Abstract

Traditional methods for geometrical camera calibration are based on calibration grids or single pixel illumination by collimated light. A new method for geometrical sensor calibration by means of Diffractive Optical Elements (DOE) in connection with a laser beam equipment is presented. This method can be especially used for 2D-sensor array systems but in principle also for line scanners.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. C. Brown, "Close-range camera calibration," Photogram. Engin. 37, 855-866 (1971)
  2. R. Y. Tsai, " A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf tv cameras and lenses, " IEEE Journal of Robotics and Automation 3, 323-344 (Aug. 1987).
  3. R. Schuster and B. Braunecker, "The Calibration of the ADC (Airborne Digital Camera) -System," Int. Arch. of Photogrammetry and Remote Sensing XXXIII, 288-294 (2000).
  4. T. A. Clarke and J. F. Fryer, " The development of camera calibration methods and models, " Photogram. Record 16, 51-66 (1998).
  5. A. Hermerschmidt, S. Krüger, and G. Wernicke, " Binary diffractive beam splitters with arbitrary diffraction angles," Opt. Lett. 32, 448-450 (2007).
  6. J. W. Goodman, "Introduction to Fourier Optics," 3rd ed., Roberts & Company Publishers (2005).
  7. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, "Stable implementation of the rigorous coupledwave analysis for surface-relief gratings: Enhanced transmittance matrix approach," J. Opt. Soc. Am. A 12, 1077-1086 (1995).
    [CrossRef]
  8. M. Ferstl, A. Hermerschmidt, D. Dias, and R. Steingrüber, "Theoretical and experimental properties of a binary linear beam splitting element with a large fan angle," J. Mod. Opt. 51, 2125-2139 (2004).
    [CrossRef]
  9. R. C. McPhedran, G. H. Derrick, and L. C. Brown, "Theory of crossed gratings," 227-275 in R. Petit (ed.), " Electromagnetic theory of gratings," Springer Verlag Berlin (1980)
  10. K. H. Strobl, W. Sepp, S. Fuchs, C. Paredes, and K. Arbter, "DLR CalLab und DLR CalDe, " http://www.robotic.dlr.de/callab/.

2007 (1)

2004 (1)

M. Ferstl, A. Hermerschmidt, D. Dias, and R. Steingrüber, "Theoretical and experimental properties of a binary linear beam splitting element with a large fan angle," J. Mod. Opt. 51, 2125-2139 (2004).
[CrossRef]

2000 (1)

R. Schuster and B. Braunecker, "The Calibration of the ADC (Airborne Digital Camera) -System," Int. Arch. of Photogrammetry and Remote Sensing XXXIII, 288-294 (2000).

1998 (1)

T. A. Clarke and J. F. Fryer, " The development of camera calibration methods and models, " Photogram. Record 16, 51-66 (1998).

1995 (1)

1987 (1)

R. Y. Tsai, " A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf tv cameras and lenses, " IEEE Journal of Robotics and Automation 3, 323-344 (Aug. 1987).

1971 (1)

D. C. Brown, "Close-range camera calibration," Photogram. Engin. 37, 855-866 (1971)

Braunecker, B.

R. Schuster and B. Braunecker, "The Calibration of the ADC (Airborne Digital Camera) -System," Int. Arch. of Photogrammetry and Remote Sensing XXXIII, 288-294 (2000).

Brown, D. C.

D. C. Brown, "Close-range camera calibration," Photogram. Engin. 37, 855-866 (1971)

Clarke, T. A.

T. A. Clarke and J. F. Fryer, " The development of camera calibration methods and models, " Photogram. Record 16, 51-66 (1998).

Dias, D.

M. Ferstl, A. Hermerschmidt, D. Dias, and R. Steingrüber, "Theoretical and experimental properties of a binary linear beam splitting element with a large fan angle," J. Mod. Opt. 51, 2125-2139 (2004).
[CrossRef]

Ferstl, M.

M. Ferstl, A. Hermerschmidt, D. Dias, and R. Steingrüber, "Theoretical and experimental properties of a binary linear beam splitting element with a large fan angle," J. Mod. Opt. 51, 2125-2139 (2004).
[CrossRef]

Fryer, J. F.

T. A. Clarke and J. F. Fryer, " The development of camera calibration methods and models, " Photogram. Record 16, 51-66 (1998).

Gaylord, T. K.

Grann, E. B.

Hermerschmidt, A.

A. Hermerschmidt, S. Krüger, and G. Wernicke, " Binary diffractive beam splitters with arbitrary diffraction angles," Opt. Lett. 32, 448-450 (2007).

