Abstract

This paper presents a novel approach to optimizing the design of phase-only computer-generated holograms (CGH) for the creation of binary images in an optical Fourier transform system. Optimization begins by selecting an image pixel with a temporal change in amplitude. The modulated image function undergoes an inverse Fourier transform followed by the imposition of a CGH constraint and the Fourier transform to yield an image function associated with the change in amplitude of the selected pixel. In iterations where the quality of the image is improved, that image function is adopted as the input for the next iteration. In cases where the image quality is not improved, the image function before the pixel changed is used as the input. Thus, the proposed approach is referred to as the pixelwise hybrid input–output (PHIO) algorithm. The PHIO algorithm was shown to achieve image quality far exceeding that of the Gerchberg–Saxton (GS) algorithm. The benefits were particularly evident when the PHIO algorithm was equipped with a dynamic range of image intensities equivalent to the amplitude freedom of the image signal. The signal variation of images reconstructed from the GS algorithm was 1.0223, but only 0.2537 when using PHIO, i.e., a 75% improvement. Nonetheless, the proposed scheme resulted in a 10% degradation in diffraction efficiency and signal-to-noise ratio.

© 2017 Optical Society of America

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References

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    [Crossref]
  4. J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 193297 (1980).
    [Crossref]
  5. F. Wyrowski and O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A5, 1058–1065 (1988).
    [Crossref]
  6. B. Y. Gu, G. Z. Yang, and B.-Z. Dong, “General theory for performing an optical transform,” Appl. Opt. 25, 3197–3206 (1986).
    [Crossref]
  7. H. Wang, W. Yue, Q. Song, J. Liu, and G. Situ, “A hybrid Gerchberg-Saxton-like algorithm for DOE and CGH,” Opt. Lasers Engng. 89, 109–115 (2017).
    [Crossref]
  8. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).
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    [Crossref]
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    [Crossref]
  11. R. G. Dorsch, A. W. Lohmann, and S. Sinzinger, “Fresnel ping-pong algorithm for two-plane computer-generated hologram display,” Appl. Opt. 33, 869–875 (1994).
    [Crossref]
  12. F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A7, 961–969 (1990).
    [Crossref]
  13. W.-F. Hsu and M.-H. Weng, “Compact holographic projection display using liquid-crystal-on-silicon spatial light modulator,” Materials 9, 768 (2016).
    [Crossref]
  14. W.-F. Hsu, Y.-W. Chen, and Y.-H. Su, “Implementation of phase-shift patterns using a holographic projection system with phase-only diffractive optical elements,” Appl. Opt. 50, 3646–3652 (2011).
    [Crossref]
  15. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [Crossref]
  16. J.-N. Gillet and Y. Sheng, “Iterative simulated quenching for designing irregular-spot-array generators,” Appl. Opt. 39, 3456–3465 (2000).
    [Crossref]
  17. F. Zhang, J. Zhu, W. Yue, J. Wang, Q. Song, G. Situ, F. Wyrowski, and H. Huang, “An approach to increase efficiency of DOE based pupil shaping technique for off-axis illumination in optical lithography,” Opt. Express 23, 4482–4493 (2015).
    [Crossref]
  18. Y. Zhao, Y.-P. Li, and Q.-G. Zhou, “Vector iterative algorithm for the design of diffractive optical elements applied to uniform illumination,” Opt. Lett. 29, 664–666 (2004).
    [Crossref]
  19. S. Bergamini, B. Darquié, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of micro-trap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. B21, 1889–1894 (2004).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  24. M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26, 2788–2798 (1987).
    [Crossref]
  25. B. B. Chhetri, S. Yang, and T. Shimomura, “Stochastic approach in the efficient design of the direct-binary-search algorithm for hologram synthesis,” Appl. Opt. 39, 5956–5964 (2000).
    [Crossref]
  26. W.-F. Hsu, “Backward iterative quantization methods for designs of multilevel diffractive optical elements,” Opt. Express 13, 5052–5063 (2005).
    [Crossref]
  27. N. Yoshikawa and T. Yatagai, “Phase optimization of a kinoforms by simulated annealing,” Appl. Opt. 33, 863–868 (1994).
    [Crossref]

2017 (2)

2016 (2)

