Abstract

An evaluation of the retention of continuous parallax in pixelated integral three-dimensional image displays is presented. The integral image capture process is first considered, to provide a starting point for the investigation. The complementary display system is then examined in detail. The viewing geometry of the display system is analyzed to provide a foundation for the work to follow, and an experimental investigation and simulations of the characteristics of emitted ray bundles are presented. Next, an analytical model of decoding lenslet array operation is derived, leading to an understanding of the process responsible for production of continuous parallax in replay. It is found that if the lateral resolution of the lenslet is matched to that of the display, continuous parallax is retained in the replayed image, where the finite aberration-limited resolution of the lenslet acts to produce a low-pass reconstruction filter. A condition is derived for optimal continuous parallax in replay, based on a relationship between pixel width and lenslet rms spot size.

© 2003 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. Breault Research Organization, “ASAP version 7.0.3,” 2001, http://www.bro.com/ .
  20. Silonex Inc., “NORP-11, 12, 13 Series CdS Photocells data sheet,” 2002, http://www.silonex.com/ .
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    [CrossRef]

2002 (1)

2001 (1)

1997 (1)

1995 (1)

T. Motoki, H. Isono, I. Yuyama, “Present status of three-dimensional television research,” Proc. IEEE 83, 1009–1021 (1995).
[CrossRef]

1994 (1)

N. Davies, M. McCormick, M. Brewin, “Design and analysis of an image transfer system using microlens arrays,” Opt. Eng. 33, 3624–3633 (1994).
[CrossRef]

1992 (1)

E. H. Adelson, J. Y. A. Wang, “Single lens stereo with plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99–106 (1992).
[CrossRef]

1988 (1)

1980 (1)

Yu. A. Dudnikov, B. K. Rozhkov, E. N. Antipova, “Obtaining a portrait of a person by the integral photography method,” Sov. J. Opt. Technol. 47, 562–563 (1980).

1969 (1)

1968 (1)

C. B. Burckhardt, “Optimum parameters and resolution limitation of integral photography,” J. Opt. Soc. Am. 58, 71–76 (1968).
[CrossRef]

1931 (1)

1908 (1)

G. Lippmann, “Epreuves reversibles,” C. R. Acad. Sci. 146, 446–451 (1908).

Adelson, E. H.

E. H. Adelson, J. Y. A. Wang, “Single lens stereo with plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99–106 (1992).
[CrossRef]

Antipova, E. N.

Yu. A. Dudnikov, B. K. Rozhkov, E. N. Antipova, “Obtaining a portrait of a person by the integral photography method,” Sov. J. Opt. Technol. 47, 562–563 (1980).

Arai, J.

Arimoto, H.

Brewin, M.

N. Davies, M. McCormick, M. Brewin, “Design and analysis of an image transfer system using microlens arrays,” Opt. Eng. 33, 3624–3633 (1994).
[CrossRef]

M. Brewin, M. Forman, N. Davies, “Electronic capture and display of full parallax 3D images,” in Stereoscopic Displays and Virtual Reality Systems II, S. S. Fisher, J. O. Merritt, M. T. Bolas, eds., Proc. SPIE2409, 118–124 (1995).
[CrossRef]

Brewin, M. A.

M. A. Brewin, “Reduced information integral imaging,” Ph.D. thesis (De Montfort University, Leicester, UK, 1998).

Burckhardt, C. B.

C. B. Burckhardt, “Optimum parameters and resolution limitation of integral photography,” J. Opt. Soc. Am. 58, 71–76 (1968).
[CrossRef]

Burkhardt, C. B.

Castle, O. M.

J. R. Moor, A. R. L. Travis, S. R. Lang, O. M. Castle, “The implementation of a multi-view autostereoscopic display,” in IEE Colloquium on Stereoscopic Television (Institute of Electrical Engineers, London, 1992), Digest No. 1992/173, pp. 4/5–4/16.

Davies, N.

N. Davies, M. McCormick, M. Brewin, “Design and analysis of an image transfer system using microlens arrays,” Opt. Eng. 33, 3624–3633 (1994).
[CrossRef]

N. Davies, M. McCormick, L. Yang, “Three dimensional imaging systems: a new development,” Appl. Opt. 27, 4520–4528 (1988).
[CrossRef] [PubMed]

M. Brewin, M. Forman, N. Davies, “Electronic capture and display of full parallax 3D images,” in Stereoscopic Displays and Virtual Reality Systems II, S. S. Fisher, J. O. Merritt, M. T. Bolas, eds., Proc. SPIE2409, 118–124 (1995).
[CrossRef]

de Montebello, R. L.

R. L. de Montebello, “Wide angle integral photography—the integram technique,” in Three-Dimensional Imaging, S. A. Benton, ed., Proc. SPIE120, 73–91 (1970).
[CrossRef]

Doherty, E. T.

