Abstract

Augmented reality (AR) using a holographic head-mounted display has been attracting a great deal of attention. In the AR system, computer-generated holograms (CGHs) are calculated and displayed on an electronic display. However, the time required for making CGHs is very long. Here, we propose a fast calculation method for arbitrary viewpoint movements in holographic AR systems. The calculation uses a Fourier transform optical system to enlarge the visual field of electroholography. In experiments, the generation time of the proposed method was approximately twice as fast as that of the conventional method. Furthermore, the quality of the CGHs generated by our method was sufficiently high.

© 2019 Optical Society of America

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References

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2019 (1)

H. Gao, F. Xu, J. Liu, Z. Dai, W. Zhou, S. Li, Y. Yu, and H. Zheng, “Holographic three-dimensional virtual reality and augmented reality display based on 4k-spatial light modulators,” Appl. Sci. 9, 1182 (2019).
[Crossref]

2018 (2)

T. Yoneyama, E. Murakami, Y. Oguro, H. Kubo, K. Yamaguchi, and Y. Sakamoto, “Holographic head-mounted display with correct accommodation and vergence stimuli,” Opt. Eng. 57, 061619 (2018).
[Crossref]

A. Gilles and P. Gioia, “Real-time layer-based computer-generated hologram calculation for the Fourier transform optical system,” Appl. Opt. 57, 8508–8517 (2018).
[Crossref]

2017 (3)

2016 (2)

2015 (1)

2014 (1)

T. Yoneyama, T. Ichikawa, and Y. Sakamoto, “Semi-portable full-color electro-holographic display with small size,” Proc. SPIE 9006, 900617 (2014).
[Crossref]

2013 (1)

2012 (2)

Y. Sato and Y. Sakamoto, “Calculation method for reconstruction at arbitrary depth in CGH with Fourier transform optical system,” Proc. SPIE 8281, 82819W (2012).
[Crossref]

T. Kozacki, M. Kujawińska, G. Finke, B. Hennelly, and N. Pandey, “Extended viewing angle holographic display system with tilted SLMs in a circular configuration,” Appl. Opt. 51, 1771–1780 (2012).
[Crossref]

2011 (4)

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, 382–390 (2011).
[Crossref]

J. Carmigniani, B. Furht, M. Anisetti, P. Ceravolo, E. Damiani, and M. Ivkovic, “Augmented reality technologies, systems and applications,” Multimedia Tools Appl. 51, 341–377 (2011).
[Crossref]

M. Oikawa, T. Shimobaba, T. Yoda, H. Nakayama, A. Shiraki, N. Masuda, and T. Ito, “Time-division color electroholography using one-chip RGB LED and synchronizing controller,” Opt. Express 19, 12008–12013 (2011).
[Crossref]

K. Yamaguchi, T. Ichikawa, and Y. Sakamoto, “Calculation method for computer-generated holograms considering various reflectance distributions based on microfacets with various surface roughnesses,” Appl. Opt. 50, H195–H202 (2011).
[Crossref]

2010 (2)

R. Van Krevelen and R. Poelman, “A survey of augmented reality technologies, applications and limitations,” Int. J. Virtual Reality 9, 1 (2010).

A. Kato and Y. Sakamoto, “An electro holography using reflective LCD for enlarging visual field and viewing zone with the Fourier transform optical system in CGH,” Proc. SPIE 7619, 761910 (2010).
[Crossref]

2009 (3)

R. Häussler, S. Reichelt, N. Leister, E. Zschau, R. Missbach, and A. Schwerdtner, “Large real-time holographic displays: from prototypes to a consumer product,” Proc. SPIE 7237, 72370S (2009).
[Crossref]

M. Lambooij, W. IJsselsteijn, M. Fortuin, and I. Heynderickx, “Visual discomfort and visual fatigue of stereoscopic displays: a review,” J. Imaging Sci. Technol. 53, 030201 (2009).
[Crossref]

Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. A. Tanjung, C. Tan, and T.-C. Chong, “Fast CGH computation using S-LUT on GPU,” Opt. Express 17, 18543–18555 (2009).
[Crossref]

2008 (3)

1999 (1)

T. M. Lehmann, C. Gonner, and K. Spitzer, “Survey: interpolation methods in medical image processing,” IEEE Trans. Med. Imaging 18, 1049–1075 (1999).
[Crossref]

1993 (1)

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

1966 (1)

J. P. Waters, “Holographic image synthesis utilizing theoretical,” Appl. Phys. Lett. 9, 405–407 (1966).
[Crossref]

1958 (1)

Akeley, K.

