Abstract

A catadioptric wide-angle lens having a rectilinear projection scheme has been developed with a view to possible applications in the security–surveillance area. The lens has been designed for a miniature camera with a video graphics array-grade 1∕3 in. color CCD sensor. The field of view of the lens is over 151°, and still distortion is under 1%. Furthermore, the modulation transfer function is better than 0.3 at 70 line pairs∕mm over the whole active area of the image sensor.

© 2006 Optical Society of America

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References

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  1. K. Yamazawa, Y. Yagi, and M. Yachida, "Obstacle detection with omnidirectional image sensor hyperomni vision," in IEEE International Conference on Robotics and Automation (IEEE, 1995), pp. 1062-1067.
  2. H. Ishiguro, "Development of low-cost compact omnidirectional vision sensors," in Panoramic Vision: Sensors, Theory, and Applications, R.Benosman and S.Kang, eds. (Springer, 2001), Chap. 3.
  3. S. Hrabar and G. S. Sukhatme, "Omnidirectional vision for an autonomous helicopter," in Proceedings of the 2003 IEEE International Conference on Robotics and Automation (IEEE, 2003), pp. 558-563.
    [CrossRef]
  4. R. W. Wood, "Fish-eye views, and vision under water," Philos. Mag. 12, 159-162 (1906).
  5. W. N. Bond, "A wide angle lens for cloud recording," Philos. Mag. 44, 999-1001 (1922).
  6. R. Hill, "A lens for whole sky photographs," Q. J. R. Meteorol. Soc. 50, 227-235 (1924).
    [CrossRef]
  7. C. Beck, "Apparatus to photograph the whole sky," J. Sci. Instrum. 2, 135-139 (1925).
    [CrossRef]
  8. K. Miyamoto, "Fish-eye lens," J. Opt. Soc. Am. 54, 1060-1061 (1964).
    [CrossRef]
  9. R. A. Hicks and R. Bajcsy, "Reflective surfaces as computational sensors," Image Vis. Comput. 19, 773-777 (2001).
    [CrossRef]
  10. J. S. Chahl and M. V. Srinivasan, "Reflective surfaces for panoramic imaging," Appl. Opt. 36, 8275-8285 (1997).
    [CrossRef]
  11. G. Kweon, K. Kim, G. Kim, and H. Kim, "Folded catadioptric panoramic lens with an equidistance projection scheme," Appl. Opt. 44, 2759-2767 (2005).
    [CrossRef] [PubMed]
  12. G. Kweon, S. Choi, Y. Choi, G. Kim, S. Yang, and Y. Lee, "A wide-angle catadioptric lens with rectilinear projection," in Optical Design and Engineering II, L. Mazuray and R. Wartmann, eds., Proc. SPIE. 5962, 59620Z (2005).
    [CrossRef]
  13. G. Kweon, K. Kim, Y. Choi, G. Kim, and S. Yang, "Catadioptric panoramic lens with a rectilinear projection scheme," J. Korean Phys. Soc. 48, 554-563 (2006).
  14. G. Kweon and M. Laikin, "Design of a mega-pixel grade catadioptric panoramic lens with the rectilinear projection scheme," J. Opt. Soc. Korea 10, 67-75 (2006).
    [CrossRef]

2006 (2)

G. Kweon, K. Kim, Y. Choi, G. Kim, and S. Yang, "Catadioptric panoramic lens with a rectilinear projection scheme," J. Korean Phys. Soc. 48, 554-563 (2006).

G. Kweon and M. Laikin, "Design of a mega-pixel grade catadioptric panoramic lens with the rectilinear projection scheme," J. Opt. Soc. Korea 10, 67-75 (2006).
[CrossRef]

2005 (2)

G. Kweon, K. Kim, G. Kim, and H. Kim, "Folded catadioptric panoramic lens with an equidistance projection scheme," Appl. Opt. 44, 2759-2767 (2005).
[CrossRef] [PubMed]

G. Kweon, S. Choi, Y. Choi, G. Kim, S. Yang, and Y. Lee, "A wide-angle catadioptric lens with rectilinear projection," in Optical Design and Engineering II, L. Mazuray and R. Wartmann, eds., Proc. SPIE. 5962, 59620Z (2005).
[CrossRef]

2001 (1)

R. A. Hicks and R. Bajcsy, "Reflective surfaces as computational sensors," Image Vis. Comput. 19, 773-777 (2001).
[CrossRef]

1997 (1)

1964 (1)

1925 (1)

C. Beck, "Apparatus to photograph the whole sky," J. Sci. Instrum. 2, 135-139 (1925).
[CrossRef]

1924 (1)

R. Hill, "A lens for whole sky photographs," Q. J. R. Meteorol. Soc. 50, 227-235 (1924).
[CrossRef]

1922 (1)

W. N. Bond, "A wide angle lens for cloud recording," Philos. Mag. 44, 999-1001 (1922).

1906 (1)

R. W. Wood, "Fish-eye views, and vision under water," Philos. Mag. 12, 159-162 (1906).

Bajcsy, R.

