Abstract

Conventional head-mounted displays present different images to each eye, and thereby create three-dimensional (3D) sensation for viewers. This method can only control the stimulus to vergence but not accommodation, which is located at the apparent location of the physical displays. The disrupted coupling between vergence and accommodation could cause considerable visual discomfort. To address this problem, in this paper a novel multi-focal plane 3D display system is proposed. A stack of switchable liquid crystal Pancharatnam-Berry phase lenses is implemented to create real depths for each eye, which is able to provide approximate focus cue and relieve the discomfort from vergence-accommodation conflict. The proposed multi-focal plane generation method has great potential for both virtual reality and augmented reality applications, where correct focus cue is highly desirable.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article

Corrections

Tao Zhan, Yun-Han Lee, and Shin-Tson Wu, "High-resolution additive light field near-eye display by switchable Pancharatnam–Berry phase lenses: errata," Opt. Express 26, 28505-28505 (2018)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-26-22-28505

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References

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    [Crossref]
  27. T. F. Coleman and Y. Li, “A reflective Newton method for minimizing a quadratic function subject to bounds on some of the variables,” SIAM J. Optim. 6(4), 1040–1058 (1996).
    [Crossref]
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    [Crossref]
  29. H. Ren, S. Xu, Y. Liu, and S. T. Wu, “Switchable focus using a polymeric lenticular microlens array and a polarization rotator,” Opt. Express 21(7), 7916–7925 (2013).
    [Crossref] [PubMed]

2017 (2)

N. Matsuda, A. Fix, and D. Lanman, “Focal surface displays,” ACM Trans. Graph. 36(4), 86 (2017).
[Crossref]

Y. H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S. T. Wu, “Recent progress in Pancharatnam-Berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3(1), 79–88 (2017).
[Crossref]

2016 (4)

Y. Ke, Y. Liu, J. Zhou, Y. Liu, H. Luo, and S. Wen, “Optical integration of Pancharatnam-Berry phase lens and dynamical phase lens,” Appl. Phys. Lett. 108(10), 101102 (2016).
[Crossref]

S. Lee, C. Jang, S. Moon, J. Cho, and B. Lee, “Additive light field displays: realization of augmented reality with holographic optical elements,” ACM Trans. Graph. 35(4), 60 (2016).
[Crossref]

Y. H. Lee, F. Peng, and S. T. Wu, “Fast-response switchable lens for 3D and wearable displays,” Opt. Express 24(2), 1668–1675 (2016).
[Crossref] [PubMed]

C.-K. Lee, S. Moon, S. Lee, D. Yoo, J.-Y. Hong, and B. Lee, “Compact three-dimensional head-mounted display system with Savart plate,” Opt. Express 24(17), 19531–19544 (2016).
[Crossref] [PubMed]

2015 (6)

2013 (4)

H. Ren, S. Xu, Y. Liu, and S. T. Wu, “Switchable focus using a polymeric lenticular microlens array and a polarization rotator,” Opt. Express 21(7), 7916–7925 (2013).
[Crossref] [PubMed]

D. Lanman and D. Luebke, “Near-eye light field displays,” ACM Trans. Graph. 32(6), 220 (2013).
[Crossref]

J. Geng, “Three-dimensional display technologies,” Adv. Opt. Photonics 5(4), 456–535 (2013).
[Crossref] [PubMed]

B. Lee, “Three-dimensional displays, past and present,” Phys. Today 66(4), 36–41 (2013).
[Crossref]

2011 (1)

2010 (1)

2009 (1)

2008 (1)

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence-accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vision 8(3), 1–30 (2008).
[Crossref] [PubMed]

2007 (1)

S. W. Lee and S. S. Lee, “Focal tunable liquid lens integrated with an electromagnetic actuator,” Appl. Phys. Lett. 90(12), 121129 (2007).
[Crossref]

2005 (1)

S. J. Watt, K. Akeley, M. O. Ernst, and M. S. Banks, “Focus cues affect perceived depth,” J. Vis. 5(10), 834–862 (2005).
[Crossref] [PubMed]

2003 (1)

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
[Crossref]

1996 (2)

E. Downing, L. Hesselink, J. Ralston, and R. Macfarlane, “A three-color, solid-state, three-dimensional display,” Science 273(5279), 1185–1189 (1996).
[Crossref]

T. F. Coleman and Y. Li, “A reflective Newton method for minimizing a quadratic function subject to bounds on some of the variables,” SIAM J. Optim. 6(4), 1040–1058 (1996).
[Crossref]

1993 (1)

M. Mon-Williams, J. P. Wann, and S. Rushton, “Binocular vision in a virtual world: visual deficits following the wearing of a head-mounted display,” Ophthalmic Physiol. Opt. 13(4), 387–391 (1993).
[Crossref] [PubMed]

1984 (1)

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. Lond. A 392 (1802), 45–57 (1984).
[Crossref]

1956 (1)

S. Pancharatnam, “Generalized theory of interference and its applications,” Proc. Indian Acad. Sci. Sect. A Phys. Sci. 44(5), 247–262 (1956).

