Abstract

The resolution limitation of integral photography (IP) is analyzed. Estimating the resolution of IP measured at the viewpoint, we derive the optimum width of the aperture or lens. It is shown that the resolution of aperture-plate IP is lower than conventional two-dimensional displays, even with an optimum design. When the ideal lens is utilized, however, lens-array IP can provide a three-dimensional display that is free from any discontinuous change of images that occur with the observer’s movement and with the same resolution that conventional two-dimensional displays feature.

© 1998 Optical Society of America

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References

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  1. H. Isono, M. Yasuda, “50-inch autostereoscopic full-color 3D TV display system,” in Stereoscopic Displays and Applications III, J. O. Merritt, S. S. Fisher, eds., Proc. SPIE1669, 176–185 (1992).
    [CrossRef]
  2. H. Isono, M. Yasuda, H. Sasazawa, “Autostereoscopic 3D LCD display using LCD-generated Parallax barrier,” in Proceedings of the 12th International Display Research Conference, Japan Display ’92 (Society for Information Display, Playa del Rey, Calif.,1992), pp. 303–306.
  3. T. Toda, S. Takahashi, F. Iwata, “3D video system using grating image,” in Practical Holography IX, S. A. Benton, ed., Proc. SPIE2406, 191–198 (1995).
    [CrossRef]
  4. S. Pastoor, K. Shenke, “Subjective assessments of the resolution of viewing directions in a multi-viewpoint 3D TV System,” Proc. SID 30/3, 217–224 (1989).
  5. Y. Kajiki, “Hologramlike video images by 45-view stereoscopic displays,” in Stereoscopic Displays and Virtual Reality Systems IV, S. S. Fisher, J. O. Merrit, M. T. Bolas, eds., Proc. SPIE3012, 154–166 (1997).
    [CrossRef]
  6. 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]
  7. C. B. Burckhardt, “Optimum parameters and resolution limitation of integral photography,” J. Opt. Soc. Am. 58, 71–76 (1967).
    [CrossRef]
  8. T. Okoshi, “Optimum design and depth resolution of lens-sheet and projection-type three-dimensional displays,” Appl. Opt. 10, 2284–2291 (1971).
    [CrossRef] [PubMed]
  9. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, NZZew York, 1968).

1997 (1)

1989 (1)

S. Pastoor, K. Shenke, “Subjective assessments of the resolution of viewing directions in a multi-viewpoint 3D TV System,” Proc. SID 30/3, 217–224 (1989).

1971 (1)

1967 (1)

Arai, J.

Burckhardt, C. B.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, NZZew York, 1968).

Hoshino, H.

Isono, H.

H. Isono, M. Yasuda, “50-inch autostereoscopic full-color 3D TV display system,” in Stereoscopic Displays and Applications III, J. O. Merritt, S. S. Fisher, eds., Proc. SPIE1669, 176–185 (1992).
[CrossRef]

H. Isono, M. Yasuda, H. Sasazawa, “Autostereoscopic 3D LCD display using LCD-generated Parallax barrier,” in Proceedings of the 12th International Display Research Conference, Japan Display ’92 (Society for Information Display, Playa del Rey, Calif.,1992), pp. 303–306.

Iwata, F.

T. Toda, S. Takahashi, F. Iwata, “3D video system using grating image,” in Practical Holography IX, S. A. Benton, ed., Proc. SPIE2406, 191–198 (1995).
[CrossRef]

Kajiki, Y.

Y. Kajiki, “Hologramlike video images by 45-view stereoscopic displays,” in Stereoscopic Displays and Virtual Reality Systems IV, S. S. Fisher, J. O. Merrit, M. T. Bolas, eds., Proc. SPIE3012, 154–166 (1997).
[CrossRef]

Okano, F.

Okoshi, T.

Pastoor, S.

S. Pastoor, K. Shenke, “Subjective assessments of the resolution of viewing directions in a multi-viewpoint 3D TV System,” Proc. SID 30/3, 217–224 (1989).

Sasazawa, H.

H. Isono, M. Yasuda, H. Sasazawa, “Autostereoscopic 3D LCD display using LCD-generated Parallax barrier,” in Proceedings of the 12th International Display Research Conference, Japan Display ’92 (Society for Information Display, Playa del Rey, Calif.,1992), pp. 303–306.

Shenke, K.

S. Pastoor, K. Shenke, “Subjective assessments of the resolution of viewing directions in a multi-viewpoint 3D TV System,” Proc. SID 30/3, 217–224 (1989).

Takahashi, S.

T. Toda, S. Takahashi, F. Iwata, “3D video system using grating image,” in Practical Holography IX, S. A. Benton, ed., Proc. SPIE2406, 191–198 (1995).
[CrossRef]

Toda, T.

T. Toda, S. Takahashi, F. Iwata, “3D video system using grating image,” in Practical Holography IX, S. A. Benton, ed., Proc. SPIE2406, 191–198 (1995).
[CrossRef]

Yasuda, M.

H. Isono, M. Yasuda, H. Sasazawa, “Autostereoscopic 3D LCD display using LCD-generated Parallax barrier,” in Proceedings of the 12th International Display Research Conference, Japan Display ’92 (Society for Information Display, Playa del Rey, Calif.,1992), pp. 303–306.

H. Isono, M. Yasuda, “50-inch autostereoscopic full-color 3D TV display system,” in Stereoscopic Displays and Applications III, J. O. Merritt, S. S. Fisher, eds., Proc. SPIE1669, 176–185 (1992).
[CrossRef]

Yuyama, I.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

Proc. SID (1)

S. Pastoor, K. Shenke, “Subjective assessments of the resolution of viewing directions in a multi-viewpoint 3D TV System,” Proc. SID 30/3, 217–224 (1989).