R. A. Hicks and R. Bajcsy, "Reflective surfaces as computational sensors," Image Vis. Comput. 19, 773-777 (2001).
[CrossRef]

Beck, C.

C. Beck, "Apparatus to photograph the whole sky," J. Sci. Instrum. 2, 135-139 (1925).
[CrossRef]

Bond, W. N.

W. N. Bond, "A wide angle lens for cloud recording," Philos. Mag. 44, 999-1001 (1922).

Chahl, J. S.

Choi, S.

G. Kweon, S. Choi, Y. Choi, G. Kim, S. Yang, and Y. Lee, "A wide-angle catadioptric lens with rectilinear projection," in Optical Design and Engineering II, L. Mazuray and R. Wartmann, eds., Proc. SPIE. 5962, 59620Z (2005).
[CrossRef]

Choi, Y.

G. Kweon, K. Kim, Y. Choi, G. Kim, and S. Yang, "Catadioptric panoramic lens with a rectilinear projection scheme," J. Korean Phys. Soc. 48, 554-563 (2006).

G. Kweon, S. Choi, Y. Choi, G. Kim, S. Yang, and Y. Lee, "A wide-angle catadioptric lens with rectilinear projection," in Optical Design and Engineering II, L. Mazuray and R. Wartmann, eds., Proc. SPIE. 5962, 59620Z (2005).
[CrossRef]

Hicks, R. A.

R. A. Hicks and R. Bajcsy, "Reflective surfaces as computational sensors," Image Vis. Comput. 19, 773-777 (2001).
[CrossRef]

Hill, R.

R. Hill, "A lens for whole sky photographs," Q. J. R. Meteorol. Soc. 50, 227-235 (1924).
[CrossRef]

Hrabar, S.

S. Hrabar and G. S. Sukhatme, "Omnidirectional vision for an autonomous helicopter," in Proceedings of the 2003 IEEE International Conference on Robotics and Automation (IEEE, 2003), pp. 558-563.
[CrossRef]

Ishiguro, H.

H. Ishiguro, "Development of low-cost compact omnidirectional vision sensors," in Panoramic Vision: Sensors, Theory, and Applications, R.Benosman and S.Kang, eds. (Springer, 2001), Chap. 3.

Kim, G.

G. Kweon, K. Kim, Y. Choi, G. Kim, and S. Yang, "Catadioptric panoramic lens with a rectilinear projection scheme," J. Korean Phys. Soc. 48, 554-563 (2006).

G. Kweon, S. Choi, Y. Choi, G. Kim, S. Yang, and Y. Lee, "A wide-angle catadioptric lens with rectilinear projection," in Optical Design and Engineering II, L. Mazuray and R. Wartmann, eds., Proc. SPIE. 5962, 59620Z (2005).
[CrossRef]

G. Kweon, K. Kim, G. Kim, and H. Kim, "Folded catadioptric panoramic lens with an equidistance projection scheme," Appl. Opt. 44, 2759-2767 (2005).
[CrossRef] [PubMed]

Kim, H.

Kim, K.

G. Kweon, K. Kim, Y. Choi, G. Kim, and S. Yang, "Catadioptric panoramic lens with a rectilinear projection scheme," J. Korean Phys. Soc. 48, 554-563 (2006).

G. Kweon, K. Kim, G. Kim, and H. Kim, "Folded catadioptric panoramic lens with an equidistance projection scheme," Appl. Opt. 44, 2759-2767 (2005).
[CrossRef] [PubMed]

Kweon, G.

G. Kweon, K. Kim, Y. Choi, G. Kim, and S. Yang, "Catadioptric panoramic lens with a rectilinear projection scheme," J. Korean Phys. Soc. 48, 554-563 (2006).