Abdollahi, H.

Akeley, K.

S. Ravikumar, K. Akeley, and M. S. Banks, “Creating effective focus cues in multi-plane 3D displays,” Opt. Express 19(21), 20940–20952 (2011).
[Crossref] [PubMed]

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence-accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vision 8(3), 1–30 (2008).
[Crossref] [PubMed]

S. J. Watt, K. Akeley, M. O. Ernst, and M. S. Banks, “Focus cues affect perceived depth,” J. Vis. 5(10), 834–862 (2005).
[Crossref] [PubMed]

Banks, M. S.

S. Ravikumar, K. Akeley, and M. S. Banks, “Creating effective focus cues in multi-plane 3D displays,” Opt. Express 19(21), 20940–20952 (2011).
[Crossref] [PubMed]

G. D. Love, D. M. Hoffman, P. J. W. Hands, J. Gao, A. K. Kirby, and M. S. Banks, “High-speed switchable lens enables the development of a volumetric stereoscopic display,” Opt. Express 17(18), 15716–15725 (2009).
[Crossref] [PubMed]

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence-accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vision 8(3), 1–30 (2008).
[Crossref] [PubMed]

S. J. Watt, K. Akeley, M. O. Ernst, and M. S. Banks, “Focus cues affect perceived depth,” J. Vis. 5(10), 834–862 (2005).
[Crossref] [PubMed]

Berry, M. V.

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. Lond. A 392 (1802), 45–57 (1984).
[Crossref]

Bhowmik, A. K.

Biener, G.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
[Crossref]

Bos, P. J.

Chen, K.

F. C. Huang, K. Chen, and G. Wetzstein, “The light field stereoscope: immersive computer graphics via factored near-eye light field displays with focus cues,” ACM Trans. Graph. 34(4), 60 (2015).
[Crossref]

Cheng, H. H.

Cho, J.

S. Lee, C. Jang, S. Moon, J. Cho, and B. Lee, “Additive light field displays: realization of augmented reality with holographic optical elements,” ACM Trans. Graph. 35(4), 60 (2016).
[Crossref]

Coleman, T. F.

T. F. Coleman and Y. Li, “A reflective Newton method for minimizing a quadratic function subject to bounds on some of the variables,” SIAM J. Optim. 6(4), 1040–1058 (1996).
[Crossref]

Downing, E.

E. Downing, L. Hesselink, J. Ralston, and R. Macfarlane, “A three-color, solid-state, three-dimensional display,” Science 273(5279), 1185–1189 (1996).
[Crossref]

Ernst, M. O.

S. J. Watt, K. Akeley, M. O. Ernst, and M. S. Banks, “Focus cues affect perceived depth,” J. Vis. 5(10), 834–862 (2005).
[Crossref] [PubMed]

Escuti, M. J.

Fix, A.

N. Matsuda, A. Fix, and D. Lanman, “Focal surface displays,” ACM Trans. Graph. 36(4), 86 (2017).
[Crossref]

Gao, J.

Gao, K.

Gauza, S.

Y. H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S. T. Wu, “Recent progress in Pancharatnam-Berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3(1), 79–88 (2017).
[Crossref]

Geng, J.

J. Geng, “Three-dimensional display technologies,” Adv. Opt. Photonics 5(4), 456–535 (2013).
[Crossref] [PubMed]

Girshick, A. R.

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence-accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vision 8(3), 1–30 (2008).
[Crossref] [PubMed]

Gou, F.

Y. H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S. T. Wu, “Recent progress in Pancharatnam-Berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3(1), 79–88 (2017).
[Crossref]

Hands, P. J. W.

Hasman, E.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
[Crossref]

Hesselink, L.

