Abstract

We present a telecentric lens that is able to gain 3D information. The proposed lens system has multiple aperture stops, which enable it to capture multidirectional parallel light rays, while a conventional telecentric lens has only one aperture stop and can capture only light rays that are perpendicular to the lens. We explain the geometry of the multiaperture telecentric system and show that correspondences fall on a line like those in a conventional stereo. As it is a single-lens sensor, we also introduce the principles of 3D reconstruction. Unlike a conventional stereo camera, the disparity of a scene point measured by the proposed lens system is linearly proportional to the depth of a scene point.

© 2011 Optical Society of America

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References

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  1. M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics (McGraw-Hill, 2010).
  2. Opto Engineering, “Telecentric lenses: basic information and working principles,” http://www.opto-engineering.com/telecentric-lenses-tutorial.html.
  3. E. H. Adelson and J. R. Bergen, in Computational Models of Visual Processing (MIT, 1991), pp. 3–20.
  4. E. H. Adelson and J. Y. A. Wang, IEEE Trans. Pattern Anal. Machine Intell. 14, 99 (1992).
    [CrossRef]
  5. B. Wilburn, N. Joshi, V. Vaish, M. Levoy, and M. Horowitz, in IEEE Society Conference on Pattern Recognition (IEEE, 2004), pp. 294–301.
  6. B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, ACM Trans. Graph. 24, 765 (2005).
    [CrossRef]
  7. A. Zomet and S. Nayar, in IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2006), pp. 339–346.
  8. D. Forsyth and J. Ponce, Computer Vision: A Modern Approach (Prentice-Hall, 2003).

2005 (1)

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, ACM Trans. Graph. 24, 765 (2005).
[CrossRef]

1992 (1)

E. H. Adelson and J. Y. A. Wang, IEEE Trans. Pattern Anal. Machine Intell. 14, 99 (1992).
[CrossRef]

Adams, A.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, ACM Trans. Graph. 24, 765 (2005).
[CrossRef]

Adelson, E. H.

E. H. Adelson and J. Y. A. Wang, IEEE Trans. Pattern Anal. Machine Intell. 14, 99 (1992).
[CrossRef]

E. H. Adelson and J. R. Bergen, in Computational Models of Visual Processing (MIT, 1991), pp. 3–20.

Antunez, E.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, ACM Trans. Graph. 24, 765 (2005).
[CrossRef]

Barth, A.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, ACM Trans. Graph. 24, 765 (2005).
[CrossRef]

Bass, M.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics (McGraw-Hill, 2010).

Bergen, J. R.

E. H. Adelson and J. R. Bergen, in Computational Models of Visual Processing (MIT, 1991), pp. 3–20.

DeCusatis, C.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics (McGraw-Hill, 2010).

Enoch, J.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics (McGraw-Hill, 2010).

Forsyth, D.

D. Forsyth and J. Ponce, Computer Vision: A Modern Approach (Prentice-Hall, 2003).

Horowitz, M.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, ACM Trans. Graph. 24, 765 (2005).
[CrossRef]

B. Wilburn, N. Joshi, V. Vaish, M. Levoy, and M. Horowitz, in IEEE Society Conference on Pattern Recognition (IEEE, 2004), pp. 294–301.

Joshi, N.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, ACM Trans. Graph. 24, 765 (2005).
[CrossRef]

B. Wilburn, N. Joshi, V. Vaish, M. Levoy, and M. Horowitz, in IEEE Society Conference on Pattern Recognition (IEEE, 2004), pp. 294–301.

Lakshminarayanan, V.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics (McGraw-Hill, 2010).

Levoy, M.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, ACM Trans. Graph. 24, 765 (2005).
[CrossRef]

B. Wilburn, N. Joshi, V. Vaish, M. Levoy, and M. Horowitz, in IEEE Society Conference on Pattern Recognition (IEEE, 2004), pp. 294–301.

Li, G.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics (McGraw-Hill, 2010).

Macdonald, C.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics (McGraw-Hill, 2010).

Mahajan, V.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics (McGraw-Hill, 2010).

Nayar, S.

A. Zomet and S. Nayar, in IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2006), pp. 339–346.

Ponce, J.

D. Forsyth and J. Ponce, Computer Vision: A Modern Approach (Prentice-Hall, 2003).

Talvala, E.-V.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, ACM Trans. Graph. 24, 765 (2005).
[CrossRef]

Vaish, V.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, ACM Trans. Graph. 24, 765 (2005).
[CrossRef]

B. Wilburn, N. Joshi, V. Vaish, M. Levoy, and M. Horowitz, in IEEE Society Conference on Pattern Recognition (IEEE, 2004), pp. 294–301.

Van Stryland, E.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics (McGraw-Hill, 2010).

Wang, J. Y. A.

E. H. Adelson and J. Y. A. Wang, IEEE Trans. Pattern Anal. Machine Intell. 14, 99 (1992).
[CrossRef]

Wilburn, B.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, ACM Trans. Graph. 24, 765 (2005).
[CrossRef]

B. Wilburn, N. Joshi, V. Vaish, M. Levoy, and M. Horowitz, in IEEE Society Conference on Pattern Recognition (IEEE, 2004), pp. 294–301.

Zomet, A.

A. Zomet and S. Nayar, in IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2006), pp. 339–346.

ACM Trans. Graph. (1)

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, ACM Trans. Graph. 24, 765 (2005).
[CrossRef]

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

E. H. Adelson and J. Y. A. Wang, IEEE Trans. Pattern Anal. Machine Intell. 14, 99 (1992).
[CrossRef]

Other (6)

B. Wilburn, N. Joshi, V. Vaish, M. Levoy, and M. Horowitz, in IEEE Society Conference on Pattern Recognition (IEEE, 2004), pp. 294–301.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics (McGraw-Hill, 2010).

Opto Engineering, “Telecentric lenses: basic information and working principles,” http://www.opto-engineering.com/telecentric-lenses-tutorial.html.

E. H. Adelson and J. R. Bergen, in Computational Models of Visual Processing (MIT, 1991), pp. 3–20.

A. Zomet and S. Nayar, in IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2006), pp. 339–346.

D. Forsyth and J. Ponce, Computer Vision: A Modern Approach (Prentice-Hall, 2003).

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Figures (8)

Fig. 1
Fig. 1

Location of an aperture stop in a telecentric lens. (a) Aperture stop on the optical axis selects light rays parallel to the optical axis. (b) Aperture stop off the optical axis selects different directional rays.

Fig. 2
Fig. 2

Proposed telecentric imaging system with two aperture stops.

Fig. 3
Fig. 3

Comparison between (a) the proposed multiaperture telecentric system and (b) the conventional stereo system for objects in different depths from the sensor. Theoretical disparity and its first derivatives when f = 20 and b = 5 are presented in (c) and (d), respectively.

Fig. 4
Fig. 4

Epipolar geometry on the image plane of the multiaperture telecentric imaging system. Set of light rays building a pencil of planes.

Fig. 5
Fig. 5

Ray diagram of the multiaperture telecentric imaging system. These stops are drawn much larger than the actual size.

Fig. 6
Fig. 6

Multiaperture telecentric imaging system using a Fresnel lens with a focal length of 215 mm .

Fig. 7
Fig. 7

Images on the screen for (a) closer and (b) farther objects.

Fig. 8
Fig. 8

Reconstruction of the filament using the proposed system. In these figures, the locations of a lens (blue), an aperture plane (red), and a screen (black) are shown, as well as the reconstructed filament in closer (blue) and farther (red) locations.

Equations (1)

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d = ( z 1 f 2 ) b .

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