Abstract

We present a photogrammetric endoscope to measure three dimensional (3D) shapes of inner cylindrical surfaces by fringe projection. The basic configuration includes two identical cameras aligned with the optical axis and facing each other, conical lenses, and a 360° helical fringe projector. The helical fringe pattern is phase shifted and acquired by both cameras. The phase patterns are used to acquire data from the surface in a regular cylindrical mesh. A prototype was built, calibrated, and tested. We present the results and an application to inspect internal welding seams and misalignment of welded joints in 150mm (6in.) diameter pipelines.

© 2008 Optical Society of America

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  1. O. D. Faugeras, Three Dimensional Computer Vision (MIT, 1993).
  2. R. Hartley and A. Zisserman, Multiple View Geometry (Cambrige University, 2003).
  3. H. C. Longet-Higgins, “A computer algorithm for reconstructing a scene from two projections,” Nature 293, 133-135 (1981).
    [CrossRef]
  4. Q. T. Luong and O. D. Faugeras, “The fundamental matrix: theory, algorithms, and stability analysis,” Int. J. Comput. Vis. 17, 43-75 (1996).
    [CrossRef]
  5. R. Zumbrunn, “Automated fast shape determination of diffuse reflecting objects at close range by means of structured light and digital phase measurement,” in Proceedings of ISPRS Intercomission Conference on Fast Processing of Photogrammetric Data (Elsevier, 1987), pp. 363-379.
  6. R. Carsten, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224-231 (2000).
    [CrossRef]
  7. R. Sitnik, M. Kujawinska, J. M. Woznicki, “Digital fringe projection system for large-volume 360-deg shape measurement,” Opt. Eng. 41, 443-449 (2002).
    [CrossRef]
  8. A. V. Fantin, A. Albertazzi, and T. L. Pinto, “Efficient mesh oriented algorithm for 3D measurement in multiple camera fringe projection,” Proc. SPIE 6616, 66161B (2007).
    [CrossRef]
  9. K. Veit, “Verringerung systematischer meßfehler bei der phasenmessenden triangulation durch kalibration,” Ph.D. dissertation (University of Erlangen-Nuremberg, 2003).
  10. O. Marklund, J. M. Huntley, and R. Cusack, “Robust unwrapping algorithm for three-dimensional phase volumes of arbitrary shape containing knotted phase singularity loops,” Opt. Eng. 46, 085601 (2007).
    [CrossRef]
  11. J. M. Huntley and H. O. Saldner, “Shape measurement by temporal phase unwrapping and spatial light modulator-based fringe projector,” in Proceedings of Sensors, Sensor Systems, and Sensor Data Processing, O. Loffeld, ed. (SPIE, 1997), pp. 185-192
  12. H. O. Saldner and J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator based fringe projector,” Opt. Eng. 36, 610-615 (1997).
    [CrossRef]
  13. A. C. Hofmann, A. G. Albertazzi, Jr., J. M. C. Santos, E. Valim, and R. S. Gondo, “A stereoscopic endoscopic optical system for measurement of the 3D weld geometry of pipes: concepts and preliminary results,” in Proceedings of The 25th International Conference on Offshore Mechanics and Arctic Engineering (American Society of Mechanical Engineers, 2006).
  14. A. C. Hofmann, “Stereoscopic endoscopic system for geometric measurement of welded joints in pipelines” (in Portuguese). Masters thesis (Universidade Federal de Santa Catarina, 2004).
  15. A. C. Hofmann, A. G. AlbertazziJr., J. M. C. Santos, E. Valim, and R. S. Gondo, “Sistema óptico endoscópico estereoscópico para medida 3D da geometria da solda de dutos--conceitos e resultados preliminares,” in Proceedings of 9a COTEQ-Conferência Internacional sobre Tecnologia de Equipamentos (Abende, 2007), pp. 1-10.

2007

A. V. Fantin, A. Albertazzi, and T. L. Pinto, “Efficient mesh oriented algorithm for 3D measurement in multiple camera fringe projection,” Proc. SPIE 6616, 66161B (2007).
[CrossRef]

O. Marklund, J. M. Huntley, and R. Cusack, “Robust unwrapping algorithm for three-dimensional phase volumes of arbitrary shape containing knotted phase singularity loops,” Opt. Eng. 46, 085601 (2007).
[CrossRef]

2002

R. Sitnik, M. Kujawinska, J. M. Woznicki, “Digital fringe projection system for large-volume 360-deg shape measurement,” Opt. Eng. 41, 443-449 (2002).
[CrossRef]

2000

R. Carsten, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224-231 (2000).
[CrossRef]

1997

H. O. Saldner and J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator based fringe projector,” Opt. Eng. 36, 610-615 (1997).
[CrossRef]

1996

Q. T. Luong and O. D. Faugeras, “The fundamental matrix: theory, algorithms, and stability analysis,” Int. J. Comput. Vis. 17, 43-75 (1996).
[CrossRef]

1981

H. C. Longet-Higgins, “A computer algorithm for reconstructing a scene from two projections,” Nature 293, 133-135 (1981).
[CrossRef]

Albertazzi, A.

