Abstract

The depth of field of a camera defines the depth range to be covered by the camera. In 3D images, the resolvable depth range is also determined by the depth of field (DOF). Hence the depth resolution and resolvable number of depth layers obtainable with a given 3D display will be defined within the DOF when the display has the same resolution as the total camera resolution of the array in the horizontal direction. The depth resolution and resolvable number of depth layers are mathematically derived in terms of the circle of confusion. The resolvable number of depth layers is approximately linearly proportional to the camera distance and inversely proportional to the aperture diameter of the camera objective. The accuracies of the derivations are examined experimentally. The results show that the DOF extends slightly and the depth resolution improves up to 20% more than that predicted by theory for the given experimental condition. This means that the depth resolution derived has more than 80% accuracy.

© 2013 Optical Society of America

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References

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  1. A. Woods, T. Docherty, and R. Koch, “Image distortions in stereoscopic video systems,” Proc. SPIE 1915, 36–48 (1993).
    [CrossRef]
  2. H. Yamanoue, “The relation between size distortion and shooting conditions for stereoscopic images,” J. SMPTE 106, 225–232 (1997).
    [CrossRef]
  3. D. B. Diner and D. H. Fender, Human Engineering in Stereoscopic Viewing Devices (Plenum, 1993).
  4. J.-Y. Son, Y. Gruts, J.-H. Chun, Y.-J. Choi, J.-E. Bahn, and V. I. Bobrinev, “Distortion analysis in stereoscopic images,” Opt. Eng.41, 680–685 (2002).
  5. J.-Y. Son, V. V. Saveljev, S.-K. Kim, and K.-T. Kim, “Comparisons of the perceived image in multiview and ip based 3 dimensional imaging systems,” Jpn. J. Appl. Phys. 46, 1057–1059 (2007).
    [CrossRef]
  6. J.-Y. Son, Y. Gruts, K.-D. Kwack, K.-H. Cha, and S.-K. Kim, “Stereoscopic image distortion in radial camera and projector configurations,” J. Opt. Soc. Am. A 24, 643–650 (2007).
    [CrossRef]
  7. T. Kanade, A. Yoshida, K. Oda, H. Kano, and M. Tanaka, “A stereo machine for video-rate dense depth mapping and its new applications,” in Proceedings of 1996 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), June 18–20, San Francisco (IEEE, 1996), pp. 196–202.
  8. J.-Y. Son, Y. Vashpanov, M.-S. Kim, M.-C. Park, and J.-S. Kim, “Image light distribution in the multiview 3-D imaging system,” J. Display Technol. 6, 336–345 (2010).
    [CrossRef]
  9. J.-Y. Son, V. I. Bobrinev, and K.-T. Kim, “Depth resolution and displayable depth of a scene in 3 dimensional images,” J. Opt. Soc. Am. A 22, 1739–1745 (2005).
    [CrossRef]
  10. G. Smith and D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge University, 1997).
  11. A. R. Greenleaf, Photographic Optics (Macmillan, 1950), pp. 25–27.
  12. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).
  13. I. P. Howard and B. J. Rogers, Binocular Vision and Stereopsis, Oxford Psychology Series No. 20 (Oxford University/Clarendon, 1995).
  14. http://imaging.nikon.com/lineup/dslr/d700/ .

2010 (1)

2007 (2)

J.-Y. Son, V. V. Saveljev, S.-K. Kim, and K.-T. Kim, “Comparisons of the perceived image in multiview and ip based 3 dimensional imaging systems,” Jpn. J. Appl. Phys. 46, 1057–1059 (2007).
[CrossRef]

J.-Y. Son, Y. Gruts, K.-D. Kwack, K.-H. Cha, and S.-K. Kim, “Stereoscopic image distortion in radial camera and projector configurations,” J. Opt. Soc. Am. A 24, 643–650 (2007).
[CrossRef]

2005 (1)

1997 (1)

H. Yamanoue, “The relation between size distortion and shooting conditions for stereoscopic images,” J. SMPTE 106, 225–232 (1997).
[CrossRef]

1993 (1)

A. Woods, T. Docherty, and R. Koch, “Image distortions in stereoscopic video systems,” Proc. SPIE 1915, 36–48 (1993).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).

Atchison, D. A.

G. Smith and D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge University, 1997).

Bahn, J.-E.

J.-Y. Son, Y. Gruts, J.-H. Chun, Y.-J. Choi, J.-E. Bahn, and V. I. Bobrinev, “Distortion analysis in stereoscopic images,” Opt. Eng.41, 680–685 (2002).

Bobrinev, V. I.

J.-Y. Son, V. I. Bobrinev, and K.-T. Kim, “Depth resolution and displayable depth of a scene in 3 dimensional images,” J. Opt. Soc. Am. A 22, 1739–1745 (2005).
[CrossRef]

J.-Y. Son, Y. Gruts, J.-H. Chun, Y.-J. Choi, J.-E. Bahn, and V. I. Bobrinev, “Distortion analysis in stereoscopic images,” Opt. Eng.41, 680–685 (2002).