A. R. Hoffman, D. M. Girshick, K. Akeley, and M. S. Banks, “Vergence-accommodation conflicts hinder visual performance and cause visual fatigue,” J. Visualization 8(3), 30–33 (2008).
[Crossref]

Anisetti, M.

J. Carmigniani, B. Furht, M. Anisetti, P. Ceravolo, E. Damiani, and M. Ivkovic, “Augmented reality technologies, systems and applications,” Multimedia Tools Appl. 51, 341–377 (2011).
[Crossref]

Banks, M. S.

A. R. Hoffman, D. M. Girshick, K. Akeley, and M. S. Banks, “Vergence-accommodation conflicts hinder visual performance and cause visual fatigue,” J. Visualization 8(3), 30–33 (2008).
[Crossref]

Carmigniani, J.

J. Carmigniani, B. Furht, M. Anisetti, P. Ceravolo, E. Damiani, and M. Ivkovic, “Augmented reality technologies, systems and applications,” Multimedia Tools Appl. 51, 341–377 (2011).
[Crossref]

Ceravolo, P.

J. Carmigniani, B. Furht, M. Anisetti, P. Ceravolo, E. Damiani, and M. Ivkovic, “Augmented reality technologies, systems and applications,” Multimedia Tools Appl. 51, 341–377 (2011).
[Crossref]

Chong, T.-C.

Dai, Z.

H. Gao, F. Xu, J. Liu, Z. Dai, W. Zhou, S. Li, Y. Yu, and H. Zheng, “Holographic three-dimensional virtual reality and augmented reality display based on 4k-spatial light modulators,” Appl. Sci. 9, 1182 (2019).
[Crossref]

Damiani, E.

J. Carmigniani, B. Furht, M. Anisetti, P. Ceravolo, E. Damiani, and M. Ivkovic, “Augmented reality technologies, systems and applications,” Multimedia Tools Appl. 51, 341–377 (2011).
[Crossref]

Duan, X.

Finke, G.

Fortuin, M.

M. Lambooij, W. IJsselsteijn, M. Fortuin, and I. Heynderickx, “Visual discomfort and visual fatigue of stereoscopic displays: a review,” J. Imaging Sci. Technol. 53, 030201 (2009).
[Crossref]

Furht, B.

J. Carmigniani, B. Furht, M. Anisetti, P. Ceravolo, E. Damiani, and M. Ivkovic, “Augmented reality technologies, systems and applications,” Multimedia Tools Appl. 51, 341–377 (2011).
[Crossref]

Gao, H.

H. Gao, F. Xu, J. Liu, Z. Dai, W. Zhou, S. Li, Y. Yu, and H. Zheng, “Holographic three-dimensional virtual reality and augmented reality display based on 4k-spatial light modulators,” Appl. Sci. 9, 1182 (2019).
[Crossref]

Gao, Q.

Gilles, A.

Gioia, P.

Girshick, D. M.

A. R. Hoffman, D. M. Girshick, K. Akeley, and M. S. Banks, “Vergence-accommodation conflicts hinder visual performance and cause visual fatigue,” J. Visualization 8(3), 30–33 (2008).
[Crossref]

Gonner, C.

T. M. Lehmann, C. Gonner, and K. Spitzer, “Survey: interpolation methods in medical image processing,” IEEE Trans. Med. Imaging 18, 1049–1075 (1999).
[Crossref]

Hahn, J.

Häussler, R.

R. Häussler, S. Reichelt, N. Leister, E. Zschau, R. Missbach, and A. Schwerdtner, “Large real-time holographic displays: from prototypes to a consumer product,” Proc. SPIE 7237, 72370S (2009).
[Crossref]

Hennelly, B.

Heynderickx, I.

M. Lambooij, W. IJsselsteijn, M. Fortuin, and I. Heynderickx, “Visual discomfort and visual fatigue of stereoscopic displays: a review,” J. Imaging Sci. Technol. 53, 030201 (2009).
[Crossref]

Hoffman, A. R.

A. R. Hoffman, D. M. Girshick, K. Akeley, and M. S. Banks, “Vergence-accommodation conflicts hinder visual performance and cause visual fatigue,” J. Visualization 8(3), 30–33 (2008).
[Crossref]

Ichikawa, T.

IJsselsteijn, W.