E. Downing, L. Hesselink, J. Ralston, and R. Macfarlane, “A three-color, solid-state, three-dimensional display,” Science 273(5279), 1185–1189 (1996).
[Crossref]

Hoffman, D. M.

G. D. Love, D. M. Hoffman, P. J. W. Hands, J. Gao, A. K. Kirby, and M. S. Banks, “High-speed switchable lens enables the development of a volumetric stereoscopic display,” Opt. Express 17(18), 15716–15725 (2009).
[Crossref] [PubMed]

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence-accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vision 8(3), 1–30 (2008).
[Crossref] [PubMed]

Hong, J.-Y.

Hoskinson, R.

Hua, H.

Huang, F. C.

F. C. Huang, K. Chen, and G. Wetzstein, “The light field stereoscope: immersive computer graphics via factored near-eye light field displays with focus cues,” ACM Trans. Graph. 34(4), 60 (2015).
[Crossref]

Jang, C.

S. Lee, C. Jang, S. Moon, J. Cho, and B. Lee, “Additive light field displays: realization of augmented reality with holographic optical elements,” ACM Trans. Graph. 35(4), 60 (2016).
[Crossref]

Ke, Y.

Y. Ke, Y. Liu, J. Zhou, Y. Liu, H. Luo, and S. Wen, “Optical integration of Pancharatnam-Berry phase lens and dynamical phase lens,” Appl. Phys. Lett. 108(10), 101102 (2016).
[Crossref]

Kim, J.

Kimball, B. R.

N. V. Tabiryan, S. V. Serak, D. E. Roberts, D. M. Steeves, and B. R. Kimball, “Thin waveplate lenses of switchable focal length-new generation in optics,” Opt. Express 23(20), 25783–25794 (2015).
[Crossref] [PubMed]

N. V. Tabiryan, S. V. Serak, D. E. Roberts, D. M. Steeves, and B. R. Kimball, “Thin waveplate lenses: new generation in optics,” Proc. SPIE 9565, 956512 (2015).
[Crossref] [PubMed]

Kirby, A. K.

Kleiner, V.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
[Crossref]

Kudenov, M. W.

Lanman, D.

N. Matsuda, A. Fix, and D. Lanman, “Focal surface displays,” ACM Trans. Graph. 36(4), 86 (2017).
[Crossref]

D. Lanman and D. Luebke, “Near-eye light field displays,” ACM Trans. Graph. 32(6), 220 (2013).
[Crossref]

Lee, B.

S. Lee, C. Jang, S. Moon, J. Cho, and B. Lee, “Additive light field displays: realization of augmented reality with holographic optical elements,” ACM Trans. Graph. 35(4), 60 (2016).
[Crossref]

C.-K. Lee, S. Moon, S. Lee, D. Yoo, J.-Y. Hong, and B. Lee, “Compact three-dimensional head-mounted display system with Savart plate,” Opt. Express 24(17), 19531–19544 (2016).
[Crossref] [PubMed]

B. Lee, “Three-dimensional displays, past and present,” Phys. Today 66(4), 36–41 (2013).
[Crossref]

Lee, C.-K.

Lee, S.

C.-K. Lee, S. Moon, S. Lee, D. Yoo, J.-Y. Hong, and B. Lee, “Compact three-dimensional head-mounted display system with Savart plate,” Opt. Express 24(17), 19531–19544 (2016).
[Crossref] [PubMed]

S. Lee, C. Jang, S. Moon, J. Cho, and B. Lee, “Additive light field displays: realization of augmented reality with holographic optical elements,” ACM Trans. Graph. 35(4), 60 (2016).
[Crossref]

Lee, S. S.

S. W. Lee and S. S. Lee, “Focal tunable liquid lens integrated with an electromagnetic actuator,” Appl. Phys. Lett. 90(12), 121129 (2007).
[Crossref]

Lee, S. W.

S. W. Lee and S. S. Lee, “Focal tunable liquid lens integrated with an electromagnetic actuator,” Appl. Phys. Lett. 90(12), 121129 (2007).
[Crossref]

Lee, Y. H.

Y. H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S. T. Wu, “Recent progress in Pancharatnam-Berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3(1), 79–88 (2017).
[Crossref]

Y. H. Lee, F. Peng, and S. T. Wu, “Fast-response switchable lens for 3D and wearable displays,” Opt. Express 24(2), 1668–1675 (2016).
[Crossref] [PubMed]

Li, Y.