W.-F. Hsu and M.-H. Weng, “Compact holographic projection display using liquid-crystal-on-silicon spatial light modulator,” Materials 9, 768 (2016).
[Crossref]

F. Buccheri, G. D. Bruce, A. Trombettoni, D. Cassettari, H. Babujian, V. E. Korepin, and S. Sodano, “Holographic optical traps for atom-based topological Kondo devices,” New J. Phys. 18, 075012 (2016).
[Crossref]

2015 (1)

2014 (1)

T. Shimobaba, M. Makowski, T. Kakue, N. Okada, Y. Endo, R. Hirayama, D. Hiyama, S. Hasegawa, Y. Nagahama, and T. Ito, “Numerical investigation of lensless zoomable holographic multiple projections to tilted planes,” Opt. Commun. 333, 274–280 (2014).
[Crossref]

2011 (1)

2008 (1)

2005 (1)

2004 (2)

Y. Zhao, Y.-P. Li, and Q.-G. Zhou, “Vector iterative algorithm for the design of diffractive optical elements applied to uniform illumination,” Opt. Lett. 29, 664–666 (2004).
[Crossref]

S. Bergamini, B. Darquié, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of micro-trap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. B21, 1889–1894 (2004).
[Crossref]

2001 (1)

2000 (2)

1994 (2)

1990 (1)

F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A7, 961–969 (1990).
[Crossref]

1988 (1)

F. Wyrowski and O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A5, 1058–1065 (1988).
[Crossref]

1987 (1)

1986 (2)

1982 (1)

1980 (1)

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

1973 (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).

Akahori, H.

Allebach, J. P.

Anderson, M.

Babujian, H.

F. Buccheri, G. D. Bruce, A. Trombettoni, D. Cassettari, H. Babujian, V. E. Korepin, and S. Sodano, “Holographic optical traps for atom-based topological Kondo devices,” New J. Phys. 18, 075012 (2016).
[Crossref]

Bergamini, S.

S. Bergamini, B. Darquié, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of micro-trap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. B21, 1889–1894 (2004).
[Crossref]

Bowman, D.

Browaeys, A.

S. Bergamini, B. Darquié, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of micro-trap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. B21, 1889–1894 (2004).
[Crossref]

Bruce, G. D.

Bryngdahl, O.

F. Wyrowski and O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A5, 1058–1065 (1988).
[Crossref]

Buccheri, F.

F. Buccheri, G. D. Bruce, A. Trombettoni, D. Cassettari, H. Babujian, V. E. Korepin, and S. Sodano, “Holographic optical traps for atom-based topological Kondo devices,” New J. Phys. 18, 075012 (2016).
[Crossref]

Cassettari, D.

Chardonnet, V.

Chen, Y.-W.

Chhetri, B. B.

Darquié, B.

S. Bergamini, B. Darquié, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of micro-trap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. B21, 1889–1894 (2004).
[Crossref]

De Groot, C.

DeMarco, B.

Denny, S. J.

Dong, B.-Z.

Dorsch, R. G.

Endo, Y.

T. Shimobaba, M. Makowski, T. Kakue, N. Okada, Y. Endo, R. Hirayama, D. Hiyama, S. Hasegawa, Y. Nagahama, and T. Ito, “Numerical investigation of lensless zoomable holographic multiple projections to tilted planes,” Opt. Commun. 333, 274–280 (2014).
[Crossref]

Fienup, J. R.

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[Crossref]

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

Gallagher, N. C.

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).

Gillet, J.-N.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

Grangier, P.

S. Bergamini, B. Darquié, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of micro-trap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. B21, 1889–1894 (2004).
[Crossref]

Gu, B. Y.

Harte, T. L.

Hasegawa, S.

T. Shimobaba, M. Makowski, T. Kakue, N. Okada, Y. Endo, R. Hirayama, D. Hiyama, S. Hasegawa, Y. Nagahama, and T. Ito, “Numerical investigation of lensless zoomable holographic multiple projections to tilted planes,” Opt. Commun. 333, 274–280 (2014).
[Crossref]

Hirayama, R.

T. Shimobaba, M. Makowski, T. Kakue, N. Okada, Y. Endo, R. Hirayama, D. Hiyama, S. Hasegawa, Y. Nagahama, and T. Ito, “Numerical investigation of lensless zoomable holographic multiple projections to tilted planes,” Opt. Commun. 333, 274–280 (2014).
[Crossref]

Hirsch, P. M.