M. Lambooij, W. IJsselsteijn, M. Fortuin, and I. Heynderickx, “Visual discomfort and visual fatigue of stereoscopic displays: a review,” J. Imaging Sci. Technol. 53, 030201 (2009).
[Crossref]

Ito, T.

Ivkovic, M.

J. Carmigniani, B. Furht, M. Anisetti, P. Ceravolo, E. Damiani, and M. Ivkovic, “Augmented reality technologies, systems and applications,” Multimedia Tools Appl. 51, 341–377 (2011).
[Crossref]

Jiao, S.

Kato, A.

A. Kato and Y. Sakamoto, “An electro holography using reflective LCD for enlarging visual field and viewing zone with the Fourier transform optical system in CGH,” Proc. SPIE 7619, 761910 (2010).
[Crossref]

Kim, E.

Kim, H.

Kim, S.

Kozacki, T.

Kubo, H.

T. Yoneyama, E. Murakami, Y. Oguro, H. Kubo, K. Yamaguchi, and Y. Sakamoto, “Holographic head-mounted display with correct accommodation and vergence stimuli,” Opt. Eng. 57, 061619 (2018).
[Crossref]

Kujawinska, M.

Kurita, M.

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, 382–390 (2011).
[Crossref]

Lambooij, M.

M. Lambooij, W. IJsselsteijn, M. Fortuin, and I. Heynderickx, “Visual discomfort and visual fatigue of stereoscopic displays: a review,” J. Imaging Sci. Technol. 53, 030201 (2009).
[Crossref]

Lee, B.

Lehmann, T. M.

T. M. Lehmann, C. Gonner, and K. Spitzer, “Survey: interpolation methods in medical image processing,” IEEE Trans. Med. Imaging 18, 1049–1075 (1999).
[Crossref]

Leister, N.

R. Häussler, S. Reichelt, N. Leister, E. Zschau, R. Missbach, and A. Schwerdtner, “Large real-time holographic displays: from prototypes to a consumer product,” Proc. SPIE 7237, 72370S (2009).
[Crossref]

Li, S.

H. Gao, F. Xu, J. Liu, Z. Dai, W. Zhou, S. Li, Y. Yu, and H. Zheng, “Holographic three-dimensional virtual reality and augmented reality display based on 4k-spatial light modulators,” Appl. Sci. 9, 1182 (2019).
[Crossref]

Li, X.

Liang, X.

Lim, Y.

Liu, J.

H. Gao, F. Xu, J. Liu, Z. Dai, W. Zhou, S. Li, Y. Yu, and H. Zheng, “Holographic three-dimensional virtual reality and augmented reality display based on 4k-spatial light modulators,” Appl. Sci. 9, 1182 (2019).
[Crossref]

Q. Gao, J. Liu, X. Duan, T. Zhao, X. Li, and P. Liu, “Compact see-through 3D head-mounted display based on wavefront modulation with holographic grating filter,” Opt. Express 25, 8412–8424 (2017).
[Crossref]

Liu, P.

Lucente, M. E.

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

Manuri, F.

A. Sanna and F. Manuri, “A survey on applications of augmented reality,” Adv. Comput. Sci. 5, 18–27 (2016).

Masuda, N.

Miller, J. 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, 382–390 (2011).
[Crossref]

Missbach, R.

R. Häussler, S. Reichelt, N. Leister, E. Zschau, R. Missbach, and A. Schwerdtner, “Large real-time holographic displays: from prototypes to a consumer product,” Proc. SPIE 7237, 72370S (2009).
[Crossref]

Murakami, E.

T. Yoneyama, E. Murakami, Y. Oguro, H. Kubo, K. Yamaguchi, and Y. Sakamoto, “Holographic head-mounted display with correct accommodation and vergence stimuli,” Opt. Eng. 57, 061619 (2018).
[Crossref]

E. Murakami, Y. Oguro, and Y. Sakamoto, “Study on compact head-mounted display system using electro-holography for augmented reality,” IEICE Trans. Electron. E100.C, 965–971 (2017).
[Crossref]

Nakayama, H.

Oguro, Y.

T. Yoneyama, E. Murakami, Y. Oguro, H. Kubo, K. Yamaguchi, and Y. Sakamoto, “Holographic head-mounted display with correct accommodation and vergence stimuli,” Opt. Eng. 57, 061619 (2018).
[Crossref]

E. Murakami, Y. Oguro, and Y. Sakamoto, “Study on compact head-mounted display system using electro-holography for augmented reality,” IEICE Trans. Electron. E100.C, 965–971 (2017).
[Crossref]

Ohara, R.