G. Kweon and M. Laikin, "Design of a mega-pixel grade catadioptric panoramic lens with the rectilinear projection scheme," J. Opt. Soc. Korea 10, 67-75 (2006).
[CrossRef]

G. Kweon, S. Choi, Y. Choi, G. Kim, S. Yang, and Y. Lee, "A wide-angle catadioptric lens with rectilinear projection," in Optical Design and Engineering II, L. Mazuray and R. Wartmann, eds., Proc. SPIE. 5962, 59620Z (2005).
[CrossRef]

G. Kweon, K. Kim, G. Kim, and H. Kim, "Folded catadioptric panoramic lens with an equidistance projection scheme," Appl. Opt. 44, 2759-2767 (2005).
[CrossRef] [PubMed]

Laikin, M.

Lee, Y.

G. Kweon, S. Choi, Y. Choi, G. Kim, S. Yang, and Y. Lee, "A wide-angle catadioptric lens with rectilinear projection," in Optical Design and Engineering II, L. Mazuray and R. Wartmann, eds., Proc. SPIE. 5962, 59620Z (2005).
[CrossRef]

Miyamoto, K.

Srinivasan, M. V.

Sukhatme, G. S.

S. Hrabar and G. S. Sukhatme, "Omnidirectional vision for an autonomous helicopter," in Proceedings of the 2003 IEEE International Conference on Robotics and Automation (IEEE, 2003), pp. 558-563.
[CrossRef]

Wood, R. W.

R. W. Wood, "Fish-eye views, and vision under water," Philos. Mag. 12, 159-162 (1906).

Yachida, M.

K. Yamazawa, Y. Yagi, and M. Yachida, "Obstacle detection with omnidirectional image sensor hyperomni vision," in IEEE International Conference on Robotics and Automation (IEEE, 1995), pp. 1062-1067.

Yagi, Y.

K. Yamazawa, Y. Yagi, and M. Yachida, "Obstacle detection with omnidirectional image sensor hyperomni vision," in IEEE International Conference on Robotics and Automation (IEEE, 1995), pp. 1062-1067.

Yamazawa, K.

K. Yamazawa, Y. Yagi, and M. Yachida, "Obstacle detection with omnidirectional image sensor hyperomni vision," in IEEE International Conference on Robotics and Automation (IEEE, 1995), pp. 1062-1067.

Yang, S.

G. Kweon, K. Kim, Y. Choi, G. Kim, and S. Yang, "Catadioptric panoramic lens with a rectilinear projection scheme," J. Korean Phys. Soc. 48, 554-563 (2006).

G. Kweon, S. Choi, Y. Choi, G. Kim, S. Yang, and Y. Lee, "A wide-angle catadioptric lens with rectilinear projection," in Optical Design and Engineering II, L. Mazuray and R. Wartmann, eds., Proc. SPIE. 5962, 59620Z (2005).
[CrossRef]

Appl. Opt. (2)

Image Vis. Comput. (1)

R. A. Hicks and R. Bajcsy, "Reflective surfaces as computational sensors," Image Vis. Comput. 19, 773-777 (2001).
[CrossRef]

J. Korean Phys. Soc. (1)

G. Kweon, K. Kim, Y. Choi, G. Kim, and S. Yang, "Catadioptric panoramic lens with a rectilinear projection scheme," J. Korean Phys. Soc. 48, 554-563 (2006).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Korea (1)

J. Sci. Instrum. (1)

C. Beck, "Apparatus to photograph the whole sky," J. Sci. Instrum. 2, 135-139 (1925).
[CrossRef]

Philos. Mag. (2)

R. W. Wood, "Fish-eye views, and vision under water," Philos. Mag. 12, 159-162 (1906).

W. N. Bond, "A wide angle lens for cloud recording," Philos. Mag. 44, 999-1001 (1922).

Proc. SPIE. (1)

G. Kweon, S. Choi, Y. Choi, G. Kim, S. Yang, and Y. Lee, "A wide-angle catadioptric lens with rectilinear projection," in Optical Design and Engineering II, L. Mazuray and R. Wartmann, eds., Proc. SPIE. 5962, 59620Z (2005).
[CrossRef]

Q. J. R. Meteorol. Soc. (1)

R. Hill, "A lens for whole sky photographs," Q. J. R. Meteorol. Soc. 50, 227-235 (1924).
[CrossRef]

Other (3)

K. Yamazawa, Y. Yagi, and M. Yachida, "Obstacle detection with omnidirectional image sensor hyperomni vision," in IEEE International Conference on Robotics and Automation (IEEE, 1995), pp. 1062-1067.

