Abstract

A 3D scene is synthesized combining multiple optically recorded digital holograms of different objects. The novel idea consists of compositing moving 3D objects in a dynamic 3D scene using a process that is analogous to stop-motion video. However in this case the movie has the exciting attribute that it can be displayed and observed in 3D. We show that 3D dynamic scenes can be projected as an alternative to complicated and heavy computations needed to generate realistic-looking computer generated holograms. The key tool for creating the dynamic action is based on a new concept that consists of a spatial, adaptive transformation of digital holograms of real-world objects allowing full control in the manipulation of the object’s position and size in a 3D volume with very high depth-of-focus. A pilot experiment to evaluate how viewers perceive depth in a conventional single-view display of the dynamic 3D scene has been performed.

© 2010 OSA

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2009 (4)

2008 (3)

2006 (1)

2005 (3)

2004 (1)

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

2003 (2)

M. L. Huebschman, B. Munjuluri, and H. R. Garner, “Dynamic holographic 3-D image projection,” Opt. Express 11(5), 437–445 (2003).
[CrossRef] [PubMed]

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[CrossRef] [PubMed]

1996 (1)

B. L. Volodin, B. Kippelen, K. Meerholz, B. Javidi, and N. Peyghambarian, “A polymeric optical pattern-recognition system for security verification,” Nature 383(6595), 58–60 (1996).
[CrossRef]

1992 (1)

1991 (1)

S. Fukushima, T. Kurokawa, and M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light-modulator,” Appl. Phys. Lett. 58(8), 787–789 (1991).
[CrossRef]

1987 (1)

1967 (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[CrossRef]

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[CrossRef] [PubMed]

Ahrenberg, L.

Becker, H.

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[CrossRef] [PubMed]

Benton, S. A.

Benzie, P.

Blanche, P.-A.

S. Ş. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Cameron, C. D.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

Choi, K.

Coomber, S. D.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

Dodgson, N. A.

N. A. Dodgson, “Autostereoscopic 3D displays,” Computer 38(8), 31–36 (2005).
[CrossRef]

Falcou, A.

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[CrossRef] [PubMed]

Ferraro, P.

Finizio, A.

Flores, D.

S. Ş. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Frohne, H.

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[CrossRef] [PubMed]

Fukushima, S.

S. Fukushima, T. Kurokawa, and M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light-modulator,” Appl. Phys. Lett. 58(8), 787–789 (1991).
[CrossRef]

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[CrossRef] [PubMed]

Garner, H. R.

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[CrossRef]

Gu, T.

S. Ş. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Hennelly, B. M.

Hilaire, P. S.

Huebschman, M. L.

Ichihashi, Y.

Ito, T.

Javidi, B.

B. L. Volodin, B. Kippelen, K. Meerholz, B. Javidi, and N. Peyghambarian, “A polymeric optical pattern-recognition system for security verification,” Nature 383(6595), 58–60 (1996).
[CrossRef]

Katz, B.

Kim, J.

Kippelen, B.

B. L. Volodin, B. Kippelen, K. Meerholz, B. Javidi, and N. Peyghambarian, “A polymeric optical pattern-recognition system for security verification,” Nature 383(6595), 58–60 (1996).
[CrossRef]

Kurokawa, T.

S. Fukushima, T. Kurokawa, and M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light-modulator,” Appl. Phys. Lett. 58(8), 787–789 (1991).
[CrossRef]

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[CrossRef]

Lee, B.

Li, G.

S. Ş. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Lim, Y.

Lin, W.

S. Ş. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Lucente, M.

Magnor, M.

Masuda, N.

Matsushita, K.

McElhinney, C. P.

Meerholz, K.

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[CrossRef] [PubMed]

B. L. Volodin, B. Kippelen, K. Meerholz, B. Javidi, and N. Peyghambarian, “A polymeric optical pattern-recognition system for security verification,” Nature 383(6595), 58–60 (1996).
[CrossRef]

Memmolo, P.

Miller, R. J.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

Miyazaki, D.

Müller, C. D.

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[CrossRef] [PubMed]

Munjuluri, B.

Nakayama, H.

Naughton, T. J.

Norwood, R. A.

S. Ş. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Nuyken, O.

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[CrossRef] [PubMed]

Ohno, M.

S. Fukushima, T. Kurokawa, and M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light-modulator,” Appl. Phys. Lett. 58(8), 787–789 (1991).
[CrossRef]

Paturzo, M.

Payne, D. A.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

Peyghambarian, N.

S. Ş. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[CrossRef] [PubMed]

B. L. Volodin, B. Kippelen, K. Meerholz, B. Javidi, and N. Peyghambarian, “A polymeric optical pattern-recognition system for security verification,” Nature 383(6595), 58–60 (1996).
[CrossRef]

Reckefuss, N.

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[CrossRef] [PubMed]

Rojahn, M.

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[CrossRef] [PubMed]

Rokutanda, S.

S. Ş. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Rosen, J.

Rudati, P.

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[CrossRef] [PubMed]

Shaked, N. T.

Shiba, K.

Shimobaba, T.

Shiraki, A.

Slinger, C. W.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

Smith, A. P.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

Smith, M. G.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

Sotsuka, K.

St Hilaire, P.

S. Ş. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Stanley, M.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

Tay, S. S.

S. Ş. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Thomas, J.

S. Ş. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Tricoles, G.

Tsuge, M.

Tunç, A. V.

