Abstract

A volumetric display that creates a distortion-free three-dimensional (3D) image in midair is described. The proposed system consists of rotating prism sheets used as an optical scanner and a dihedral corner reflector array (DCRA), which is a distortion-free imaging element. Two prism sheets are arranged in a symmetrical configuration to reduce an unnatural motion parallax caused by optical aberrations. A cross-section of the 3D image is formed by the DCRA in midair and moved by the rotating prism sheets to create a 3D displayable space. A 3D volume image was displayed without image distortion or unnatural motion parallax.

© 2013 Optical Society of America

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2013 (2)

2011 (2)

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-Dimensional Displays: A Review and Applications Analysis,” IEEE Trans. Broadcast57(2), 362–371 (2011).
[CrossRef]

M. Gately, Y. Zhai, M. Yeary, E. Petrich, and L. Sawalha, “A Three-Dimensional Swept Volume Display Based on LED Arrays,” J. Disp. Technol.7(9), 503–514 (2011).
[CrossRef]

2010 (1)

D. Miyazaki, N. Hirano, Y. Maeda, K. Ohno, and S. Maekawa, “Volumetric Display Using a Roof Mirror Grid Array,” in Stereoscopic Displays and Applications XXI, SPIE7524, 75240N, 75240N-9 (2010).
[CrossRef]

2009 (1)

H. H. Refai, “Static Volumetric Three-Dimensional Display,” J. Disp. Technol.5(10), 391–397 (2009).
[CrossRef]

2007 (2)

2006 (2)

2005 (1)

2004 (2)

A. Sullivan, “DepthCube Solid-state 3D Volumetric Display,” in Stereoscopic Display and Virtual Reality Systems XI, SPIE5291, 279–284 (2004).
[CrossRef]

P. Rosen, Z. Pizlo, C. Hoffmann, and V. Popescu, “Perception of 3d spatial relations for 3d displays,” In Stereoscopic Displays and Virtual Reality Systems XI, SPIE5291, 9–16 (2004).
[CrossRef]

2002 (2)

S. Yano, S. Ide, T. Mitsuhashi, and H. Thwaites, “A study of visual fatigue and visual comfort for 3D HDTV/HDTV images,” Displays23(4), 191–201 (2002).
[CrossRef]

K. Langhans, D. Bahr, D. Bezecny, D. Homann, K. Oltmann, K. Oltmann, C. Guill, E. Rieper, and G. Ardey, “FELIX 3D display: an interactive tool for volumetric imaging,” Proc. SPIE4660, 176–190 (2002).
[CrossRef]

2001 (1)

1996 (2)

E. Downing, L. Hesselink, J. Ralston, and R. Macfarlane, “A three-color, solid-state, three-dimensional display,” Science273(5279), 1185–1189 (1996).
[CrossRef]

D. Bahr, K. Langhans, M. Gerken, C. Vogt, D. Bezecny, and D. Homann, “FELIX: A volumetric 3D laser display,” Proc. SPIE2650, 265–273 (1996).
[CrossRef]

Ardey, G.

K. Langhans, D. Bahr, D. Bezecny, D. Homann, K. Oltmann, K. Oltmann, C. Guill, E. Rieper, and G. Ardey, “FELIX 3D display: an interactive tool for volumetric imaging,” Proc. SPIE4660, 176–190 (2002).
[CrossRef]

Bahr, D.

K. Langhans, D. Bahr, D. Bezecny, D. Homann, K. Oltmann, K. Oltmann, C. Guill, E. Rieper, and G. Ardey, “FELIX 3D display: an interactive tool for volumetric imaging,” Proc. SPIE4660, 176–190 (2002).
[CrossRef]

D. Bahr, K. Langhans, M. Gerken, C. Vogt, D. Bezecny, and D. Homann, “FELIX: A volumetric 3D laser display,” Proc. SPIE2650, 265–273 (1996).
[CrossRef]

Balakrishnan, R.

T. Grossman and R. Balakrishnan, “An evaluation of depth perception on volumetric displays,” in Proceedings of The 8th International Working Conference on Advanced Visual Interfaces (Italy, 2006), 193–200.
[CrossRef]

Bezecny, D.

