Abstract

To an ultra-wide-angle and panoramic optical system, the aberrations of point object at any field angle are separated into two types: the aperture-ray aberrations of off-axis point object and the chief-ray aberrations. A simple form of the triangular formulae of tracing an oblique-incidence ray is derived to calculate the chief-ray parameters and their aberrations; moreover, the aperture-ray aberrations of an off-axis point object are analyzed with the plane-symmetric aberration theory. Based on the two types of aberrations, we present a merit function for ultra-wide-angle and panoramic optical systems; the optimization program with the differential-evolution algorithm is then developed. To validate the optimization method we finally optimize a fish-eye lens and a catadioptric omnidirectional imaging system.

© 2012 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. B. Martin, “Design issue of a hyper-field fisheye lens,” Proc. SPIE 5524, 84–392 (2004).
    [CrossRef]
  2. I. Powell, “Panoramic lens,” Appl. Opt. 33, 7356–7361(1994).
    [CrossRef]
  3. J. Kumler and M. Bauer, “Fisheye lens designs and their relative performance,” Proc. SPIE 4093, 360–369(2000).
    [CrossRef]
  4. J. S. Chahl and M. V. Srinvasan, “Reflective surfaces for panoramic imaging,” Appl. Opt. 36, 8275–8285 (1997).
    [CrossRef]
  5. G.-I. Kweon, K. T. Kim, G. H. Kim, and H.-S. Kim, “Folded catadioptric panoramic lens with equidistance projection scheme,” Appl. Opt. 44, 2759–2767 (2005).
    [CrossRef]
  6. S.-S. Lin and R. Bajcsy, “Single-viewpoint, catadioptric cone mirror omnidirectional imaging theory and analysis,” J. Opt. Soc. Am. 23, 2997–3015 (2006).
    [CrossRef]
  7. L.-P. Wang, L.-C. Zhang, F.-Y. He, and C.-S. Jin, “Design of aspheric mirror for panoramic imaging system using multi-population genetic algorithm,” Opt. Precis. Eng. 17, 1020–1025 (2009).
    [CrossRef]
  8. M. Born and E. Wolf, Principle of Optics7th ed. (Cambridge University, 2005).
  9. W. J. Smith, Modern Lens Design (McGraw-Hill, 1992).
  10. Y.-Z. Wand, Fisheye Lens Optics (Science, 2006).
  11. S. Baker, “A theory of single-viewpoint catadioptric image formation,” Int. J. Comput. Vis. 35, 175–196 (1999).
    [CrossRef]
  12. R. Swaminathan, M. D. Grossberg, and S. K. Nayer, “Non-single viewpoint catadioptric cameras: geometry and analysis,” Int. J. Comput. Vis. 66, 211–229 (2006).
    [CrossRef]
  13. H. Noda, T. Namioka, and M. Seya, “Geometrical theory of the grating,” J. Opt. Soc. Am. 64, 1031–1036 (1974).
    [CrossRef]
  14. T. Namioka, M. Koike, and D. Content, “Geometric theory of the ellipsoidal grating,” Appl. Opt. 33, 7261–7274 (1994).
    [CrossRef]
  15. T. Namioka, M. Koike, and S. Masui, “Geometric theory for the design of multielement optical system,” Opt. Precis. Eng.9, 459–467 (2001).
  16. M. P. Chrisp, “Aberrations of holographic toroidal grating systems,” Appl. Opt. 22, 1508–1518 (1983).
    [CrossRef]
  17. B. D. Stone and G. W. Forbes, “Second-order design methods for definitive studies of plane-symmetric, two-mirror systems,” J. Opt. Soc. Am. A 11, 3292–3307 (1994).
    [CrossRef]
  18. L.-J. Lu, “Aberration theory of plane-symmetric grating systems,” J. Synchrotron Radiat. 15, 399–410(2008).
    [CrossRef]
  19. L.-J. Lu and Z.-Y. Deng, “Geometric characteristics of aberrations of plane-symmetric optical systems,” Appl. Opt. 48, 6946–6960 (2009).
    [CrossRef]
  20. L.-J. Lu and D.-L. Lin, “Aberrations of plane-symmetric multi-element optical systems,” Optik 121, 1198–1218(2010).
    [CrossRef]
  21. H. Jung, Y. Lee, P. Yoon, and J. Kim, “Radial distortion refinement by inverse mapping-based extrapolation,” in 18th International Conference on Pattern Recognition, Vol. 1 (IEEE, 2006), pp. 675–678.
  22. R. Muller, “Fish-eye lens system,” U.S. patent 4,525,038 (25June1985).
  23. CODE V, Optical Design Program, Reference Manual (Optical Research Associates, 2003).