P. M. Hirsch, J. A. Jordan, and L. B. Lesem, “Method of making an object-dependent diffuser,” U.S. patent3,619,022 (9November1971).

Hiyama, D.

T. Shimobaba, M. Makowski, T. Kakue, N. Okada, Y. Endo, R. Hirayama, D. Hiyama, S. Hasegawa, Y. Nagahama, and T. Ito, “Numerical investigation of lensless zoomable holographic multiple projections to tilted planes,” Opt. Commun. 333, 274–280 (2014).
[Crossref]

Hsu, W.-F.

Huang, H.

Ireland, P.

Ito, T.

T. Shimobaba, M. Makowski, T. Kakue, N. Okada, Y. Endo, R. Hirayama, D. Hiyama, S. Hasegawa, Y. Nagahama, and T. Ito, “Numerical investigation of lensless zoomable holographic multiple projections to tilted planes,” Opt. Commun. 333, 274–280 (2014).
[Crossref]

Jacubowiez, L.

S. Bergamini, B. Darquié, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of micro-trap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. B21, 1889–1894 (2004).
[Crossref]

Jones, M.

S. Bergamini, B. Darquié, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of micro-trap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. B21, 1889–1894 (2004).
[Crossref]

Jordan, J. A.

P. M. Hirsch, J. A. Jordan, and L. B. Lesem, “Method of making an object-dependent diffuser,” U.S. patent3,619,022 (9November1971).

Kakue, T.

T. Shimobaba, M. Makowski, T. Kakue, N. Okada, Y. Endo, R. Hirayama, D. Hiyama, S. Hasegawa, Y. Nagahama, and T. Ito, “Numerical investigation of lensless zoomable holographic multiple projections to tilted planes,” Opt. Commun. 333, 274–280 (2014).
[Crossref]

Korepin, V. E.

F. Buccheri, G. D. Bruce, A. Trombettoni, D. Cassettari, H. Babujian, V. E. Korepin, and S. Sodano, “Holographic optical traps for atom-based topological Kondo devices,” New J. Phys. 18, 075012 (2016).
[Crossref]

Le Goc, G.

Lesem, L. B.

P. M. Hirsch, J. A. Jordan, and L. B. Lesem, “Method of making an object-dependent diffuser,” U.S. patent3,619,022 (9November1971).

Li, Y.-P.

Liu, B.

Liu, J.

H. Wang, W. Yue, Q. Song, J. Liu, and G. Situ, “A hybrid Gerchberg-Saxton-like algorithm for DOE and CGH,” Opt. Lasers Engng. 89, 109–115 (2017).
[Crossref]

Lohmann, A. W.

Makowski, M.

T. Shimobaba, M. Makowski, T. Kakue, N. Okada, Y. Endo, R. Hirayama, D. Hiyama, S. Hasegawa, Y. Nagahama, and T. Ito, “Numerical investigation of lensless zoomable holographic multiple projections to tilted planes,” Opt. Commun. 333, 274–280 (2014).
[Crossref]

Mellin, S. D.

Nagahama, Y.

T. Shimobaba, M. Makowski, T. Kakue, N. Okada, Y. Endo, R. Hirayama, D. Hiyama, S. Hasegawa, Y. Nagahama, and T. Ito, “Numerical investigation of lensless zoomable holographic multiple projections to tilted planes,” Opt. Commun. 333, 274–280 (2014).
[Crossref]

Nordin, G. P.

Okada, N.

T. Shimobaba, M. Makowski, T. Kakue, N. Okada, Y. Endo, R. Hirayama, D. Hiyama, S. Hasegawa, Y. Nagahama, and T. Ito, “Numerical investigation of lensless zoomable holographic multiple projections to tilted planes,” Opt. Commun. 333, 274–280 (2014).
[Crossref]

Pasienski, M.

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).

Seldowitz, M. A.

Sheng, Y.

Shimobaba, T.

T. Shimobaba, M. Makowski, T. Kakue, N. Okada, Y. Endo, R. Hirayama, D. Hiyama, S. Hasegawa, Y. Nagahama, and T. Ito, “Numerical investigation of lensless zoomable holographic multiple projections to tilted planes,” Opt. Commun. 333, 274–280 (2014).
[Crossref]

Shimomura, T.

