging,” Nat. Electron. 1(4), 254–259 (2018).
[Crossref]

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]

Hirsch, P. M.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The Kinoform: A New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13(2), 150–155 (1969).
[Crossref]

Hiyama, D.

Hong, J.

Hoshikawa, N.

Ichihashi, Y.

T. Sugie, T. Akamatsu, T. Nishitsuji, R. Hirayama, N. Masuda, H. Nakayama, Y. Ichihashi, A. Shiraki, M. Oikawa, N. Takada, Y. Endo, T. Kakue, T. Shimobaba, and T. Ito, “High-performance parallel computing for next-generation holographic imaging,” Nat. Electron. 1(4), 254–259 (2018).
[Crossref]

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]

Ito, T.

Jia, J.

Jin, G.

Jordan, J. A.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The Kinoform: A New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13(2), 150–155 (1969).
[Crossref]

Kakarenko, K.

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, E.-S.

Kim, H.

Kim, S.

Kim, S.-C.

Kim, Y.

Kolenovic, E.

M. Agour, E. Kolenovic, C. Falldorf, and C. von Kopylow, “Suppression of higher diffraction orders and intensity improvement of optically reconstructed holograms from a spatial light modulator,” J. Opt. A: Pure Appl. Opt. 11(10), 105405 (2009).
[Crossref]

Kolodziejczyk, A.

Kong, D.

Lee, B.

Lesem, L. B.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The Kinoform: A New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13(2), 150–155 (1969).
[Crossref]

Li, X.

Liu, J.

Liu, J.-P.

Liu, S.

Liu, Y.-Z.

Lucente, M. E.

M. E. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
[Crossref]

Makowski, M.

Masuda, N.

Matsushima, K.

Min, S.-W.

Nagahama, Y.

Nakayama, H.

T. Sugie, T. Akamatsu, T. Nishitsuji, R. Hirayama, N. Masuda, H. Nakayama, Y. Ichihashi, A. Shiraki, M. Oikawa, N. Takada, Y. Endo, T. Kakue, T. Shimobaba, and T. Ito, “High-performance parallel computing for next-generation holographic imaging,” Nat. Electron. 1(4), 254–259 (2018).
[Crossref]

Nishitsuji, T.

T. Sugie, T. Akamatsu, T. Nishitsuji, R. Hirayama, N. Masuda, H. Nakayama, Y. Ichihashi, A. Shiraki, M. Oikawa, N. Takada, Y. Endo, T. Kakue, T. Shimobaba, and T. Ito, “High-performance parallel computing for next-generation holographic imaging,” Nat. Electron. 1(4), 254–259 (2018).
[Crossref]

T. Shimobaba, T. Takahashi, Y. Yamamoto, T. Nishitsuji, A. Shiraki, N. Hoshikawa, T. Kakue, and T. Ito, “Efficient diffraction calculations using implicit convolution,” OSA Continuum 1(2), 642–650 (2018).
[Crossref]

Oi, R.

Oikawa, M.

Okada, N.

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]

Palima, D.

Pan, Y.

Park, J.-H.

Park, S.

Pu, Y.-Y.

Qi, Y.

Sano, M.

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref]

Shimobaba, T.

Shiraki, A.

T. Sugie, T. Akamatsu, T. Nishitsuji, R. Hirayama, N. Masuda, H. Nakayama, Y. Ichihashi, A. Shiraki, M. Oikawa, N. Takada, Y. Endo, T. Kakue, T. Shimobaba, and T. Ito, “High-performance parallel computing for next-generation holographic imaging,” Nat. Electron. 1(4), 254–259 (2018).
[Crossref]

T. Shimobaba, T. Takahashi, Y. Yamamoto, T. Nishitsuji, A. Shiraki, N. Hoshikawa, T. Kakue, and T. Ito, “Efficient diffraction calculations using implicit convolution,” OSA Continuum 1(2), 642–650 (2018).
[Crossref]

N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, “Computer generated holography using a graphics processing unit,” Opt. Express 14(2), 603–608 (2006).
[Crossref]

Si, J.

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref]

Sugie, T.