K. Langhans, D. Bahr, D. Bezecny, D. Homann, K. Oltmann, K. Oltmann, C. Guill, E. Rieper, and G. Ardey, “FELIX 3D display: an interactive tool for volumetric imaging,” Proc. SPIE4660, 176–190 (2002).
[CrossRef]

D. Bahr, K. Langhans, M. Gerken, C. Vogt, D. Bezecny, and D. Homann, “FELIX: A volumetric 3D laser display,” Proc. SPIE2650, 265–273 (1996).
[CrossRef]

Cossairt, O. S.

Dodgson, N. A.

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-Dimensional Displays: A Review and Applications Analysis,” IEEE Trans. Broadcast57(2), 362–371 (2011).
[CrossRef]

Dorval, R. K.

Downing, E.

E. Downing, L. Hesselink, J. Ralston, and R. Macfarlane, “A three-color, solid-state, three-dimensional display,” Science273(5279), 1185–1189 (1996).
[CrossRef]

Fainman, Y.

Favalora, G. E.

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-Dimensional Displays: A Review and Applications Analysis,” IEEE Trans. Broadcast57(2), 362–371 (2011).
[CrossRef]

O. S. Cossairt, J. Napoli, S. L. Hill, R. K. Dorval, and G. E. Favalora, “Occlusion-capable multiview volumetric three-dimensional display,” Appl. Opt.46(8), 1244–1250 (2007).
[CrossRef] [PubMed]

Gately, M.

M. Gately, Y. Zhai, M. Yeary, E. Petrich, and L. Sawalha, “A Three-Dimensional Swept Volume Display Based on LED Arrays,” J. Disp. Technol.7(9), 503–514 (2011).
[CrossRef]

Gerken, M.

D. Bahr, K. Langhans, M. Gerken, C. Vogt, D. Bezecny, and D. Homann, “FELIX: A volumetric 3D laser display,” Proc. SPIE2650, 265–273 (1996).
[CrossRef]

Grossman, T.

T. Grossman and R. Balakrishnan, “An evaluation of depth perception on volumetric displays,” in Proceedings of The 8th International Working Conference on Advanced Visual Interfaces (Italy, 2006), 193–200.
[CrossRef]

Guill, C.

K. Langhans, D. Bahr, D. Bezecny, D. Homann, K. Oltmann, K. Oltmann, C. Guill, E. Rieper, and G. Ardey, “FELIX 3D display: an interactive tool for volumetric imaging,” Proc. SPIE4660, 176–190 (2002).
[CrossRef]

Hesselink, L.

E. Downing, L. Hesselink, J. Ralston, and R. Macfarlane, “A three-color, solid-state, three-dimensional display,” Science273(5279), 1185–1189 (1996).
[CrossRef]

Hill, S. L.

Hirano, N.

D. Miyazaki, N. Hirano, Y. Maeda, S. Yamamoto, T. Mukai, and S. Maekawa, “Floating volumetric image formation using a dihedral corner reflector array device,” Appl. Opt.52(1), A281–A289 (2013).
[CrossRef] [PubMed]

D. Miyazaki, N. Hirano, Y. Maeda, K. Ohno, and S. Maekawa, “Volumetric Display Using a Roof Mirror Grid Array,” in Stereoscopic Displays and Applications XXI, SPIE7524, 75240N, 75240N-9 (2010).
[CrossRef]

Y. Maeda, D. Miyazaki, N. Hirano, and S. Maekawa, “Three-Dimensional Display Using a Roof Mirror Grid Array and a Prism Sheet,” in Proceedings of The 17th International Display Workshops, Japan, 1301–1304 (2010).

Hisatake, S.

Hoffmann, C.

P. Rosen, Z. Pizlo, C. Hoffmann, and V. Popescu, “Perception of 3d spatial relations for 3d displays,” In Stereoscopic Displays and Virtual Reality Systems XI, SPIE5291, 9–16 (2004).
[CrossRef]

Holliman, N. S.

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-Dimensional Displays: A Review and Applications Analysis,” IEEE Trans. Broadcast57(2), 362–371 (2011).
[CrossRef]

Homann, D.

K. Langhans, D. Bahr, D. Bezecny, D. Homann, K. Oltmann, K. Oltmann, C. Guill, E. Rieper, and G. Ardey, “FELIX 3D display: an interactive tool for volumetric imaging,” Proc. SPIE4660, 176–190 (2002).
[CrossRef]

D. Bahr, K. Langhans, M. Gerken, C. Vogt, D. Bezecny, and D. Homann, “FELIX: A volumetric 3D laser display,” Proc. SPIE2650, 265–273 (1996).
[CrossRef]

Ide, S.