Dudnikov, Yu. A.

Yu. A. Dudnikov, B. K. Rozhkov, E. N. Antipova, “Obtaining a portrait of a person by the integral photography method,” Sov. J. Opt. Technol. 47, 562–563 (1980).

Faubert, J.

J. Faubert, “Motion parallax, stereoscopy, and the perception of depth: practical and theoretical issues,” Three-Dimensional Video and Display: Devices and Systems, B. Javidi, ed., Vol. CR76 of SPIE Critical Review Series (SPIE Optical Engineering Press, Bellingham, Wash., 2001), pp. 168–191.

Forman, M.

M. Brewin, M. Forman, N. Davies, “Electronic capture and display of full parallax 3D images,” in Stereoscopic Displays and Virtual Reality Systems II, S. S. Fisher, J. O. Merritt, M. T. Bolas, eds., Proc. SPIE2409, 118–124 (1995).
[CrossRef]

Hoshino, H.

Isono, H.

T. Motoki, H. Isono, I. Yuyama, “Present status of three-dimensional television research,” Proc. IEEE 83, 1009–1021 (1995).
[CrossRef]

Ives, H. E.

Javidi, B.

Lang, S. R.

J. R. Moor, A. R. L. Travis, S. R. Lang, O. M. Castle, “The implementation of a multi-view autostereoscopic display,” in IEE Colloquium on Stereoscopic Television (Institute of Electrical Engineers, London, 1992), Digest No. 1992/173, pp. 4/5–4/16.

Lee, Byoungho

Lippmann, G.

G. Lippmann, “Epreuves reversibles,” C. R. Acad. Sci. 146, 446–451 (1908).

McCormick, M.

N. Davies, M. McCormick, M. Brewin, “Design and analysis of an image transfer system using microlens arrays,” Opt. Eng. 33, 3624–3633 (1994).
[CrossRef]

N. Davies, M. McCormick, L. Yang, “Three dimensional imaging systems: a new development,” Appl. Opt. 27, 4520–4528 (1988).
[CrossRef] [PubMed]

Min, Sung-Wook

Moor, J. R.

J. R. Moor, A. R. L. Travis, S. R. Lang, O. M. Castle, “The implementation of a multi-view autostereoscopic display,” in IEE Colloquium on Stereoscopic Television (Institute of Electrical Engineers, London, 1992), Digest No. 1992/173, pp. 4/5–4/16.

Motoki, T.

T. Motoki, H. Isono, I. Yuyama, “Present status of three-dimensional television research,” Proc. IEEE 83, 1009–1021 (1995).
[CrossRef]

Okano, F.

Okoshi, T.

T. Okoshi, Three Dimensional Imaging Techniques (Academic, London, 1976).

Pedrotti, F. L.

F. L. Pedrotti, S. J. Pedrotti, L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J.1993).

Pedrotti, L. S.

F. L. Pedrotti, S. J. Pedrotti, L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J.1993).

Pedrotti, S. J.

F. L. Pedrotti, S. J. Pedrotti, L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J.1993).

Rozhkov, B. K.

Yu. A. Dudnikov, B. K. Rozhkov, E. N. Antipova, “Obtaining a portrait of a person by the integral photography method,” Sov. J. Opt. Technol. 47, 562–563 (1980).

Travis, A. R. L.

J. R. Moor, A. R. L. Travis, S. R. Lang, O. M. Castle, “The implementation of a multi-view autostereoscopic display,” in IEE Colloquium on Stereoscopic Television (Institute of Electrical Engineers, London, 1992), Digest No. 1992/173, pp. 4/5–4/16.

Valyus, N. A.

N. A. Valyus, Stereoscopy (Focal Press, London, 1966).

Wang, J. Y. A.

E. H. Adelson, J. Y. A. Wang, “Single lens stereo with plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99–106 (1992).
[CrossRef]

Yang, L.

Yuyama, I.

F. Okano, H. Hoshino, J. Arai, I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598–1603 (1997).
[CrossRef] [PubMed]

T. Motoki, H. Isono, I. Yuyama, “Present status of three-dimensional television research,” Proc. IEEE 83, 1009–1021 (1995).
[CrossRef]

Appl. Opt. (4)

C. R. Acad. Sci. (1)

G. Lippmann, “Epreuves reversibles,” C. R. Acad. Sci. 146, 446–451 (1908).

IEEE Trans. Pattern Anal. Mach. Intell. (1)

E. H. Adelson, J. Y. A. Wang, “Single lens stereo with plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99–106 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

C. B. Burckhardt, “Optimum parameters and resolution limitation of integral photography,” J. Opt. Soc. Am. 58, 71–76 (1968).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

N. Davies, M. McCormick, M. Brewin, “Design and analysis of an image transfer system using microlens arrays,” Opt. Eng. 33, 3624–3633 (1994).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

T. Motoki, H. Isono, I. Yuyama, “Present status of three-dimensional television research,” Proc. IEEE 83, 1009–1021 (1995).
[CrossRef]

Sov. J. Opt. Technol. (1)

Yu. A. Dudnikov, B. K. Rozhkov, E. N. Antipova, “Obtaining a portrait of a person by the integral photography method,” Sov. J. Opt. Technol. 47, 562–563 (1980).