S. Ş. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Volodin, B. L.

B. L. Volodin, B. Kippelen, K. Meerholz, B. Javidi, and N. Peyghambarian, “A polymeric optical pattern-recognition system for security verification,” Nature 383(6595), 58–60 (1996).
[CrossRef]

Voorakaranam, R.

S. Ş. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Wang, P.

S. Ş. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Watson, J.

Watson, P. J.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

Wiederhirn, V.

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[CrossRef] [PubMed]

Yamamoto, M.

S. Ş. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[CrossRef] [PubMed]

Appl. Opt. (5)

Appl. Phys. Lett. (2)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[CrossRef]

S. Fukushima, T. Kurokawa, and M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light-modulator,” Appl. Phys. Lett. 58(8), 787–789 (1991).
[CrossRef]

Computer (1)

N. A. Dodgson, “Autostereoscopic 3D displays,” Computer 38(8), 31–36 (2005).
[CrossRef]

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

Nature (4)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[CrossRef] [PubMed]

S. Ş. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[CrossRef] [PubMed]

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[CrossRef] [PubMed]

B. L. Volodin, B. Kippelen, K. Meerholz, B. Javidi, and N. Peyghambarian, “A polymeric optical pattern-recognition system for security verification,” Nature 383(6595), 58–60 (1996).
[CrossRef]

Opt. Express (5)

Opt. Lett. (1)

Proc. SPIE (1)

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

Other (8)

I. P. Howard and B. J. Rogers Seeing in depth, vol. 2 (I Porteous, Toronto, 2002).

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2005).

M. R. Chatterjee and S. Chen, Digital Holography and Three-Dimensional Display: Principles and Applications (ed. Poon, T. Springer, New York, 2006), Chap. 13.

S. A. Benton and V. M. Bove, Jr, Holographic Imaging (Wiley Inter-Science 2008).

H. M. Ozaktas and L. Onural, eds., Three-Dimensional Television Capture, Transmission, Display Series: Signals and Communication Technology (Springer, 2008)

S. A. Benton, Selected Papers on Three-Dimensional Displays (SPIE Optical Engineering Press, Bellingham, Washington, 2001)

Y. Frauel, T. J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” in Proceedings of the IEEE,94, 636–653 (2006).

L. A. Lessard and H. I. Bjelkhagen, eds., Practical Holography XXI: Materials and Applications (Special Issue) Proc. SPIE 6488, (2007).

Supplementary Material (8)

» Media 1: MOV (2914 KB)     
» Media 2: MOV (2849 KB)     
» Media 3: MOV (2369 KB)     
» Media 4: MOV (6210 KB)     
» Media 5: MOV (5546 KB)     
» Media 6: MOV (372 KB)     
» Media 7: MOV (742 KB)     
» Media 8: MOV (233 KB)     

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Figures (8)

Fig. 1
Fig. 1

(a) Scheme of the movement (back-and-forth along the z-axis) performed by a single object through subsequent deformations of the same hologram; (b) numerical reconstruction of the hologram after its stretching with a deformation parameter of 0.8, 1, 1.2, respectively (from left to right); in the upper row the distance of reconstruction is fixed at the recording distance, while in the lower row it is changed to obtain in-focus images.

Fig. 2
Fig. 2

Holograms acquired during the object rotation: Numerical reconstructions of four different digital holograms recorded while the object rotates by 360° around its vertical axis from a fixed position (Media 1).

Fig. 3
Fig. 3

Set-up used for the optical projection of the 3D scene; MO: microscope objective, SF: spatial filter, L: lens, BS: beam splitter, SLM: spatial light modulator, M: mirror.

Fig. 4
Fig. 4

Scheme of the 3D scene projection and three frames of the 3D scene optically reconstructed using a SLM-LCOS and a projection screen positioned at a distance l1 (a- Media 2) and at a distance l3 (b-Media 3).

Fig. 5
Fig. 5

3D scene with more than one object reconstructed optically using a SLM-LCOS: (a) Scheme of the movements performed by the two objects (back-and-forth along the z-axis with rotation); (b) four frames of the 3D scene optically reconstructed moving the projection screen at four different distances; a frame of the movie acquired fixing the screen at a distance l1 (c-Media 4) and at a distance l3. (d-Media 5).

Fig. 6
Fig. 6

Numerical (a-Media 6) and optical (b-Media 7) reconstructions of a 3D scene with three objects.

Fig. 7
Fig. 7

Perception experiment: the observer looks at two windows. The one on the right shows the video clip (Media 8) while the other on the left shows a random-pattern stereoscopic image.

Fig. 8
Fig. 8

Perception experiment: In the stereoscopic image there was a central rectangle whose perceptual distance in depth could be adjusted by changing the disparity between the images seen by the left and the right eye using a graphical slider.

Equations (5)

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b ( x , y ) = 1 i λ d h ( ξ , η ) r ( ξ , η ) e i k d [ 1 + ( x ξ ) 2 2 d 2 + ( y η ) 2 2 d 2 ] d ξ d η
B ( x , y , d ) = 1 i λ d e i k d h ( α ξ , α η ) e i k α 2 ( x ξ ) 2 2 d α 2 e i k α 2 ( y η ) 2 2 d α 2 d ξ d η =
= 1 i α 2 λ d e i k d h ( ξ ' , η ' ) e i k ( x ' ξ ' ) 2 2 D e i k ( y ' η ' ) 2 2 D d ξ ' d η ' = 1 α 2 b ( x ' , y ' , D )
M l a t = 1 m λ c λ r z i z o
1 z i = 1 z c ± 1 m 2 λ c λ r ( 1 z 0 1 z r )

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