Sinzinger, S.

Situ, G.

Sodano, S.

F. Buccheri, G. D. Bruce, A. Trombettoni, D. Cassettari, H. Babujian, V. E. Korepin, and S. Sodano, “Holographic optical traps for atom-based topological Kondo devices,” New J. Phys. 18, 075012 (2016).
[Crossref]

Song, Q.

Su, Y.-H.

Sweeney, D. W.

Trombettoni, A.

F. Buccheri, G. D. Bruce, A. Trombettoni, D. Cassettari, H. Babujian, V. E. Korepin, and S. Sodano, “Holographic optical traps for atom-based topological Kondo devices,” New J. Phys. 18, 075012 (2016).
[Crossref]

Wang, H.

H. Wang, W. Yue, Q. Song, J. Liu, and G. Situ, “A hybrid Gerchberg-Saxton-like algorithm for DOE and CGH,” Opt. Lasers Engng. 89, 109–115 (2017).
[Crossref]

Wang, J.

Weng, M.-H.

W.-F. Hsu and M.-H. Weng, “Compact holographic projection display using liquid-crystal-on-silicon spatial light modulator,” Materials 9, 768 (2016).
[Crossref]

Wyrowski, F.

F. Zhang, J. Zhu, W. Yue, J. Wang, Q. Song, G. Situ, F. Wyrowski, and H. Huang, “An approach to increase efficiency of DOE based pupil shaping technique for off-axis illumination in optical lithography,” Opt. Express 23, 4482–4493 (2015).
[Crossref]

F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A7, 961–969 (1990).
[Crossref]

F. Wyrowski and O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A5, 1058–1065 (1988).
[Crossref]

Yang, G. Z.

Yang, S.

Yatagai, T.

Yoshikawa, N.

Yue, W.

Zhang, F.

Zhao, Y.

Zhou, Q.-G.

Zhu, J.

Appl. Opt. (10)

N. C. Gallagher and B. Liu, “Method for computing kinoforms that reduces image reconstruction error,” Appl. Opt. 12, 2328–2335 (1973).
[Crossref]

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[Crossref]

H. Akahori, “Spectrum leveling by an iterative algorithm with a dummy area for synthesizing the kinoform,” Appl. Opt. 25, 802–811 (1986).
[Crossref]

B. Y. Gu, G. Z. Yang, and B.-Z. Dong, “General theory for performing an optical transform,” Appl. Opt. 25, 3197–3206 (1986).
[Crossref]

M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26, 2788–2798 (1987).
[Crossref]

N. Yoshikawa and T. Yatagai, “Phase optimization of a kinoforms by simulated annealing,” Appl. Opt. 33, 863–868 (1994).
[Crossref]

R. G. Dorsch, A. W. Lohmann, and S. Sinzinger, “Fresnel ping-pong algorithm for two-plane computer-generated hologram display,” Appl. Opt. 33, 869–875 (1994).
[Crossref]

J.-N. Gillet and Y. Sheng, “Iterative simulated quenching for designing irregular-spot-array generators,” Appl. Opt. 39, 3456–3465 (2000).
[Crossref]

B. B. Chhetri, S. Yang, and T. Shimomura, “Stochastic approach in the efficient design of the direct-binary-search algorithm for hologram synthesis,” Appl. Opt. 39, 5956–5964 (2000).
[Crossref]

W.-F. Hsu, Y.-W. Chen, and Y.-H. Su, “Implementation of phase-shift patterns using a holographic projection system with phase-only diffractive optical elements,” Appl. Opt. 50, 3646–3652 (2011).
[Crossref]

J. Opt. Soc. Am. (3)

S. Bergamini, B. Darquié, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of micro-trap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. B21, 1889–1894 (2004).
[Crossref]

F. Wyrowski and O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A5, 1058–1065 (1988).
[Crossref]

F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A7, 961–969 (1990).
[Crossref]

Materials (1)

W.-F. Hsu and M.-H. Weng, “Compact holographic projection display using liquid-crystal-on-silicon spatial light modulator,” Materials 9, 768 (2016).
[Crossref]

New J. Phys. (1)