S. Yano, S. Ide, T. Mitsuhashi, and H. Thwaites, “A study of visual fatigue and visual comfort for 3D HDTV/HDTV images,” Displays23(4), 191–201 (2002).
[CrossRef]

Kobayashi, T.

Langhans, K.

K. Langhans, D. Bahr, D. Bezecny, D. Homann, K. Oltmann, K. Oltmann, C. Guill, E. Rieper, and G. Ardey, “FELIX 3D display: an interactive tool for volumetric imaging,” Proc. SPIE4660, 176–190 (2002).
[CrossRef]

D. Bahr, K. Langhans, M. Gerken, C. Vogt, D. Bezecny, and D. Homann, “FELIX: A volumetric 3D laser display,” Proc. SPIE2650, 265–273 (1996).
[CrossRef]

Lasher, M.

Macfarlane, R.

E. Downing, L. Hesselink, J. Ralston, and R. Macfarlane, “A three-color, solid-state, three-dimensional display,” Science273(5279), 1185–1189 (1996).
[CrossRef]

Maeda, Y.

D. Miyazaki, N. Hirano, Y. Maeda, S. Yamamoto, T. Mukai, and S. Maekawa, “Floating volumetric image formation using a dihedral corner reflector array device,” Appl. Opt.52(1), A281–A289 (2013).
[CrossRef] [PubMed]

Y. Maeda, D. Miyazaki, and T. Mukai, “Volumetric display using a rotating prism sheet as an optical image scanner,” Appl. Opt.52(1), A182–A187 (2013).
[CrossRef] [PubMed]

D. Miyazaki, N. Hirano, Y. Maeda, K. Ohno, and S. Maekawa, “Volumetric Display Using a Roof Mirror Grid Array,” in Stereoscopic Displays and Applications XXI, SPIE7524, 75240N, 75240N-9 (2010).
[CrossRef]

Y. Maeda, D. Miyazaki, N. Hirano, and S. Maekawa, “Three-Dimensional Display Using a Roof Mirror Grid Array and a Prism Sheet,” in Proceedings of The 17th International Display Workshops, Japan, 1301–1304 (2010).

Maekawa, S.

D. Miyazaki, N. Hirano, Y. Maeda, S. Yamamoto, T. Mukai, and S. Maekawa, “Floating volumetric image formation using a dihedral corner reflector array device,” Appl. Opt.52(1), A281–A289 (2013).
[CrossRef] [PubMed]

D. Miyazaki, N. Hirano, Y. Maeda, K. Ohno, and S. Maekawa, “Volumetric Display Using a Roof Mirror Grid Array,” in Stereoscopic Displays and Applications XXI, SPIE7524, 75240N, 75240N-9 (2010).
[CrossRef]

S. Maekawa, K. Nitta, and O. Matoba, “Transmissive Optical Imaging Device with Micromirror Array,” Proc. SPIE6392, 63920E, 63920E-8 (2006).
[CrossRef]

Y. Maeda, D. Miyazaki, N. Hirano, and S. Maekawa, “Three-Dimensional Display Using a Roof Mirror Grid Array and a Prism Sheet,” in Proceedings of The 17th International Display Workshops, Japan, 1301–1304 (2010).

Matoba, O.

S. Maekawa, K. Nitta, and O. Matoba, “Transmissive Optical Imaging Device with Micromirror Array,” Proc. SPIE6392, 63920E, 63920E-8 (2006).
[CrossRef]

Matsushita, K.

Mitsuhashi, T.

S. Yano, S. Ide, T. Mitsuhashi, and H. Thwaites, “A study of visual fatigue and visual comfort for 3D HDTV/HDTV images,” Displays23(4), 191–201 (2002).
[CrossRef]

Miyazaki, D.

Mukai, T.

Napoli, J.

Nitta, K.

S. Maekawa, K. Nitta, and O. Matoba, “Transmissive Optical Imaging Device with Micromirror Array,” Proc. SPIE6392, 63920E, 63920E-8 (2006).
[CrossRef]

Ohno, K.

D. Miyazaki, N. Hirano, Y. Maeda, K. Ohno, and S. Maekawa, “Volumetric Display Using a Roof Mirror Grid Array,” in Stereoscopic Displays and Applications XXI, SPIE7524, 75240N, 75240N-9 (2010).
[CrossRef]

Oltmann, K.