2010

L.-J. Lu and D.-L. Lin, “Aberrations of plane-symmetric multi-element optical systems,” Optik 121, 1198–1218(2010).
[CrossRef]

2009

L.-P. Wang, L.-C. Zhang, F.-Y. He, and C.-S. Jin, “Design of aspheric mirror for panoramic imaging system using multi-population genetic algorithm,” Opt. Precis. Eng. 17, 1020–1025 (2009).
[CrossRef]

L.-J. Lu and Z.-Y. Deng, “Geometric characteristics of aberrations of plane-symmetric optical systems,” Appl. Opt. 48, 6946–6960 (2009).
[CrossRef]

2008

L.-J. Lu, “Aberration theory of plane-symmetric grating systems,” J. Synchrotron Radiat. 15, 399–410(2008).
[CrossRef]

2006

S.-S. Lin and R. Bajcsy, “Single-viewpoint, catadioptric cone mirror omnidirectional imaging theory and analysis,” J. Opt. Soc. Am. 23, 2997–3015 (2006).
[CrossRef]

R. Swaminathan, M. D. Grossberg, and S. K. Nayer, “Non-single viewpoint catadioptric cameras: geometry and analysis,” Int. J. Comput. Vis. 66, 211–229 (2006).
[CrossRef]

2005

2004

C. B. Martin, “Design issue of a hyper-field fisheye lens,” Proc. SPIE 5524, 84–392 (2004).
[CrossRef]

2000

J. Kumler and M. Bauer, “Fisheye lens designs and their relative performance,” Proc. SPIE 4093, 360–369(2000).
[CrossRef]

1999

S. Baker, “A theory of single-viewpoint catadioptric image formation,” Int. J. Comput. Vis. 35, 175–196 (1999).
[CrossRef]

1997

1994

1983

1974

Bajcsy, R.

S.-S. Lin and R. Bajcsy, “Single-viewpoint, catadioptric cone mirror omnidirectional imaging theory and analysis,” J. Opt. Soc. Am. 23, 2997–3015 (2006).
[CrossRef]

Baker, S.

S. Baker, “A theory of single-viewpoint catadioptric image formation,” Int. J. Comput. Vis. 35, 175–196 (1999).
[CrossRef]

Bauer, M.

J. Kumler and M. Bauer, “Fisheye lens designs and their relative performance,” Proc. SPIE 4093, 360–369(2000).
[CrossRef]

Chahl, J. S.

Chrisp, M. P.

Content, D.

Deng, Z.-Y.

Forbes, G. W.

Grossberg, M. D.

R. Swaminathan, M. D. Grossberg, and S. K. Nayer, “Non-single viewpoint catadioptric cameras: geometry and analysis,” Int. J. Comput. Vis. 66, 211–229 (2006).
[CrossRef]

He, F.-Y.

L.-P. Wang, L.-C. Zhang, F.-Y. He, and C.-S. Jin, “Design of aspheric mirror for panoramic imaging system using multi-population genetic algorithm,” Opt. Precis. Eng. 17, 1020–1025 (2009).
[CrossRef]

Jin, C.-S.

L.-P. Wang, L.-C. Zhang, F.-Y. He, and C.-S. Jin, “Design of aspheric mirror for panoramic imaging system using multi-population genetic algorithm,” Opt. Precis. Eng. 17, 1020–1025 (2009).
[CrossRef]

Jung, H.

H. Jung, Y. Lee, P. Yoon, and J. Kim, “Radial distortion refinement by inverse mapping-based extrapolation,” in 18th International Conference on Pattern Recognition, Vol. 1 (IEEE, 2006), pp. 675–678.

Kim, G. H.

Kim, H.-S.

Kim, J.

H. Jung, Y. Lee, P. Yoon, and J. Kim, “Radial distortion refinement by inverse mapping-based extrapolation,” in 18th International Conference on Pattern Recognition, Vol. 1 (IEEE, 2006), pp. 675–678.

Kim, K. T.

Koike, M.

T. Namioka, M. Koike, and D. Content, “Geometric theory of the ellipsoidal grating,” Appl. Opt. 33, 7261–7274 (1994).
[CrossRef]

T. Namioka, M. Koike, and S. Masui, “Geometric theory for the design of multielement optical system,” Opt. Precis. Eng.9, 459–467 (2001).

Kumler, J.

J. Kumler and M. Bauer, “Fisheye lens designs and their relative performance,” Proc. SPIE 4093, 360–369(2000).
[CrossRef]

Kweon, G.-I.

Lee, Y.

H. Jung, Y. Lee, P. Yoon, and J. Kim, “Radial distortion refinement by inverse mapping-based extrapolation,” in 18th International Conference on Pattern Recognition, Vol. 1 (IEEE, 2006), pp. 675–678.

Lin, D.-L.

L.-J. Lu and D.-L. Lin, “Aberrations of plane-symmetric multi-element optical systems,” Optik 121, 1198–1218(2010).
[CrossRef]

Lin, S.-S.

S.-S. Lin and R. Bajcsy, “Single-viewpoint, catadioptric cone mirror omnidirectional imaging theory and analysis,” J. Opt. Soc. Am. 23, 2997–3015 (2006).
[CrossRef]

Lu, L.-J.

L.-J. Lu and D.-L. Lin, “Aberrations of plane-symmetric multi-element optical systems,” Optik 121, 1198–1218(2010).
[CrossRef]

L.-J. Lu and Z.-Y. Deng, “Geometric characteristics of aberrations of plane-symmetric optical systems,” Appl. Opt. 48, 6946–6960 (2009).
[CrossRef]

L.-J. Lu, “Aberration theory of plane-symmetric grating systems,” J. Synchrotron Radiat. 15, 399–410(2008).
[CrossRef]

Martin, C. B.

