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

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References

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  1. D. C. Brown, “Close-range camera calibration,” Photogrammetric Engineering37, 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 Automation3, 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 SensingXXXIII, 288–294 (2000).
  4. T. A. Clarke and J. F. Fryer, “The development of camera calibration methods and models,”Photogrammetric Record16, 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 coupled-wave 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)

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

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]

1995 (1)

1980 (1)

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)

Arbter, K.

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

Braunecker, B.

R. Schuster and B. Braunecker, “The Calibration of the ADC (Airborne Digital Camera) -System,” Int. Arch. of Photogrammetry and Remote SensingXXXIII, 288–294 (2000).

Brown, D. C.

D. C. Brown, “Close-range camera calibration,” Photogrammetric Engineering37, 855–866 (1971)

Brown, L. C.

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)

Clarke, T. A.

T. A. Clarke and J. F. Fryer, “The development of camera calibration methods and models,”Photogrammetric Record16, 51–66 (1998).

Derrick, G. H.

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)

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,”Photogrammetric Record16, 51–66 (1998).

Fuchs, S.

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

Gaylord, T. K.

Goodman, J. W.

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

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.

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

McPhedran, R. C.

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)

Moharam, M. G.

Paredes, C.

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

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 SensingXXXIII, 288–294 (2000).

Sepp, W.

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

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]

Strobl, K. H.

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

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 Automation3, 323–344 (Aug. 1987).

Wernicke, G.

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

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)

Other (8)

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/.

D. C. Brown, “Close-range camera calibration,” Photogrammetric Engineering37, 855–866 (1971)

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 Automation3, 323–344 (Aug. 1987).

R. Schuster and B. Braunecker, “The Calibration of the ADC (Airborne Digital Camera) -System,” Int. Arch. of Photogrammetry and Remote SensingXXXIII, 288–294 (2000).

T. A. Clarke and J. F. Fryer, “The development of camera calibration methods and models,”Photogrammetric Record16, 51–66 (1998).

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

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

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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

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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

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