K. Langhans, D. Bahr, D. Bezecny, D. Homann, K. Oltmann, K. Oltmann, C. Guill, E. Rieper, and G. Ardey, “FELIX 3D display: an interactive tool for volumetric imaging,” Proc. SPIE4660, 176–190 (2002).
[CrossRef]

K. Langhans, D. Bahr, D. Bezecny, D. Homann, K. Oltmann, K. Oltmann, C. Guill, E. Rieper, and G. Ardey, “FELIX 3D display: an interactive tool for volumetric imaging,” Proc. SPIE4660, 176–190 (2002).
[CrossRef]

Petrich, E.

M. Gately, Y. Zhai, M. Yeary, E. Petrich, and L. Sawalha, “A Three-Dimensional Swept Volume Display Based on LED Arrays,” J. Disp. Technol.7(9), 503–514 (2011).
[CrossRef]

Pizlo, Z.

P. Rosen, Z. Pizlo, C. Hoffmann, and V. Popescu, “Perception of 3d spatial relations for 3d displays,” In Stereoscopic Displays and Virtual Reality Systems XI, SPIE5291, 9–16 (2004).
[CrossRef]

Pockett, L.

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-Dimensional Displays: A Review and Applications Analysis,” IEEE Trans. Broadcast57(2), 362–371 (2011).
[CrossRef]

Popescu, V.

P. Rosen, Z. Pizlo, C. Hoffmann, and V. Popescu, “Perception of 3d spatial relations for 3d displays,” In Stereoscopic Displays and Virtual Reality Systems XI, SPIE5291, 9–16 (2004).
[CrossRef]

Ralston, J.

E. Downing, L. Hesselink, J. Ralston, and R. Macfarlane, “A three-color, solid-state, three-dimensional display,” Science273(5279), 1185–1189 (1996).
[CrossRef]

Refai, H. H.

H. H. Refai, “Static Volumetric Three-Dimensional Display,” J. Disp. Technol.5(10), 391–397 (2009).
[CrossRef]

Rieper, E.

K. Langhans, D. Bahr, D. Bezecny, D. Homann, K. Oltmann, K. Oltmann, C. Guill, E. Rieper, and G. Ardey, “FELIX 3D display: an interactive tool for volumetric imaging,” Proc. SPIE4660, 176–190 (2002).
[CrossRef]

Rosen, P.

P. Rosen, Z. Pizlo, C. Hoffmann, and V. Popescu, “Perception of 3d spatial relations for 3d displays,” In Stereoscopic Displays and Virtual Reality Systems XI, SPIE5291, 9–16 (2004).
[CrossRef]

Sawalha, L.

M. Gately, Y. Zhai, M. Yeary, E. Petrich, and L. Sawalha, “A Three-Dimensional Swept Volume Display Based on LED Arrays,” J. Disp. Technol.7(9), 503–514 (2011).
[CrossRef]

Shiba, K.

Sotsuka, K.

Suda, S.

Sullivan, A.

A. Sullivan, “DepthCube Solid-state 3D Volumetric Display,” in Stereoscopic Display and Virtual Reality Systems XI, SPIE5291, 279–284 (2004).
[CrossRef]

Takahara, J.

Thwaites, H.

S. Yano, S. Ide, T. Mitsuhashi, and H. Thwaites, “A study of visual fatigue and visual comfort for 3D HDTV/HDTV images,” Displays23(4), 191–201 (2002).
[CrossRef]

Vogt, C.

D. Bahr, K. Langhans, M. Gerken, C. Vogt, D. Bezecny, and D. Homann, “FELIX: A volumetric 3D laser display,” Proc. SPIE2650, 265–273 (1996).
[CrossRef]

Yamamoto, S.

Yano, S.

S. Yano, S. Ide, T. Mitsuhashi, and H. Thwaites, “A study of visual fatigue and visual comfort for 3D HDTV/HDTV images,” Displays23(4), 191–201 (2002).
[CrossRef]

Yeary, M.

M. Gately, Y. Zhai, M. Yeary, E. Petrich, and L. Sawalha, “A Three-Dimensional Swept Volume Display Based on LED Arrays,” J. Disp. Technol.7(9), 503–514 (2011).
[CrossRef]

Zhai, Y.