Other (5)

Y. Kajiki, “Hologramlike video images by 45-view stereoscopic displays,” in Stereoscopic Displays and Virtual Reality Systems IV, S. S. Fisher, J. O. Merrit, M. T. Bolas, eds., Proc. SPIE3012, 154–166 (1997).
[CrossRef]

H. Isono, M. Yasuda, “50-inch autostereoscopic full-color 3D TV display system,” in Stereoscopic Displays and Applications III, J. O. Merritt, S. S. Fisher, eds., Proc. SPIE1669, 176–185 (1992).
[CrossRef]

H. Isono, M. Yasuda, H. Sasazawa, “Autostereoscopic 3D LCD display using LCD-generated Parallax barrier,” in Proceedings of the 12th International Display Research Conference, Japan Display ’92 (Society for Information Display, Playa del Rey, Calif.,1992), pp. 303–306.

T. Toda, S. Takahashi, F. Iwata, “3D video system using grating image,” in Practical Holography IX, S. A. Benton, ed., Proc. SPIE2406, 191–198 (1995).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, NZZew York, 1968).

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Figures (11)

Fig. 1
Fig. 1

An IP setup that produces an image of a striped arrow.

Fig. 2
Fig. 2

Sampling of the real image by the pitch of the exit pupil.

Fig. 3
Fig. 3

Resolution of IP versus the image position zi, according to the depth factor D(=αi max/βnyq). (a) D1, (b) D=1.

Fig. 4
Fig. 4

Area where the resolution degradation does not occur versus the depth factor D. When D=1, it is possible to produce an image without resolution degradation at the middle position of the viewing distance L and at a great distance from the exit pupil.

Fig. 5
Fig. 5

IP aperture.

Fig. 6
Fig. 6

Examples of the resolution of aperture-plate IP. The viewing distance and the pitch of the aperture are assumed to be 2 m and 2.78 mm, respectively, and the Nyquist frequency (i.e., the 2-D resolution βnyq)=360 cpr. The gap g between the aperture and the element image is 1 mm (solid curves) or 5 mm (dashed curves). Thick curves show the overall resolution. The figure shows that a larger gap yields higher resolution.

Fig. 7
Fig. 7

Lens of the array.

Fig. 8
Fig. 8

Examples of the resolution of lens-array IP of parallel-projection type. The viewing distance is assumed to be 2 m. The lens width, which is equal to the lens pitch, is (a) 0.694 mm or (b) 2.78 mm.

Fig. 9
Fig. 9

Examples of the resolution of lens-array IP in which the focal length f of the lens is adjusted as proposed in Eq. (22). The viewing distance is assumed to be 2 m. The lens width, which is equal to the lens pitch, is (a) 0.694 mm or (b) 2.78 mm.

Fig. 10
Fig. 10

Viewing area of IP. Dashed lines are connected from the center of each element image to the center of the corresponding exit pupil. They cross at a single point Q, which is the center of the viewing area. At the fringe of the viewing area, the observer views the fringe of each element image (solid lines). Therefore this condition provides the optimum design for the widest viewing area.

Fig. 11
Fig. 11

Viewing area of IP versus the Nyquist frequency βnyq, i.e., the 2-D resolution. The viewing distance is assumed to be 2 m. Solid curves show that the gap g between the exit pupil and the element image is a certain value (1, 3, and 10 mm). Dashed curves indicate the maximum viewing area that an aperture-plate IP can treat, when the depth factor D is 0.1, 0.3, and 1.

Tables (2)

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Table 1 Parameters of Integral Photography

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Table 2 Examples of Integral-Photographya Designs

Equations (36)

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αi=fi|L-zi|.
βi=fizi=αizi|L-zi|.
βi max=αi maxzi|L-zi|.
βnyq=L/2pe.
βmax=min(βi max, βnyq)=minαi maxzi|L-zi|, βnyq.
D=αi max/βnyq.
βmax=βnyqminDzi|L-zi|, 1.
zn=L1+D,
zf=L1-D(D<1)(D1).
G(x)=exp(jπx2/λg),
MTFa(α)=1wa-(wa-αλ)/2+(wa-αλ)/2G(x+αλ/2)G*(x-αλ/2)dx,=1-αλwasincwa1-αλwaα/g(0αwa/λ)0(α>wa/λ),
waopt=2λg,
αcopt=2g/λ.
βmax=min2g/λzi|L-z2|, βnyq.
G(x)=exp[jπx2eerr(zi)/λ],
eerr(zi)=1L-zi+1g-1f.
MTFl(α)=1wl-(wl-αλ)/2+(wl-αλ)/2G(x+αλ/2)G*(x-αλ/2)dx=1-αλwlsincwl1-αλwlαeerr(zi)(0αwl/λ)0(α>wl/λ),
αcdif=wl/λ,
αcerr(zi)=2eerr(zi)1wl+[wl2-4λ/eerr(zi)]1/21eerr(zi)wl.
αc=min[αcdif, αcerr(zi)].
βmax=minαcdifzi|L-zi|, αcerr(zi)×zi|L-zi|, βnyq.
1f=1g+1L.
eerr(zi)=1L-zi-1L.
αcerr(zi)zi|L-zi|LwlLpe=2βnyq,
βmax=minαcdifzi|L-zi|, βnyq.
wlopt=pe,
βmax=minpeλzi|L-zi|, βnyq.
2ϴ=2 arctan(wd/2g).
wd=pe(L+g)/Lpe.
2ϴ=2 arctan(L/4βnyqg).
2ϴmaxapIP=2 arctan(L/D2βnyq3λ).
pe=L2βnyq,
g=L4βnyq tan ϴ.
αpαi max,
αp=g/2pp.
ppL8Dβnyq2 tan ϴ.

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