Cha, K.-H.

Choi, Y.-J.

J.-Y. Son, Y. Gruts, J.-H. Chun, Y.-J. Choi, J.-E. Bahn, and V. I. Bobrinev, “Distortion analysis in stereoscopic images,” Opt. Eng.41, 680–685 (2002).

Chun, J.-H.

J.-Y. Son, Y. Gruts, J.-H. Chun, Y.-J. Choi, J.-E. Bahn, and V. I. Bobrinev, “Distortion analysis in stereoscopic images,” Opt. Eng.41, 680–685 (2002).

Diner, D. B.

D. B. Diner and D. H. Fender, Human Engineering in Stereoscopic Viewing Devices (Plenum, 1993).

Docherty, T.

A. Woods, T. Docherty, and R. Koch, “Image distortions in stereoscopic video systems,” Proc. SPIE 1915, 36–48 (1993).
[CrossRef]

Fender, D. H.

D. B. Diner and D. H. Fender, Human Engineering in Stereoscopic Viewing Devices (Plenum, 1993).

Greenleaf, A. R.

A. R. Greenleaf, Photographic Optics (Macmillan, 1950), pp. 25–27.

Gruts, Y.

J.-Y. Son, Y. Gruts, K.-D. Kwack, K.-H. Cha, and S.-K. Kim, “Stereoscopic image distortion in radial camera and projector configurations,” J. Opt. Soc. Am. A 24, 643–650 (2007).
[CrossRef]

J.-Y. Son, Y. Gruts, J.-H. Chun, Y.-J. Choi, J.-E. Bahn, and V. I. Bobrinev, “Distortion analysis in stereoscopic images,” Opt. Eng.41, 680–685 (2002).

Howard, I. P.

I. P. Howard and B. J. Rogers, Binocular Vision and Stereopsis, Oxford Psychology Series No. 20 (Oxford University/Clarendon, 1995).

Kanade, T.

T. Kanade, A. Yoshida, K. Oda, H. Kano, and M. Tanaka, “A stereo machine for video-rate dense depth mapping and its new applications,” in Proceedings of 1996 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), June 18–20, San Francisco (IEEE, 1996), pp. 196–202.

Kano, H.

T. Kanade, A. Yoshida, K. Oda, H. Kano, and M. Tanaka, “A stereo machine for video-rate dense depth mapping and its new applications,” in Proceedings of 1996 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), June 18–20, San Francisco (IEEE, 1996), pp. 196–202.

Kim, J.-S.

Kim, K.-T.

J.-Y. Son, V. V. Saveljev, S.-K. Kim, and K.-T. Kim, “Comparisons of the perceived image in multiview and ip based 3 dimensional imaging systems,” Jpn. J. Appl. Phys. 46, 1057–1059 (2007).
[CrossRef]

J.-Y. Son, V. I. Bobrinev, and K.-T. Kim, “Depth resolution and displayable depth of a scene in 3 dimensional images,” J. Opt. Soc. Am. A 22, 1739–1745 (2005).
[CrossRef]

Kim, M.-S.

Kim, S.-K.

J.-Y. Son, Y. Gruts, K.-D. Kwack, K.-H. Cha, and S.-K. Kim, “Stereoscopic image distortion in radial camera and projector configurations,” J. Opt. Soc. Am. A 24, 643–650 (2007).
[CrossRef]

J.-Y. Son, V. V. Saveljev, S.-K. Kim, and K.-T. Kim, “Comparisons of the perceived image in multiview and ip based 3 dimensional imaging systems,” Jpn. J. Appl. Phys. 46, 1057–1059 (2007).
[CrossRef]

Koch, R.

A. Woods, T. Docherty, and R. Koch, “Image distortions in stereoscopic video systems,” Proc. SPIE 1915, 36–48 (1993).
[CrossRef]

Kwack, K.-D.

Oda, K.

T. Kanade, A. Yoshida, K. Oda, H. Kano, and M. Tanaka, “A stereo machine for video-rate dense depth mapping and its new applications,” in Proceedings of 1996 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), June 18–20, San Francisco (IEEE, 1996), pp. 196–202.

Park, M.-C.

Rogers, B. J.

I. P. Howard and B. J. Rogers, Binocular Vision and Stereopsis, Oxford Psychology Series No. 20 (Oxford University/Clarendon, 1995).

Saveljev, V. V.

J.-Y. Son, V. V. Saveljev, S.-K. Kim, and K.-T. Kim, “Comparisons of the perceived image in multiview and ip based 3 dimensional imaging systems,” Jpn. J. Appl. Phys. 46, 1057–1059 (2007).
[CrossRef]

Smith, G.

G. Smith and D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge University, 1997).

Son, J.-Y.

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).

Tanaka, M.