M. Gately, Y. Zhai, M. Yeary, E. Petrich, and L. Sawalha, “A Three-Dimensional Swept Volume Display Based on LED Arrays,” J. Disp. Technol.7(9), 503–514 (2011).
[CrossRef]

Appl. Opt. (5)

Displays (1)

S. Yano, S. Ide, T. Mitsuhashi, and H. Thwaites, “A study of visual fatigue and visual comfort for 3D HDTV/HDTV images,” Displays23(4), 191–201 (2002).
[CrossRef]

IEEE Trans. Broadcast (1)

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-Dimensional Displays: A Review and Applications Analysis,” IEEE Trans. Broadcast57(2), 362–371 (2011).
[CrossRef]

J. Disp. Technol. (2)

H. H. Refai, “Static Volumetric Three-Dimensional Display,” J. Disp. Technol.5(10), 391–397 (2009).
[CrossRef]

M. Gately, Y. Zhai, M. Yeary, E. Petrich, and L. Sawalha, “A Three-Dimensional Swept Volume Display Based on LED Arrays,” J. Disp. Technol.7(9), 503–514 (2011).
[CrossRef]

Opt. Express (2)

Proc. SPIE (3)

D. Bahr, K. Langhans, M. Gerken, C. Vogt, D. Bezecny, and D. Homann, “FELIX: A volumetric 3D laser display,” Proc. SPIE2650, 265–273 (1996).
[CrossRef]

K. Langhans, D. Bahr, D. Bezecny, D. Homann, K. Oltmann, K. Oltmann, C. Guill, E. Rieper, and G. Ardey, “FELIX 3D display: an interactive tool for volumetric imaging,” Proc. SPIE4660, 176–190 (2002).
[CrossRef]

S. Maekawa, K. Nitta, and O. Matoba, “Transmissive Optical Imaging Device with Micromirror Array,” Proc. SPIE6392, 63920E, 63920E-8 (2006).
[CrossRef]

Science (1)

E. Downing, L. Hesselink, J. Ralston, and R. Macfarlane, “A three-color, solid-state, three-dimensional display,” Science273(5279), 1185–1189 (1996).
[CrossRef]

SPIE (3)

P. Rosen, Z. Pizlo, C. Hoffmann, and V. Popescu, “Perception of 3d spatial relations for 3d displays,” In Stereoscopic Displays and Virtual Reality Systems XI, SPIE5291, 9–16 (2004).
[CrossRef]

D. Miyazaki, N. Hirano, Y. Maeda, K. Ohno, and S. Maekawa, “Volumetric Display Using a Roof Mirror Grid Array,” in Stereoscopic Displays and Applications XXI, SPIE7524, 75240N, 75240N-9 (2010).
[CrossRef]

A. Sullivan, “DepthCube Solid-state 3D Volumetric Display,” in Stereoscopic Display and Virtual Reality Systems XI, SPIE5291, 279–284 (2004).
[CrossRef]

Other (8)

Y. Maeda, D. Miyazaki, N. Hirano, and S. Maekawa, “Three-Dimensional Display Using a Roof Mirror Grid Array and a Prism Sheet,” in Proceedings of The 17th International Display Workshops, Japan, 1301–1304 (2010).

G.E. Favalora, D.M. Hall, M.G. Giovinco, J. Napoli, and R.K. Dorval, “A Multi-Megavoxel Volumetric 3-D Display System for Distributed Collaboration,” IEEE Globecom 2000 Conference - “Application of Virtual Reality Technologies for Future Telecommunication System” (2000).

G. E. Favalora, J. Napoli, D. M. Hall, R. K. Dorval, M. G. Giovinco, M. J. Richmond, and W. S. Chun, “100 Million-voxel Volumetric Display,” in Cockpit Displays IX: Displays for Defense Applications, D. G. Hopper, ed., Proc. SPIE 4712, 300–312 (2002).

B. G. Blundell and A. J. Schwarz, “Volumetric Three-Dimensional Display Systems,” (John Wiley & Sons, New York, 2000).

S.-N. Yang and J. E. Sheedy, “Effects of Vergence and Accommodative Responses on Viewer’s Comfort in Viewing 3D Stimuli,” in Stereoscopic Displays and Applications XXII, A. J. Woods, N. S. Holliman, and N. A. Dodgson, eds., Proc. SPIE 7863, 78630Q (2011).

T. Grossman and R. Balakrishnan, “An evaluation of depth perception on volumetric displays,” in Proceedings of The 8th International Working Conference on Advanced Visual Interfaces (Italy, 2006), 193–200.
[CrossRef]

S. Maekawa, K. Nitta, and O. Matoba, “Advances in Passive Imaging Elements with Micromirror Array,” in Stereoscopic Displays and Applications XIX, A. J. Woods, N. S. Holliman, and J. O. Merritt, eds, Proc. SPIE 6803, 68030B (2008).