H. Ishiguro, "Development of low-cost compact omnidirectional vision sensors," in Panoramic Vision: Sensors, Theory, and Applications, R.Benosman and S.Kang, eds. (Springer, 2001), Chap. 3.

S. Hrabar and G. S. Sukhatme, "Omnidirectional vision for an autonomous helicopter," in Proceedings of the 2003 IEEE International Conference on Robotics and Automation (IEEE, 2003), pp. 558-563.
[CrossRef]

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Figures (25)

Fig. 1
Fig. 1

(Color online) Schematic illustrating the operating principle of the catadioptric lens.

Fig. 2
Fig. 2

(Color online) Schematic illustrating the relation between the image sensor dimension and the semi-FOVs of the imaging system along the vertical, the horizontal, and the diagonal directions.

Fig. 3
Fig. 3

(Color online) Initial layout of the catadioptric imaging system.

Fig. 4
Fig. 4

(Color online) Profile of a rectilinear wide-angle mirror.

Fig. 5
Fig. 5

(Color online) Calculated ray trajectories for the rectilinear wide-angle mirror in Fig. 4.

Fig. 6
Fig. 6

(Color online) Discrepancy between the mirror profile in Fig. 4 and the best numerical fit to the even aspheric lens formula with seven aspherical deformation terms.

Fig. 7
Fig. 7

(Color online) Optical layout of the catadioptric wide-angle lens.

Fig. 8
Fig. 8

(Color online) Ray aberration plot.

Fig. 9
Fig. 9

(Color online) Spot diagram.

Fig. 10
Fig. 10

(Color online) MTF.

Fig. 11
Fig. 11

(Color online) Field curvature and the distortion.

Fig. 12
Fig. 12

(Color online) Distortion grid plot.

Fig. 13
Fig. 13

(Color online) Relative illumination.

Fig. 14
Fig. 14

(Color online) Mechanical drawing of the completed catadioptric wide-angle lens.

Fig. 15
Fig. 15

(Color online) Photograph of the completed catadioptric lens with a bullet camera on a pole.

Fig. 16
Fig. 16

(Color online) Sample image of a room captured with the catadioptric imaging system.

Fig. 17
Fig. 17

(Color online) Photograph of a quick setup for testing the orientation dependence of the rectilinearity.

Fig. 18
Fig. 18

(Color online) Still video image corresponding to the setup in Fig. 17.

Fig. 19
Fig. 19

(Color online) Photograph of another setup for testing the suitability of the lens in the security area.

Fig. 20
Fig. 20

(Color online) Sample video image of the university bookstore.

Fig. 21
Fig. 21

(Color online) Another sample video image of the university bookstore at a different spot.

Fig. 22
Fig. 22

(Color online) MTF of a design for a 1∕4 in. CCD sensor.

Fig. 23
Fig. 23

(Color online) Field curvature and the distortion.

Fig. 24
Fig. 24

(Color online) MTF of a design with a larger mirror for a 1∕3 in. CCD sensor.

Fig. 25
Fig. 25

(Color online) Field curvature and the distortion.

Tables (5)

Tables Icon

Table 1 Fitting Coefficients of the Mirror Profile to the Even Aspheric Lens Formula

Tables Icon

Table 2 Lens Prescriptions Optimized for a 1∕3 in. CCD Sensor

Tables Icon

Table 3 Lens Prescriptions Optimized for a 1∕4 in. CCD Sensor

Tables Icon

Table 4 Fitting Coefficients of the Larger Mirror Profile to the Even Aspheric Lens Formula

Tables Icon

Table 5 Lens Prescriptions Optimized for a 1∕3 in. CCD Sensor with a Larger Mirror

Equations (6)

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

r ( θ ) = r ( 0 ) exp [ 0 θ sin θ + cot ϕ ( θ ) cos θ cos θ cot ϕ ( θ ) sin θ  d θ ] ,
ϕ = θ + ( π δ ) 2 .
ξ = f tan θ .
δ ( θ ) = tan 1 [ tan δ r tan θ r tan θ ] .
θ D = tan 1 ( W 2 + H 2 2 f ) .
h ( ρ ) = ρ 2 / R 1 + 1 ( 1 + k ) ( ρ / R ) 2 + i = 1 n C i ρ 2 + 2 i

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