T. Kanade, A. Yoshida, K. Oda, H. Kano, and M. Tanaka, “A stereo machine for video-rate dense depth mapping and its new applications,” in Proceedings of 1996 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), June 18–20, San Francisco (IEEE, 1996), pp. 196–202.

Vashpanov, Y.

Woods, A.

A. Woods, T. Docherty, and R. Koch, “Image distortions in stereoscopic video systems,” Proc. SPIE 1915, 36–48 (1993).
[CrossRef]

Yamanoue, H.

H. Yamanoue, “The relation between size distortion and shooting conditions for stereoscopic images,” J. SMPTE 106, 225–232 (1997).
[CrossRef]

Yoshida, A.

T. Kanade, A. Yoshida, K. Oda, H. Kano, and M. Tanaka, “A stereo machine for video-rate dense depth mapping and its new applications,” in Proceedings of 1996 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), June 18–20, San Francisco (IEEE, 1996), pp. 196–202.

J. Display Technol. (1)

J. Opt. Soc. Am. A (2)

J. SMPTE (1)

H. Yamanoue, “The relation between size distortion and shooting conditions for stereoscopic images,” J. SMPTE 106, 225–232 (1997).
[CrossRef]

Jpn. J. Appl. Phys. (1)

J.-Y. Son, V. V. Saveljev, S.-K. Kim, and K.-T. Kim, “Comparisons of the perceived image in multiview and ip based 3 dimensional imaging systems,” Jpn. J. Appl. Phys. 46, 1057–1059 (2007).
[CrossRef]

Proc. SPIE (1)

A. Woods, T. Docherty, and R. Koch, “Image distortions in stereoscopic video systems,” Proc. SPIE 1915, 36–48 (1993).
[CrossRef]

Other (8)

D. B. Diner and D. H. Fender, Human Engineering in Stereoscopic Viewing Devices (Plenum, 1993).

J.-Y. Son, Y. Gruts, J.-H. Chun, Y.-J. Choi, J.-E. Bahn, and V. I. Bobrinev, “Distortion analysis in stereoscopic images,” Opt. Eng.41, 680–685 (2002).

G. Smith and D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge University, 1997).

A. R. Greenleaf, Photographic Optics (Macmillan, 1950), pp. 25–27.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).

I. P. Howard and B. J. Rogers, Binocular Vision and Stereopsis, Oxford Psychology Series No. 20 (Oxford University/Clarendon, 1995).

http://imaging.nikon.com/lineup/dslr/d700/ .

T. Kanade, A. Yoshida, K. Oda, H. Kano, and M. Tanaka, “A stereo machine for video-rate dense depth mapping and its new applications,” in Proceedings of 1996 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), June 18–20, San Francisco (IEEE, 1996), pp. 196–202.

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Figures (11)

Fig. 1.
Fig. 1.

Recording geometry of a parallel-type stereo camera.

Fig. 2.
Fig. 2.

Geometry for determining β.

Fig. 3.
Fig. 3.

Viewing geometry that defines the perceivable image depth and depth resolution.

Fig. 4.
Fig. 4.

ΔL in Eq. (2) as a function of t for f values of 50 and 85 mm.

Fig. 5.
Fig. 5.

L1 and L2 in Eq. (3) for f=50 and 85 mm and D=14.28 and 21.25 mm, as a function of L.

Fig. 6.
Fig. 6.

Nl and Pn as a function of t. (a) f=50mm and (b) f=85mm.

Fig. 7.
Fig. 7.

Example of a line pattern used for the experiment.

Fig. 8.
Fig. 8.

Experimental setup.

Fig. 9.
Fig. 9.

Experimental results. (a) f=50mm and L=1.5m, (b) f=50mm and L=3.0m, (c) f=85mm and L=1.5m, and (d) f=85mm and L=3.0m.

Fig. 10.
Fig. 10.

Same as Figs. 9(a) and 9(c) when the duty cycle is 25%, for t=200mm.

Fig. 11.
Fig. 11.

Same as Figs. 9(a) and 9(c) when the width of each depth layer is reduced for t=200mm.

Tables (1)

Tables Icon

Table 1. Depth of Field and Number of Resolvable Depth Layers

Equations (8)

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

ΔL=pL(Lf)tfp(Lf),
ΔL=wL(Lf)tfw(Lf).
OD=L2L1=2LfD(Lf)w(Df)2(Lf)2w2,
L1=LfDfD+(Lf)w,L2=LfDfD(Lf)w.
Pn=pn[tan1{tfD+(Lf)wLfD}tan1{tfD(Lf)wLfD}]2wtan1(np/2f)=pntan1[2tLfD(Lf)w(LfD)2+t2{f2D2(Lf)2w2}]2wtan1(np/2f).
Nl=L1L21ΔLdL=L1L2tfw(Lf)wL(Lf)dL=twln(L2f)L1(L1f)L2lnL2L1=twlnD+wDwlnfD+(Lf)wfD(Lf)w.
Pn2tD.
Nl=2tD2LwfD=2(ftLw)fD2tD.

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