T. Sugie, T. Akamatsu, T. Nishitsuji, R. Hirayama, N. Masuda, H. Nakayama, Y. Ichihashi, A. Shiraki, M. Oikawa, N. Takada, Y. Endo, T. Kakue, T. Shimobaba, and T. Ito, “High-performance parallel computing for next-generation holographic imaging,” Nat. Electron. 1(4), 254–259 (2018).
[Crossref]

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]

N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, “Computer generated holography using a graphics processing unit,” Opt. Express 14(2), 603–608 (2006).
[Crossref]

Sun, P.

Suszek, J.

Sypek, M.

Takada, N.

T. Sugie, T. Akamatsu, T. Nishitsuji, R. Hirayama, N. Masuda, H. Nakayama, Y. Ichihashi, A. Shiraki, M. Oikawa, N. Takada, Y. Endo, T. Kakue, T. Shimobaba, and T. Ito, “High-performance parallel computing for next-generation holographic imaging,” Nat. Electron. 1(4), 254–259 (2018).
[Crossref]

Takahashi, T.

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

Tanaka, T.

Tao, X.

von Kopylow, C.

M. Agour, E. Kolenovic, C. Falldorf, and C. von Kopylow, “Suppression of higher diffraction orders and intensity improvement of optically reconstructed holograms from a spatial light modulator,” J. Opt. A: Pure Appl. Opt. 11(10), 105405 (2009).
[Crossref]

Wang, C.

Wang, H.-Z.

Wang, J.

Wang, Q.-H.

Wang, X.

Wang, Y.

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref]

Wei, W.

Xia, J.

Xiahui, T.

Xiao, D.

Xie, J.

xiong, Q. Y.

Yamamoto, K.

Yamamoto, Y.

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]

Yu, X.

Zhang, H.

Zhao, Y.

Zheng, Z.

Appl. Opt. (6)

IBM J. Res. Dev. (1)

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The Kinoform: A New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13(2), 150–155 (1969).
[Crossref]

IEEE Trans. Image Process. (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref]

J. Disp. Technol. (1)

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]

J. Electron. Imaging (1)

M. E. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

M. Agour, E. Kolenovic, C. Falldorf, and C. von Kopylow, “Suppression of higher diffraction orders and intensity improvement of optically reconstructed holograms from a spatial light modulator,” J. Opt. A: Pure Appl. Opt. 11(10), 105405 (2009).
[Crossref]

J. Opt. Soc. Am. A (1)

Nat. Electron. (1)

T. Sugie, T. Akamatsu, T. Nishitsuji, R. Hirayama, N. Masuda, H. Nakayama, Y. Ichihashi, A. Shiraki, M. Oikawa, N. Takada, Y. Endo, T. Kakue, T. Shimobaba, and T. Ito, “High-performance parallel computing for next-generation holographic imaging,” Nat. Electron. 1(4), 254–259 (2018).
[Crossref]

Opt. Commun. (1)

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3(5), 312–315 (1971).
[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(7), 075801 (2012).
[Crossref]

Opt. Express (13)

X. Wang, H. Zhang, L. Cao, and G. Jin, “Generalized single-sideband three-dimensional computer-generated holography,” Opt. Express 27(3), 2612–2620 (2019).
[Crossref]

N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, “Computer generated holography using a graphics processing unit,” Opt. Express 14(2), 603–608 (2006).
[Crossref]

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]

J.-S. Chen and D. P. Chu, “Improved layer-based method for rapid hologram generation and real-time interactive holographic display applications,” Opt. Express 23(14), 18143–18155 (2015).
[Crossref]

Y.-Z. Liu, J.-W. Dong, Y.-Y. Pu, B.-C. Chen, H.-X. He, and H.-Z. Wang, “High-speed full analytical holographic computations for true-life scenes,” Opt. Express 18(4), 3345–3351 (2010).
[Crossref]

Y. Qi, C. Chang, and J. Xia, “Speckleless holographic display by complex modulation based on double-phase method,” Opt. Express 24(26), 30368–30378 (2016).
[Crossref]

P. Sun, S. Chang, S. Liu, X. Tao, C. Wang, and Z. Zheng, “Holographic near-eye display system based on double-convergence light gerchberg-saxton algorithm,” Opt. Express 26(8), 10140–10151 (2018).
[Crossref]

J. Jia, J. Si, and D. Chu, “Fast two-step layer-based method for computer generated hologram using sub-sparse 2D fast Fourier transform,” Opt. Express 26(13), 17487–17497 (2018).
[Crossref]

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]

K. Matsushima and T. Shimobaba, “Band-Limited Angular Spectrum Method for Numerical Simulation of Free-Space Propagation in Far and Near Fields,” Opt. Express 17(22), 19662–19673 (2009).
[Crossref]

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]

M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, M. Sypek, and A. Kolodziejczyk, “Simple holographic projection in color,” Opt. Express 20(22), 25130–25136 (2012).
[Crossref]

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

Opt. Lett. (3)

OSA Continuum (1)

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), chap. 2.2.

