Abstract

Diffractive optical elements (DOEs) can generate multiple two-dimensional (2D) diffraction grids that can be used to calibrate cameras for photogrammetry. However, several factors limit the accuracy and the functionality of this technique. One of the most important is the DOE fabrication itself. A large DOE with wide 2D fan-out grids is very difficult and costly to develop. Consequently, the calibration is limited to small aperture cameras and/or limited angles. To overcome these problems, we present a low cost solution. We propose to use two large, commercially available, crossed phase DOEs that generate 15×15 equally spaced dots. As the DOEs are not perfect, the unwanted secondary diffractive orders are used as calibration targets to expand the calibration field of view. We show that the use of the primary and secondary diffractive orders provides a valuable calibration tool for wide angle aerial cameras.

© 2011 Optical Society of America

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References

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  1. B. Espiau, in Proceedings of ISER, 3rd International Symposium on Experimental Robotics (1993), pp. 187–193.
  2. J. Hu, A. Razdan, and J. A. ZehnderJ. Atmos. Ocean. Technol. 26 (2009).
  3. Q. Wang, L. Fu, and Z. Liu, in Control and Decision Conference (2010), Vol. 35, pp. 3354–3358.
  4. W. Wu and Z. Sun, Appl. Res. Comput. 02, 04 (2004).
  5. J. Heikkila, IEEE Trans. Pattern Anal. Machine Intell. 22, 1066 (2000).
    [CrossRef]
  6. J. Ha and D. Kang, Pattern Recogn. 38, 143 (2005).
    [CrossRef]
  7. Z. Hu and F. Wu, Chin. J. Comput. 25, 1149 (2002).
  8. M. Kroepfl, E. Kruck, and M. Gruber, in International Archives of Photogrammetry and Remote Sensing (2004), Vol. 35, Part B1, pp. 42–44.
  9. M. Bauer, D. Grießbach, A. Hermerschmidt, S. Krüger, M. Scheele, and A. Schischmanow, Opt. Express 16, 20241 (2008).
    [CrossRef]
  10. C. Ricolfe-Viala and A. J. Sanchez-Salmeron, Opt. Express 19, 10769 (2011).
    [CrossRef]

2011 (1)

2009 (1)

J. Hu, A. Razdan, and J. A. ZehnderJ. Atmos. Ocean. Technol. 26 (2009).

2008 (1)

2005 (1)

J. Ha and D. Kang, Pattern Recogn. 38, 143 (2005).
[CrossRef]

2004 (1)

W. Wu and Z. Sun, Appl. Res. Comput. 02, 04 (2004).

2002 (1)

Z. Hu and F. Wu, Chin. J. Comput. 25, 1149 (2002).

2000 (1)

J. Heikkila, IEEE Trans. Pattern Anal. Machine Intell. 22, 1066 (2000).
[CrossRef]

Bauer, M.

Espiau, B.

B. Espiau, in Proceedings of ISER, 3rd International Symposium on Experimental Robotics (1993), pp. 187–193.

Fu, L.

Q. Wang, L. Fu, and Z. Liu, in Control and Decision Conference (2010), Vol. 35, pp. 3354–3358.

Grießbach, D.

Gruber, M.

M. Kroepfl, E. Kruck, and M. Gruber, in International Archives of Photogrammetry and Remote Sensing (2004), Vol. 35, Part B1, pp. 42–44.

Ha, J.

J. Ha and D. Kang, Pattern Recogn. 38, 143 (2005).
[CrossRef]

Heikkila, J.

J. Heikkila, IEEE Trans. Pattern Anal. Machine Intell. 22, 1066 (2000).
[CrossRef]

Hermerschmidt, A.

Hu, J.

J. Hu, A. Razdan, and J. A. ZehnderJ. Atmos. Ocean. Technol. 26 (2009).

Hu, Z.

Z. Hu and F. Wu, Chin. J. Comput. 25, 1149 (2002).

Kang, D.

J. Ha and D. Kang, Pattern Recogn. 38, 143 (2005).
[CrossRef]

Kroepfl, M.

M. Kroepfl, E. Kruck, and M. Gruber, in International Archives of Photogrammetry and Remote Sensing (2004), Vol. 35, Part B1, pp. 42–44.

Kruck, E.

M. Kroepfl, E. Kruck, and M. Gruber, in International Archives of Photogrammetry and Remote Sensing (2004), Vol. 35, Part B1, pp. 42–44.

Krüger, S.

Liu, Z.

Q. Wang, L. Fu, and Z. Liu, in Control and Decision Conference (2010), Vol. 35, pp. 3354–3358.

Razdan, A.

J. Hu, A. Razdan, and J. A. ZehnderJ. Atmos. Ocean. Technol. 26 (2009).

Ricolfe-Viala, C.

Sanchez-Salmeron, A. J.

Scheele, M.

Schischmanow, A.

Sun, Z.

W. Wu and Z. Sun, Appl. Res. Comput. 02, 04 (2004).

Wang, Q.

Q. Wang, L. Fu, and Z. Liu, in Control and Decision Conference (2010), Vol. 35, pp. 3354–3358.

Wu, F.

Z. Hu and F. Wu, Chin. J. Comput. 25, 1149 (2002).

Wu, W.

W. Wu and Z. Sun, Appl. Res. Comput. 02, 04 (2004).

Zehnder, J. A.

J. Hu, A. Razdan, and J. A. ZehnderJ. Atmos. Ocean. Technol. 26 (2009).

Appl. Res. Comput. (1)

W. Wu and Z. Sun, Appl. Res. Comput. 02, 04 (2004).

Chin. J. Comput. (1)

Z. Hu and F. Wu, Chin. J. Comput. 25, 1149 (2002).

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

J. Heikkila, IEEE Trans. Pattern Anal. Machine Intell. 22, 1066 (2000).
[CrossRef]

J. Atmos. Ocean. Technol. (1)

J. Hu, A. Razdan, and J. A. ZehnderJ. Atmos. Ocean. Technol. 26 (2009).

Opt. Express (2)

Pattern Recogn. (1)

J. Ha and D. Kang, Pattern Recogn. 38, 143 (2005).
[CrossRef]

Other (3)

Q. Wang, L. Fu, and Z. Liu, in Control and Decision Conference (2010), Vol. 35, pp. 3354–3358.

M. Kroepfl, E. Kruck, and M. Gruber, in International Archives of Photogrammetry and Remote Sensing (2004), Vol. 35, Part B1, pp. 42–44.

B. Espiau, in Proceedings of ISER, 3rd International Symposium on Experimental Robotics (1993), pp. 187–193.

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Figures (4)

Fig. 1.
Fig. 1.

Overlaps of the DOE orders and entrance pupil position of the camera under calibration.

Fig. 2.
Fig. 2.

DOE orders calibration grids produced by the cross DOE arrangement (brightness and contrast exaggerated).

Fig. 3.
Fig. 3.

Picture of the calibration setup with the crossed gratings.

Fig. 4.
Fig. 4.

Centroid algorithm results from an arbitrary diffractive order (gray scale).

Equations (4)

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

XEP=D-DEPtan(FOV)=D-EFL/F#tan(FOV),
d=[X,Y,(1(X2+Y2)1/2,0)]T,
X=λfx+rx+(λfy+ry)·sin(θ),
Y=(λfy+ry)·cos(θ),

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