Other (11)

R. L. de Montebello, “Wide angle integral photography—the integram technique,” in Three-Dimensional Imaging, S. A. Benton, ed., Proc. SPIE120, 73–91 (1970).
[CrossRef]

Breault Research Organization, “ASAP version 7.0.3,” 2001, http://www.bro.com/ .

Silonex Inc., “NORP-11, 12, 13 Series CdS Photocells data sheet,” 2002, http://www.silonex.com/ .

M. A. Brewin, “Reduced information integral imaging,” Ph.D. thesis (De Montfort University, Leicester, UK, 1998).

F. L. Pedrotti, S. J. Pedrotti, L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J.1993).

M. Brewin, M. Forman, N. Davies, “Electronic capture and display of full parallax 3D images,” in Stereoscopic Displays and Virtual Reality Systems II, S. S. Fisher, J. O. Merritt, M. T. Bolas, eds., Proc. SPIE2409, 118–124 (1995).
[CrossRef]

N. A. Valyus, Stereoscopy (Focal Press, London, 1966).

T. Okoshi, Three Dimensional Imaging Techniques (Academic, London, 1976).

J. R. Moor, A. R. L. Travis, S. R. Lang, O. M. Castle, “The implementation of a multi-view autostereoscopic display,” in IEE Colloquium on Stereoscopic Television (Institute of Electrical Engineers, London, 1992), Digest No. 1992/173, pp. 4/5–4/16.

I. Sexton, “Assorted problems with stereo displays (presentation),” 1996, http://www.cse.dmu.ac.uk/IRC/minutes/premins/sep15/ .

J. Faubert, “Motion parallax, stereoscopy, and the perception of depth: practical and theoretical issues,” Three-Dimensional Video and Display: Devices and Systems, B. Javidi, ed., Vol. CR76 of SPIE Critical Review Series (SPIE Optical Engineering Press, Bellingham, Wash., 2001), pp. 168–191.

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Figures (13)

Fig. 1
Fig. 1

Integral three-dimensional image capture geometry.

Fig. 2
Fig. 2

Approximated continuous LeSD; inset, magnified for one lenslet.

Fig. 3
Fig. 3

Pixel-sampled LeSD; inset, magnified for one lenslet.

Fig. 4
Fig. 4

Illuminance profiles at a horizontal cross section through LeSC data.

Fig. 5
Fig. 5

Viewing geometry for an II.

Fig. 6
Fig. 6

Beam spread due to finite pixel size.

Fig. 7
Fig. 7

Experimental arrangement for observed luminance profile measurement.

Fig. 8
Fig. 8

LeSC for luminance profile measurement experiment.

Fig. 9
Fig. 9

Normalized illuminance profile observed by using a photocell for the surface of a lenslet with a test LeSC.

Fig. 10
Fig. 10

Simulation of photocell-based integral replay experiment: illuminance at the detector plane.

Fig. 11
Fig. 11

Origin of continuous perspectives in integral replay: (a) hypothetical line-spread function, (b) LeSC luminance and beam illuminance at a detector.

Fig. 12
Fig. 12

Luminous beam intensity for three pixel widths.

Fig. 13
Fig. 13

Relationship between rms spot size and optimal LeSC pixel width.

Tables (2)

Tables Icon

Table 1 Lenslet Array Parameters for Luminance Profile Measurement Experiment

Tables Icon

Table 2 Lenslet Array Parameters for Optimal Pixel Width Determination

Equations (10)

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

p f = D ap + t D ap + R p l .
α i = - arctan p f s i t - R .
w b = p l + p f l D v + δ t - R ,
α max = α i | s i = - 0.5 = arctan p f 2 ( t - R ) .
L B ( η x ) = h ( a )     M L ( - x ) ,
I B ( θ ) L B ( η x ) ,
h ( a ) = exp - a 2 2 σ 2 , - p f 2 a < p f 2 ,
M L ( x ) = 1 for | x | < p f 10 0.75 for p f 10 | x | < 3 p f 10 0.25 for 3 p f 10 | x | p f 2 .
p ˆ p = a 1 r spot 2 + a 2 r spot + a 3 ( µ m ) ,
l c = p f p ˆ p .

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