F. Buccheri, G. D. Bruce, A. Trombettoni, D. Cassettari, H. Babujian, V. E. Korepin, and S. Sodano, “Holographic optical traps for atom-based topological Kondo devices,” New J. Phys. 18, 075012 (2016).
[Crossref]

Opt. Commun. (1)

T. Shimobaba, M. Makowski, T. Kakue, N. Okada, Y. Endo, R. Hirayama, D. Hiyama, S. Hasegawa, Y. Nagahama, and T. Ito, “Numerical investigation of lensless zoomable holographic multiple projections to tilted planes,” Opt. Commun. 333, 274–280 (2014).
[Crossref]

Opt. Eng. (1)

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

Opt. Express (5)

Opt. Lasers Engng. (1)

H. Wang, W. Yue, Q. Song, J. Liu, and G. Situ, “A hybrid Gerchberg-Saxton-like algorithm for DOE and CGH,” Opt. Lasers Engng. 89, 109–115 (2017).
[Crossref]

Opt. Lett. (1)

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 (2)

P. M. Hirsch, J. A. Jordan, and L. B. Lesem, “Method of making an object-dependent diffuser,” U.S. patent3,619,022 (9November1971).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

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Figures (12)

Fig. 1.
Fig. 1.

Schematic diagram showing optical Fourier transform system for diffractive imaging.

Fig. 2.
Fig. 2.

Schematic diagram of error-reduction approach.

Fig. 3.
Fig. 3.

Flowchart of pixelwise hybrid input–output (PHIO) algorithm.

Fig. 4.
Fig. 4.

Desired (target) image comprising 128×128 binary pixels.

Fig. 5.
Fig. 5.

Evolution of image parameters (a) root-mean-square error e; diffraction efficiency η; (b) signal-to-noise ratio σ; signal variation υ; and (c) the rejection and acceptance rates of the tenth CGH derived using the PHIO algorithm.

Fig. 6.
Fig. 6.

(a) Bird’s-eye view and (b) side view of the simulation image reconstructed from CGH derived using the PHIO algorithm.

Fig. 7.
Fig. 7.

Schematic diagram showing use of dynamic range for intensity clamping.

Fig. 8.
Fig. 8.

CGH performance in 20 sets of dynamic range boundaries (a, b). Note that e, root-mean-squared error; η, diffraction efficiency; σ, signal-to-noise ratio; υ, signal variation.

Fig. 9.
Fig. 9.

(a) Bird’s-eye view and (b) side view of the simulation image reconstructed from CGH derived using the PHIO algorithm with a=b=0.1.

Fig. 10.
Fig. 10.

(a) Target and (b) simulation images reconstructed from CGH derived using the PHIO algorithm with a=0.05 and b=0.1 for the second target.

Fig. 11.
Fig. 11.

(a) Bird’s-eye view and (b) side view of the simulation image reconstructed from CGH derived using the GS algorithm.

Fig. 12.
Fig. 12.

Histograms of images reconstructed from CGHs derived using GS (red), PHIO (green), and PHIO algorithm with dynamic range of a=0.1 and b=0.1 (blue).

Tables (1)

Tables Icon

Table 1. Image Performance (Signal Variation υ; Root-Mean-Square Error e; Diffraction Efficiency η; Signal-to-Noise Ratio σ) of CGHs Designed Using the GS Algorithm, PHIO, and PHIO with a=b=0.1

Equations (10)

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

F(u)=|F(u)|exp[jψ(u)]=F{f(x)}=f(x)exp(j2πu·x)dx,
Gk+1(u)={α1Gk(u)+β1Gk(u)for  uγ,α2Gk(u)β2Gk(u)for  uγ,
Gk+1(u)={p{Gk(u)}for  uγ,p{Gk(u)}for  uγ,
p{G(u)}={|F(us)|·exp[jϕ(us)]for  u=us,G(u)otherwise,
e=meanS+N|IFIG|2,
η=SIG/S+NIG,
σ=minSIG/maxNIG,
υ=(maxSIGminSIG)/meanSIG,
C=w1e+w2η+w3σ+w4υ,
p{G(u)}={(1±a)·exp[jϕ(us)]|F(us)|=1&|G(us)1|>a,b·exp[jϕ(us)]|F(us)|=0&|G(us)|>b,G(u)otherwise,

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