C. B. Martin, “Design issue of a hyper-field fisheye lens,” Proc. SPIE 5524, 84–392 (2004).
[CrossRef]

Masui, S.

T. Namioka, M. Koike, and S. Masui, “Geometric theory for the design of multielement optical system,” Opt. Precis. Eng.9, 459–467 (2001).

Muller, R.

R. Muller, “Fish-eye lens system,” U.S. patent 4,525,038 (25June1985).

Namioka, T.

Nayer, S. K.

R. Swaminathan, M. D. Grossberg, and S. K. Nayer, “Non-single viewpoint catadioptric cameras: geometry and analysis,” Int. J. Comput. Vis. 66, 211–229 (2006).
[CrossRef]

Noda, H.

Powell, I.

Seya, M.

Smith, W. J.

W. J. Smith, Modern Lens Design (McGraw-Hill, 1992).

Srinvasan, M. V.

Stone, B. D.

Swaminathan, R.

R. Swaminathan, M. D. Grossberg, and S. K. Nayer, “Non-single viewpoint catadioptric cameras: geometry and analysis,” Int. J. Comput. Vis. 66, 211–229 (2006).
[CrossRef]

Wand, Y.-Z.

Y.-Z. Wand, Fisheye Lens Optics (Science, 2006).

Wang, L.-P.

L.-P. Wang, L.-C. Zhang, F.-Y. He, and C.-S. Jin, “Design of aspheric mirror for panoramic imaging system using multi-population genetic algorithm,” Opt. Precis. Eng. 17, 1020–1025 (2009).
[CrossRef]

Yoon, P.

H. Jung, Y. Lee, P. Yoon, and J. Kim, “Radial distortion refinement by inverse mapping-based extrapolation,” in 18th International Conference on Pattern Recognition, Vol. 1 (IEEE, 2006), pp. 675–678.

Zhang, L.-C.

L.-P. Wang, L.-C. Zhang, F.-Y. He, and C.-S. Jin, “Design of aspheric mirror for panoramic imaging system using multi-population genetic algorithm,” Opt. Precis. Eng. 17, 1020–1025 (2009).
[CrossRef]

Appl. Opt.

Int. J. Comput. Vis.

S. Baker, “A theory of single-viewpoint catadioptric image formation,” Int. J. Comput. Vis. 35, 175–196 (1999).
[CrossRef]

R. Swaminathan, M. D. Grossberg, and S. K. Nayer, “Non-single viewpoint catadioptric cameras: geometry and analysis,” Int. J. Comput. Vis. 66, 211–229 (2006).
[CrossRef]

J. Opt. Soc. Am.

S.-S. Lin and R. Bajcsy, “Single-viewpoint, catadioptric cone mirror omnidirectional imaging theory and analysis,” J. Opt. Soc. Am. 23, 2997–3015 (2006).
[CrossRef]

H. Noda, T. Namioka, and M. Seya, “Geometrical theory of the grating,” J. Opt. Soc. Am. 64, 1031–1036 (1974).
[CrossRef]

J. Opt. Soc. Am. A

J. Synchrotron Radiat.

L.-J. Lu, “Aberration theory of plane-symmetric grating systems,” J. Synchrotron Radiat. 15, 399–410(2008).
[CrossRef]

Opt. Precis. Eng.

L.-P. Wang, L.-C. Zhang, F.-Y. He, and C.-S. Jin, “Design of aspheric mirror for panoramic imaging system using multi-population genetic algorithm,” Opt. Precis. Eng. 17, 1020–1025 (2009).
[CrossRef]

Optik

L.-J. Lu and D.-L. Lin, “Aberrations of plane-symmetric multi-element optical systems,” Optik 121, 1198–1218(2010).
[CrossRef]

Proc. SPIE

C. B. Martin, “Design issue of a hyper-field fisheye lens,” Proc. SPIE 5524, 84–392 (2004).
[CrossRef]

J. Kumler and M. Bauer, “Fisheye lens designs and their relative performance,” Proc. SPIE 4093, 360–369(2000).
[CrossRef]

Other

T. Namioka, M. Koike, and S. Masui, “Geometric theory for the design of multielement optical system,” Opt. Precis. Eng.9, 459–467 (2001).

M. Born and E. Wolf, Principle of Optics7th ed. (Cambridge University, 2005).

W. J. Smith, Modern Lens Design (McGraw-Hill, 1992).

Y.-Z. Wand, Fisheye Lens Optics (Science, 2006).

H. Jung, Y. Lee, P. Yoon, and J. Kim, “Radial distortion refinement by inverse mapping-based extrapolation,” in 18th International Conference on Pattern Recognition, Vol. 1 (IEEE, 2006), pp. 675–678.

R. Muller, “Fish-eye lens system,” U.S. patent 4,525,038 (25June1985).

CODE V, Optical Design Program, Reference Manual (Optical Research Associates, 2003).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Metrics