J. Kim, Y. Li, M. N. Miskiewicz, C. Oh, M. W. Kudenov, and M. J. Escuti, “Fabrication of ideal geometric-phase holograms with arbitrary wavefronts,” Optica 2(11), 958–964 (2015).
[Crossref]

T. F. Coleman and Y. Li, “A reflective Newton method for minimizing a quadratic function subject to bounds on some of the variables,” SIAM J. Optim. 6(4), 1040–1058 (1996).
[Crossref]

Liu, G.

Y. H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S. T. Wu, “Recent progress in Pancharatnam-Berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3(1), 79–88 (2017).
[Crossref]

Liu, S.

Liu, Y.

Y. Ke, Y. Liu, J. Zhou, Y. Liu, H. Luo, and S. Wen, “Optical integration of Pancharatnam-Berry phase lens and dynamical phase lens,” Appl. Phys. Lett. 108(10), 101102 (2016).
[Crossref]

Y. Ke, Y. Liu, J. Zhou, Y. Liu, H. Luo, and S. Wen, “Optical integration of Pancharatnam-Berry phase lens and dynamical phase lens,” Appl. Phys. Lett. 108(10), 101102 (2016).
[Crossref]

H. Ren, S. Xu, Y. Liu, and S. T. Wu, “Switchable focus using a polymeric lenticular microlens array and a polarization rotator,” Opt. Express 21(7), 7916–7925 (2013).
[Crossref] [PubMed]

Love, G. D.

Luebke, D.

D. Lanman and D. Luebke, “Near-eye light field displays,” ACM Trans. Graph. 32(6), 220 (2013).
[Crossref]

Luo, H.

Y. Ke, Y. Liu, J. Zhou, Y. Liu, H. Luo, and S. Wen, “Optical integration of Pancharatnam-Berry phase lens and dynamical phase lens,” Appl. Phys. Lett. 108(10), 101102 (2016).
[Crossref]

Macfarlane, R.

E. Downing, L. Hesselink, J. Ralston, and R. Macfarlane, “A three-color, solid-state, three-dimensional display,” Science 273(5279), 1185–1189 (1996).
[Crossref]

Matsuda, N.

N. Matsuda, A. Fix, and D. Lanman, “Focal surface displays,” ACM Trans. Graph. 36(4), 86 (2017).
[Crossref]

Miskiewicz, M. N.

Mon-Williams, M.

M. Mon-Williams, J. P. Wann, and S. Rushton, “Binocular vision in a virtual world: visual deficits following the wearing of a head-mounted display,” Ophthalmic Physiol. Opt. 13(4), 387–391 (1993).
[Crossref] [PubMed]

Moon, S.

S. Lee, C. Jang, S. Moon, J. Cho, and B. Lee, “Additive light field displays: realization of augmented reality with holographic optical elements,” ACM Trans. Graph. 35(4), 60 (2016).
[Crossref]

C.-K. Lee, S. Moon, S. Lee, D. Yoo, J.-Y. Hong, and B. Lee, “Compact three-dimensional head-mounted display system with Savart plate,” Opt. Express 24(17), 19531–19544 (2016).
[Crossref] [PubMed]

Niv, A.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
[Crossref]

Oh, C.

Pancharatnam, S.

S. Pancharatnam, “Generalized theory of interference and its applications,” Proc. Indian Acad. Sci. Sect. A Phys. Sci. 44(5), 247–262 (1956).

Park, H. S.

Peng, F.

Y. H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S. T. Wu, “Recent progress in Pancharatnam-Berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3(1), 79–88 (2017).
[Crossref]

Y. H. Lee, F. Peng, and S. T. Wu, “Fast-response switchable lens for 3D and wearable displays,” Opt. Express 24(2), 1668–1675 (2016).
[Crossref] [PubMed]

Ralston, J.

E. Downing, L. Hesselink, J. Ralston, and R. Macfarlane, “A three-color, solid-state, three-dimensional display,” Science 273(5279), 1185–1189 (1996).
[Crossref]

Ravikumar, S.

Ren, H.

Roberts, D. E.

N. V. Tabiryan, S. V. Serak, D. E. Roberts, D. M. Steeves, and B. R. Kimball, “Thin waveplate lenses: new generation in optics,” Proc. SPIE 9565, 956512 (2015).
[Crossref] [PubMed]

N. V. Tabiryan, S. V. Serak, D. E. Roberts, D. M. Steeves, and B. R. Kimball, “Thin waveplate lenses of switchable focal length-new generation in optics,” Opt. Express 23(20), 25783–25794 (2015).
[Crossref] [PubMed]

Rushton, S.