M. Ferstl, A. Hermerschmidt, D. Dias, and R. Steingrüber, "Theoretical and experimental properties of a binary linear beam splitting element with a large fan angle," J. Mod. Opt. 51, 2125-2139 (2004).
[CrossRef]

Krüger, S.

Moharam, M. G.

Pommet, D. A.

Schuster, R.

R. Schuster and B. Braunecker, "The Calibration of the ADC (Airborne Digital Camera) -System," Int. Arch. of Photogrammetry and Remote Sensing XXXIII, 288-294 (2000).

Steingrüber, R.

M. Ferstl, A. Hermerschmidt, D. Dias, and R. Steingrüber, "Theoretical and experimental properties of a binary linear beam splitting element with a large fan angle," J. Mod. Opt. 51, 2125-2139 (2004).
[CrossRef]

Tsai, R. Y.

R. Y. Tsai, " A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf tv cameras and lenses, " IEEE Journal of Robotics and Automation 3, 323-344 (Aug. 1987).

Wernicke, G.

IEEE Journal of Robotics and Automation (1)

R. Y. Tsai, " A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf tv cameras and lenses, " IEEE Journal of Robotics and Automation 3, 323-344 (Aug. 1987).

Int. Arch. of Photogrammetry and Remote Sensing (1)

R. Schuster and B. Braunecker, "The Calibration of the ADC (Airborne Digital Camera) -System," Int. Arch. of Photogrammetry and Remote Sensing XXXIII, 288-294 (2000).

J. Mod. Opt. (1)

M. Ferstl, A. Hermerschmidt, D. Dias, and R. Steingrüber, "Theoretical and experimental properties of a binary linear beam splitting element with a large fan angle," J. Mod. Opt. 51, 2125-2139 (2004).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Photogram. Engin. (1)

D. C. Brown, "Close-range camera calibration," Photogram. Engin. 37, 855-866 (1971)

Photogram. Record (1)

T. A. Clarke and J. F. Fryer, " The development of camera calibration methods and models, " Photogram. Record 16, 51-66 (1998).

Other (3)

J. W. Goodman, "Introduction to Fourier Optics," 3rd ed., Roberts & Company Publishers (2005).

R. C. McPhedran, G. H. Derrick, and L. C. Brown, "Theory of crossed gratings," 227-275 in R. Petit (ed.), " Electromagnetic theory of gratings," Springer Verlag Berlin (1980)

K. H. Strobl, W. Sepp, S. Fuchs, C. Paredes, and K. Arbter, "DLR CalLab und DLR CalDe, " http://www.robotic.dlr.de/callab/.

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.


Figures (4)

Fig. 1.
Fig. 1.

Scheme of camera calibration with DOE

Fig. 2.
Fig. 2.

Original Dalsa image

Fig. 3.
Fig. 3.

Corrected image

Fig. 4.
Fig. 4.

Calibration pattern (+) with radial distortion vectors for Dalsa 1M28-SA

Tables (4)

Tables Icon

Table 1. DOE parameter

Tables Icon

Table 2. Camera parameters

Tables Icon

Table 3. Calibration results for the Dalsa 1M28-SA

Tables Icon

Table 4. Calibration results for the Nikon D2X

Equations (12)

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

d = [ λ f x , λ f y , ( 1 λ 2 ( f x 2 + f y 2 ) ) 1 2 , 0 ] T
r = [ sin ( β ) , sin ( α ) cos ( β ) , cos ( α ) cos ( β ) ] T
d = [ λ f x + r x , λ f y + r y , ( 1 ( λ f x + r x ) 2 ( λ f y + r y ) 2 ) 1 2 , 0 ] T .
d = [ R t 0 1 ] d
[ x y 1 ] = [ X Z Y Z 1 ]
[ u v 1 ] = K [ x y 1 ]
K = [ f 0 u 0 0 f v 0 0 0 1 ]
[ x ̂ y ̂ ] = [ x y ] + δ ( x , y )
δ ( x , y ) = [ x y ] ( k 1 r 2 + k 2 r 4 + k 3 r 6 + )
r 2 = x 2 + y 2
[ x y ] [ u ̂ v ̂ ] = [ u 0 v 0 ] + f [ x y ] ( 1 + k 1 r 2 + k 2 r 4 + k 3 r 6 + )
min m [ u ̂ u 0 v ̂ v 0 ] f [ x y ] ( 1 + k 1 r 2 + k 2 r 4 + k 3 r 6 + ) 2

Metrics