P. O. V. Team, “Persistency of Vision Ray Tracer (POV-Ray),” http://www.povray.org .

Supplementary Material (1)

» Media 1: MOV (3138 KB)     

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Figures (16)

Fig. 1
Fig. 1

Schematic illustration of the volumetric display system based on optical scanning of an inclined image plane.

Fig. 2
Fig. 2

Diagram of a double prism sheet arranged in an axially symmetric configuration.

Fig. 3
Fig. 3

Outcome of a ray tracing simulation of rays passing through the double prism sheet.

Fig. 4
Fig. 4

Illustration of principal rays from point light sources and the amount of motion parallax without a prism sheet (left), with one prism sheet (center), and with the proposed setup of a double prism sheet (right).

Fig. 5
Fig. 5

Graph of motion parallax a 1 (no prism sheet), a 2 (one prism sheet) and a 3 (the proposed setup of two prism sheets) versus incident angle θ i1 . In this case, n=1.49 , d 1 =20 [cm], d 2 =10 [cm], d 3 =60 [cm], θ p =40 [deg], and θ i2 = θ i1 +15 [deg].

Fig. 6
Fig. 6

Schematic illustration of image plane movement achieved by rotating the symmetrically arranged prism sheets (a) and the volume of the swept space (b), (c), and (d). Panel (b) is the side view, (c) is the front view, and (d) is the overhead view.

Fig. 7
Fig. 7

Imaging by the DCRA. Panel (a) is a schematic diagram, (b) shows the ray paths simulated by FRED, and (c) is an irradiance (power/area) spread function on a plane at the image points.

Fig. 8
Fig. 8

Schematics of the slit-type DCRA used in this study. Panel (a) is an overhead view and (b) is a top view.

Fig. 9
Fig. 9

Picture of the double prism sheet arranged in a symmetrical configuration on the bearing with the timing belt. The area of the prism sheet was 10 centimeters square. The thickness of the prism sheet was 2 mm and the prism pitch was 0.3 cm.

Fig. 10
Fig. 10

Setup with the symmetrically-arranged prism sheets in POV-Ray. When the screen was seen through the air, the fixed prism sheets were removed. When the screen was seen through one prism sheet, the bottom prism sheet remained in and the upper prism sheet was removed.

Fig. 11
Fig. 11

Experimental setup of the proposed volumetric display. Panel (a) is a schematic diagram and (b) is a picture taken from the side.

Fig. 12
Fig. 12

Movement of the image plane by rotating the symmetrically arranged prism sheets. The blue marker was put on to make rotation of the prism sheets more visible. The strip-shaped bluish-white light is stray light.

Fig. 13
Fig. 13

Results of the POV-Ray simulation. The red points are point light sources. The upper panels were observed from the left and the bottom panels were observed from the right.

Fig. 14
Fig. 14

3D floating volume image produced by the proposed volumetric display. Panel (a) was captured in a dark room and (b) was captured in a lighted environment (Media 1).

Fig. 15
Fig. 15

Diagram of stray light passing through the prism sheet. Red lines show reflected rays, including surface reflection and TIR.

Fig. 16
Fig. 16

Diagrams of stray light passing through the prism sheet when stray light suppression methods are applied. (a) Anti-reflective coating. (b) Anti-reflective coating and light shields attached to vertical planes of the prism sheet.

Equations (8)

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a 1 =( d 1 + d 2 + d 3 )( tan θ i2 tan θ i1 ).
θ o1 = sin 1 [ nsin{ sin 1 ( sin( θ i1 + θ p ) n ) θ p } ]
θ o2 = sin 1 [ nsin{ sin 1 ( sin( θ i2 + θ p ) n ) θ p } ],
a 2 = d 1 ( tan θ i2 tan θ i1 )+( d 2 + d 3 )( tan θ o2 tan θ o1 )
a 3 =( d 1 + d 3 )( tan θ i2 tan θ i1 )+ d 2 ( tan θ o2 tan θ o1 ),
l= d 2 ( tan θ o1 tan θ i1 ).
V=( 2w+πl )lhcos θ inc ,
V=( 4+π ) l 2 hcos θ inc =( 4+π ) { d 2 ( tan θ o1 tan θ i1 ) } 2 hcos θ inc .

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