M. Mon-Williams, J. P. Wann, and S. Rushton, “Binocular vision in a virtual world: visual deficits following the wearing of a head-mounted display,” Ophthalmic Physiol. Opt. 13(4), 387–391 (1993).
[Crossref] [PubMed]

Serak, S. V.

N. V. Tabiryan, S. V. Serak, D. E. Roberts, D. M. Steeves, and B. R. Kimball, “Thin waveplate lenses: new generation in optics,” Proc. SPIE 9565, 956512 (2015).
[Crossref] [PubMed]

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N. V. Tabiryan, S. V. Serak, D. E. Roberts, D. M. Steeves, and B. R. Kimball, “Thin waveplate lenses: new generation in optics,” Proc. SPIE 9565, 956512 (2015).
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Y. H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S. T. Wu, “Recent progress in Pancharatnam-Berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3(1), 79–88 (2017).
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Y. Ke, Y. Liu, J. Zhou, Y. Liu, H. Luo, and S. Wen, “Optical integration of Pancharatnam-Berry phase lens and dynamical phase lens,” Appl. Phys. Lett. 108(10), 101102 (2016).
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F. C. Huang, K. Chen, and G. Wetzstein, “The light field stereoscope: immersive computer graphics via factored near-eye light field displays with focus cues,” ACM Trans. Graph. 34(4), 60 (2015).
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Figures (7)

Fig. 1
Fig. 1 (a) Example of relative phase change profile of a PBL with 0.5D optical power for LCP 550nm incident light. (b) Example of centrosymmetric spatial distribution of local optical axis in PBLs, in which azimuthal angles are approximately proportional to the square of the radius.
Fig. 2
Fig. 2 (a) The principle of the additive light field display is illustrated with a stack of PBLs. Each virtual image panel, formed by a specific state of PBLs stack, generates independent additive light fields, which are merged into a single light field. (b) Time-multiplexing driving scheme of 4 additive virtual panels. (c) Illustration of active and passive driving modes of PBLs.
Fig. 3
Fig. 3 Schematic diagram of additive light field mapping procedure. (a) A ray, generated from the 8th pixel in virtual panel 1 and the 7th pixel in virtual panel 2, appears like the 9th pixel in the 3D scene when seen from the 8th view point. (b) Matric description of merging the pixels in 2 virtual panels into the final light field. All the pixels in virtual panels are reshaped into a single vector in the way shown in the figure. Each row of the mapping matrix is calculated by the structure of the virtual panels.
Fig. 4
Fig. 4 (a) Simulation results of additive light field display with 25 view points and 4 virtual panels. The 25 images of the 3D scene (three teapots with different depths) is rendered computationally. (b) Optimized images to be displayed on the 4 virtual panels (depth increases from left to right).
Fig. 5
Fig. 5 (a) 3D scenes used for testing when observed from the center view point. (b) Relation of normalized brightness and PSNR with different contents. (c) Relation of normalized brightness and PSNR with different numbers of virtual panels (depths).
Fig. 6
Fig. 6 The optical setup of exposure procedure in the PBL fabrication process.
Fig. 7
Fig. 7 Experimental results of the high-resolution additive light field 3D display system. The optimized images for the discrete virtual panels in Fig. 4(b) are utilized in this demonstration. The focal depth of the camera increases from (a) to (c). Red pot is the closest to the viewer while the green one is the farthest.

Tables (1)

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Table 1 Parameters of the prototype system

Equations (7)

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J ± = 1 2 [ 1 ± j ] ,
J ± ' = R ( ψ ) W ( π ) R ( ψ ) J ± = [ cos ψ sin ψ sin ψ cos ψ ] [ e j π 2 0 0 e j π 2 ] [ cos ψ sin ψ sin ψ cos ψ ] 1 2 [ 1 ± j ] = j e ± 2 j ψ 2 [ 1 j ] = j e ± 2 j ψ J ,
± 2 ψ ( r ) = φ ( r ) = ω c ( r 2 + F 2 F ) ,
I t o t a l = I 1 + I 2 + + I i ,
θ x = tan 1 r x r z , θ y = tan 1 r y r z ,
L ( x , y , θ x , θ y ) = i = 1 N I i ( x + h i tan θ x , y + h i tan θ y ) ,
arg min L T 2 , L = M [ I 1 I 2 I N ] , T = [ T 1 T 2 T K ] ,

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