Oi, R.

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, 382–390 (2011).
[Crossref]

Oikawa, M.

Okuyama, F.

Pan, Y.

Pandey, N.

Park, G.

Poelman, R.

R. Van Krevelen and R. Poelman, “A survey of augmented reality technologies, applications and limitations,” Int. J. Virtual Reality 9, 1 (2010).

Reichelt, S.

R. Häussler, S. Reichelt, N. Leister, E. Zschau, R. Missbach, and A. Schwerdtner, “Large real-time holographic displays: from prototypes to a consumer product,” Proc. SPIE 7237, 72370S (2009).
[Crossref]

Sakamoto, Y.

T. Yoneyama, E. Murakami, Y. Oguro, H. Kubo, K. Yamaguchi, and Y. Sakamoto, “Holographic head-mounted display with correct accommodation and vergence stimuli,” Opt. Eng. 57, 061619 (2018).
[Crossref]

E. Murakami, Y. Oguro, and Y. Sakamoto, “Study on compact head-mounted display system using electro-holography for augmented reality,” IEICE Trans. Electron. E100.C, 965–971 (2017).
[Crossref]

R. Watanabe, K. Yamaguchi, and Y. Sakamoto, “Fast calculation method of computer generated hologram animation for viewpoint parallel shift and rotation using Fourier transform optical system,” Appl. Opt. 55, A167–A177 (2016).
[Crossref]

R. Ohara, M. Kurita, T. Yonerama, F. Okuyama, and Y. Sakamoto, “Response of accommodation and vergence to electro-holographic images,” Appl. Opt. 54, 615–621 (2015).
[Crossref]

T. Yoneyama, T. Ichikawa, and Y. Sakamoto, “Semi-portable full-color electro-holographic display with small size,” Proc. SPIE 9006, 900617 (2014).
[Crossref]

T. Ichikawa, T. Yoneyama, and Y. Sakamoto, “CGH calculation with the ray tracing method for the Fourier transform optical system,” Opt. Express 21, 32019–32031 (2013).
[Crossref]

Y. Sato and Y. Sakamoto, “Calculation method for reconstruction at arbitrary depth in CGH with Fourier transform optical system,” Proc. SPIE 8281, 82819W (2012).
[Crossref]

K. Yamaguchi, T. Ichikawa, and Y. Sakamoto, “Calculation method for computer-generated holograms considering various reflectance distributions based on microfacets with various surface roughnesses,” Appl. Opt. 50, H195–H202 (2011).
[Crossref]

A. Kato and Y. Sakamoto, “An electro holography using reflective LCD for enlarging visual field and viewing zone with the Fourier transform optical system in CGH,” Proc. SPIE 7619, 761910 (2010).
[Crossref]

R. Watanabe, T. Sugawara, and Y. Sakamoto, “Fast calculation method of computer generated hologram using ray tracing method for Fourier transform optical system,” in 10th International Symposium on Display Holography P-16 (2015).

Sanna, A.

A. Sanna and F. Manuri, “A survey on applications of augmented reality,” Adv. Comput. Sci. 5, 18–27 (2016).

Sato, Y.

Y. Sato and Y. Sakamoto, “Calculation method for reconstruction at arbitrary depth in CGH with Fourier transform optical system,” Proc. SPIE 8281, 82819W (2012).
[Crossref]

Schwerdtner, A.

R. Häussler, S. Reichelt, N. Leister, E. Zschau, R. Missbach, and A. Schwerdtner, “Large real-time holographic displays: from prototypes to a consumer product,” Proc. SPIE 7237, 72370S (2009).
[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, 382–390 (2011).
[Crossref]

Shimobaba, T.

Shiraki, A.

Solanki, S.

Spitzer, K.

T. M. Lehmann, C. Gonner, and K. Spitzer, “Survey: interpolation methods in medical image processing,” IEEE Trans. Med. Imaging 18, 1049–1075 (1999).
[Crossref]

Sugawara, T.

R. Watanabe, T. Sugawara, and Y. Sakamoto, “Fast calculation method of computer generated hologram using ray tracing method for Fourier transform optical system,” in 10th International Symposium on Display Holography P-16 (2015).

Tan, C.

Tanjung, R. B. A.

Van Krevelen, R.

R. Van Krevelen and R. Poelman, “A survey of augmented reality technologies, applications and limitations,” Int. J. Virtual Reality 9, 1 (2010).

Watanabe, R.