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Figures (13)

Fig. 1.
Fig. 1. Angular-spectrum method.
Fig. 2.
Fig. 2. Generation of POH with zero-padding method.
Fig. 3.
Fig. 3. Intermediate angular-spectrum method.
Fig. 4.
Fig. 4. Generation of IPOH and the reconstruction system.
Fig. 5.
Fig. 5. The calculation time and the $Ratio$ of the proposed method and the zero-padding method with different resolution of the input image.
Fig. 6.
Fig. 6. Numerical reconstruction results: (a) input image, reconstructed image with (b) zero-padding method and (c) proposed method.
Fig. 7.
Fig. 7. Numerical results: (a) PSNR and (b) speckle contrast of the reconstructed results of zero-padding method and proposed method with different $N_s$. (c) The calculation time and (d) time ratio of the zero-padding method and proposed method with different $N_s$.
Fig. 8.
Fig. 8. Schematic of optical setup.
Fig. 9.
Fig. 9. Optical results of the zero-padding method and proposed method. (a) and (c) are the reconstruction results of the zero-padding method without and with 4-$f$ filter system, respectively. (b) and (d) are the reconstruction results of the proposed method without and with DC filter, respectively.
Fig. 10.
Fig. 10. Optical results of the zero-padding method and proposed method with RPI method. (a)-(c) Reconstruction results of the zero-padding method when the exposure time is 1/6 s, 1/3 s, 1/2 s, respectively. (d)-(f) Reconstruction results of the proposed method when exposure time is 1/6 s, 1/3 s, 1/2 s, respectively.
Fig. 11.
Fig. 11. 3-D reconstructed results of the proposed method in on-axis holographic reconstruction with the reconstruction distance: (a) $z=0.26$ m, (b) $z=0.28$ m, (c) $z=0.30$ m and (d) $z=0.32$ m.
Fig. 12.
Fig. 12. Reconstruction quality of the proposed method with different focal length: (a) PSNR and (b) SSIM of the reconstruction results.
Fig. 13.
Fig. 13. Objects with different sampling interval

Tables (1)

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Table 1. Calculation Times and Time Ratio

Equations (15)

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U z ( x 1 , y 1 ) = I F F T { F F T { U 0 ( x , y ) } H f ( f x , f y ) } ,
H f ( f x , f y ) = e x p ( i k z 1 ( λ f x ) 2 ( λ f y ) 2 ) ,
U i ( f x i , f y i ) = F F T { U 0 ( x , y ) } H f i ( f x i , f y i ) ,
H f i ( f x i , f y i ) = e x p ( i k z 1 ( λ f x i ) 2 ( λ f y i ) 2 ) .
Δ f x i = Δ x S L M λ f , Δ f y i = Δ y S L M λ f .
ϕ ( f x i ) = k z 1 ( λ f x i ) 2 , f l = 1 2 π ϕ f x i = f x i z [ λ 2 f x i 2 ] .
1 Δ f x i 2 | f l | .
z λ 2 f x i 2 2 Δ f x i f x i ,
z λ f 4 f 2 Δ x S L M 2 N 2 2 Δ x S L M 2 N ,
Δ x F = λ f Δ x S L M N , Δ y F = λ f Δ y S L M N ,
S x = λ f Δ x S L M Δ x N = λ f ( Δ x S L M ) 2 N , S y = λ f Δ y S L M Δ y N = λ f ( Δ y S L M ) 2 N .
R a t i o = T z e r o p a d d i n g T p r o p o s e d .
P S N R = 10 l o g { 255 2 1 M N i = 0 M 1 j = 0 N 1 ( I 0 ( i , j ) I r ( i , j ) ) 2 } ,
C = σ μ ,
f m a x = s i n θ λ = 1 2 Δ x , s i n θ = λ 2 Δ x .

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