R. Watanabe, K. Yamaguchi, and Y. Sakamoto, “Fast calculation method of computer generated hologram animation for viewpoint parallel shift and rotation using Fourier transform optical system,” Appl. Opt. 55, A167–A177 (2016).
[Crossref]

R. Watanabe, T. Sugawara, and Y. Sakamoto, “Fast calculation method of computer generated hologram using ray tracing method for Fourier transform optical system,” in 10th International Symposium on Display Holography P-16 (2015).

Waters, J. P.

J. P. Waters, “Holographic image synthesis utilizing theoretical,” Appl. Phys. Lett. 9, 405–407 (1966).
[Crossref]

Xu, F.

H. Gao, F. Xu, J. Liu, Z. Dai, W. Zhou, S. Li, Y. Yu, and H. Zheng, “Holographic three-dimensional virtual reality and augmented reality display based on 4k-spatial light modulators,” Appl. Sci. 9, 1182 (2019).
[Crossref]

Xu, X.

Yamaguchi, K.

Yamamoto, K.

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, 382–390 (2011).
[Crossref]

Yoda, T.

Yonerama, T.

Yoneyama, T.

T. Yoneyama, E. Murakami, Y. Oguro, H. Kubo, K. Yamaguchi, and Y. Sakamoto, “Holographic head-mounted display with correct accommodation and vergence stimuli,” Opt. Eng. 57, 061619 (2018).
[Crossref]

T. Yoneyama, T. Ichikawa, and Y. Sakamoto, “Semi-portable full-color electro-holographic display with small size,” Proc. SPIE 9006, 900617 (2014).
[Crossref]

T. Ichikawa, T. Yoneyama, and Y. Sakamoto, “CGH calculation with the ray tracing method for the Fourier transform optical system,” Opt. Express 21, 32019–32031 (2013).
[Crossref]

Yu, Y.

H. Gao, F. Xu, J. Liu, Z. Dai, W. Zhou, S. Li, Y. Yu, and H. Zheng, “Holographic three-dimensional virtual reality and augmented reality display based on 4k-spatial light modulators,” Appl. Sci. 9, 1182 (2019).
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Supplementary Material (2)

NameDescription
» Visualization 1       Results of the proposed method. (In the paper, all reconstructed images could not be displayed due to space limitations.)
» Visualization 2       Results of the proposed method. The CGH videos were generated while changing the speed of the viewpoint movements. (In the paper, all reconstructed images cannot be displayed due to space limitations.)

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Figures (24)

Fig. 1.
Fig. 1. Optical systems for electroholography: (a) ordinary optical system, (b) Fourier transform optical system.
Fig. 2.
Fig. 2. Calculation procedure of the conventional method [18].
Fig. 3.
Fig. 3. Optical system using a convergent spherical reference light.
Fig. 4.
Fig. 4. Fast calculation procedure for viewpoint movements.
Fig. 5.
Fig. 5. Parallel shift in the x direction.
Fig. 6.
Fig. 6. Rotation of a hologram plane on the y axis.
Fig. 7.
Fig. 7. Forward movement and the scaled hologram plane.
Fig. 8.
Fig. 8. Optical path difference caused by scaling.
Fig. 9.
Fig. 9. Position error caused by scaling: (a) correct object light waves, (b) scaled object light waves.
Fig. 10.
Fig. 10. Recalculation frequency of the front–back direction.
Fig. 11.
Fig. 11. Ray tracing from the elementary holograms in the viewpoint movements.
Fig. 12.
Fig. 12. Holographic display used in the experiments.
Fig. 13.
Fig. 13. Scene settings in the experiments: (a) scene A, (b) scene B, (c) scene C.
Fig. 14.
Fig. 14. Reconstructed images calculated using different reference lights of scene A, (a) normal reference light, (b) convergent reference light.
Fig. 15.
Fig. 15. Reconstructed images calculated using different reference lights of scene B, (a) normal reference light (focusing at z = 600 mm ), (b) convergent reference light (focusing at z = 600 mm ), (c) normal reference light (focusing at z = 700 mm ), (d) convergent reference light (focusing at z = 700 mm ).
Fig. 16.
Fig. 16. Reconstructed images calculated by different reference lights of scene B, (a) normal reference light (focusing at z = 200 mm ), (b) convergent reference light (focusing at z = 200 mm ), (c) normal reference light (focusing at z = 900 mm ), (d) convergent reference light (focusing at z = 900 mm ).
Fig. 17.
Fig. 17. Detail of the scene setting and the viewpoint movements in the experiments.
Fig. 18.
Fig. 18. Graph showing the generation time in various recalculation frequency R f . (a) Parallel shift, (b) rotation, (c) front–back movement, (d) combination.
Fig. 19.
Fig. 19. Graph of the relationship between the number of ray tracings and the recalculation frequency.
Fig. 20.
Fig. 20. Reconstructed images of the front–back movement (255th frame): (a)  R f = ( 1 , 1 , 1 ) (conventional), (b)  R f = ( 2 , 2 , 2 ) , (c)  R f = ( 4 , 2 , 1 ) , (d)  R f = ( 4 , 4 , 4 ) , (e)  R f = ( 8 , 4 , 2 ) , (f)  R f = ( 8 , 8 , 8 ) . (The reconstructed images of all frames are shown in Visualization 1.)
Fig. 21.
Fig. 21. Evaluation unit of the DCR method.
Fig. 22.
Fig. 22. Results of the subjective evaluation.
Fig. 23.
Fig. 23. Graph showing the relationship between the calculation time and the speed of viewpoint movements.
Fig. 24.
Fig. 24. Reconstructed images with the different speed for the parallel shift (please see Visualization 2). (a) Conventional ( 1 × / 150th frame), (b) proposed ( 1 × / 150th frame), (c) conventional ( 8 × / 20th frame), (d) proposed ( 8 × / 20th frame).

Tables (7)

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Table 1. Parameters of a Holographic Display Used in the Experiments

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Table 2. Computer Specifications for the CGH Calculation

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Table 3. Calculation Time Comparison Based on the Difference between the Normal and Convergent Reference Lights

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Table 4. Details of the Viewpoint Movements in the Experiments

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Table 5. Calculation Time of the Conventional Scheme and the Proposed Scheme (“conv” Means the Conventional Scheme, and “prop” Means the Proposed Scheme)

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Table 6. Generation Time of the CGH Movies at Various Recalculation Frequencies R f

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Table 7. Five-Point Scale of the DCR Method

Equations (23)

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θ ORD = 2 sin 1 ( λ 2 p ) ,
w = 2 f tan ( θ ORD 2 ) .
θ FTOS = 2 tan 1 ( w + L 2 f ) ,
z o = f A f A ,
x o = x i z o B ,
y o = y i z o B ,
A = z i ( f d ) + d 2 z i d f ,
B = A + d f A f .
u ( x h , y h ) = o = 1 O a o r o exp { j ( k r o + ϕ o ) } ,
r o = ( x o x h ) 2 + ( y o y h ) 2 + z o 2 ) ,
R c ( x h , y h ) = R 0 exp ( j k r h ( x h , y h ) ) .
I ( x h , y h ) = | u ( x h , y h ) + R c ( x h , y h ) | 2 = | u ( x h , y h ) | 2 + | R c ( x h , y h ) | 2 + u ( x h , y h ) R c * ( x h , y h ) + u * ( x h , y h ) R c ( x h , y h ) ,
L ( x h , y h ) = ( u ( x h , y h ) R c * ( x h , y h ) + u * ( x h , y h ) R c ( x h , y h ) ) exp ( j k α ) ,
α ( x h , y h ) = r h f = x h 2 + y h 2 + f 2 f .
u ( x h , y h ) R c * ( x h , y h ) exp ( j k α ) = u ( x h , y h ) R 0 exp ( j k r h ) exp ( j k ( r h f ) ) = u ( x h , y h ) R 0 exp ( j k f ) ,
u * ( x h , y h ) R c ( x h , y h ) exp ( j k α ) = u * ( x h , y h ) R 0 exp ( j k r h ) exp ( j k ( r h f ) ) = u * ( x h , y h ) R 0 exp ( j k ( 2 r h f ) ) .
L ( x h , y h ) = u ( x h , y h ) R 0 exp ( j k f ) + u * ( x h , y h ) R 0 exp ( j k ( 2 r h f ) ) .
u N ( x h , y h ) = u N 1 ( x h Δ x , y h ) ,
ϕ rot ( x h , y h ) = k x h sin θ rot ,
u N ( x h , y h ) = u N 1 ( x h , y h ) exp ( j ϕ rot ) .
s r = D c D p = D p + Δ D D p ,
r d ( x c , y c ) = ( r c ( x c , y c ) D c ) ( r p ( x p , y p ) D p ) ,
u N ( x c , y c ) = D p D c exp ( j k r d ( x c , y c ) ) u s ( x c , y c ) .

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