A. V. Fantin, A. Albertazzi, and T. L. Pinto, “Efficient mesh oriented algorithm for 3D measurement in multiple camera fringe projection,” Proc. SPIE 6616, 66161B (2007).
[CrossRef]

Albertazzi, A. G.

A. C. Hofmann, A. G. Albertazzi, Jr., J. M. C. Santos, E. Valim, and R. S. Gondo, “A stereoscopic endoscopic optical system for measurement of the 3D weld geometry of pipes: concepts and preliminary results,” in Proceedings of The 25th International Conference on Offshore Mechanics and Arctic Engineering (American Society of Mechanical Engineers, 2006).

A. C. Hofmann, A. G. AlbertazziJr., J. M. C. Santos, E. Valim, and R. S. Gondo, “Sistema óptico endoscópico estereoscópico para medida 3D da geometria da solda de dutos--conceitos e resultados preliminares,” in Proceedings of 9a COTEQ-Conferência Internacional sobre Tecnologia de Equipamentos (Abende, 2007), pp. 1-10.

Carsten, R.

R. Carsten, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224-231 (2000).
[CrossRef]

Cusack, R.

O. Marklund, J. M. Huntley, and R. Cusack, “Robust unwrapping algorithm for three-dimensional phase volumes of arbitrary shape containing knotted phase singularity loops,” Opt. Eng. 46, 085601 (2007).
[CrossRef]

Fantin, A. V.

A. V. Fantin, A. Albertazzi, and T. L. Pinto, “Efficient mesh oriented algorithm for 3D measurement in multiple camera fringe projection,” Proc. SPIE 6616, 66161B (2007).
[CrossRef]

Faugeras, O. D.

Q. T. Luong and O. D. Faugeras, “The fundamental matrix: theory, algorithms, and stability analysis,” Int. J. Comput. Vis. 17, 43-75 (1996).
[CrossRef]

O. D. Faugeras, Three Dimensional Computer Vision (MIT, 1993).

Gondo, R. S.

A. C. Hofmann, A. G. Albertazzi, Jr., J. M. C. Santos, E. Valim, and R. S. Gondo, “A stereoscopic endoscopic optical system for measurement of the 3D weld geometry of pipes: concepts and preliminary results,” in Proceedings of The 25th International Conference on Offshore Mechanics and Arctic Engineering (American Society of Mechanical Engineers, 2006).

A. C. Hofmann, A. G. AlbertazziJr., J. M. C. Santos, E. Valim, and R. S. Gondo, “Sistema óptico endoscópico estereoscópico para medida 3D da geometria da solda de dutos--conceitos e resultados preliminares,” in Proceedings of 9a COTEQ-Conferência Internacional sobre Tecnologia de Equipamentos (Abende, 2007), pp. 1-10.

Hartley, R.

R. Hartley and A. Zisserman, Multiple View Geometry (Cambrige University, 2003).

Hofmann, A. C.

A. C. Hofmann, A. G. Albertazzi, Jr., J. M. C. Santos, E. Valim, and R. S. Gondo, “A stereoscopic endoscopic optical system for measurement of the 3D weld geometry of pipes: concepts and preliminary results,” in Proceedings of The 25th International Conference on Offshore Mechanics and Arctic Engineering (American Society of Mechanical Engineers, 2006).

A. C. Hofmann, “Stereoscopic endoscopic system for geometric measurement of welded joints in pipelines” (in Portuguese). Masters thesis (Universidade Federal de Santa Catarina, 2004).

A. C. Hofmann, A. G. AlbertazziJr., J. M. C. Santos, E. Valim, and R. S. Gondo, “Sistema óptico endoscópico estereoscópico para medida 3D da geometria da solda de dutos--conceitos e resultados preliminares,” in Proceedings of 9a COTEQ-Conferência Internacional sobre Tecnologia de Equipamentos (Abende, 2007), pp. 1-10.

Huntley, J. M.

O. Marklund, J. M. Huntley, and R. Cusack, “Robust unwrapping algorithm for three-dimensional phase volumes of arbitrary shape containing knotted phase singularity loops,” Opt. Eng. 46, 085601 (2007).
[CrossRef]

H. O. Saldner and J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator based fringe projector,” Opt. Eng. 36, 610-615 (1997).
[CrossRef]

J. M. Huntley and H. O. Saldner, “Shape measurement by temporal phase unwrapping and spatial light modulator-based fringe projector,” in Proceedings of Sensors, Sensor Systems, and Sensor Data Processing, O. Loffeld, ed. (SPIE, 1997), pp. 185-192

Kujawinska, M.

R. Sitnik, M. Kujawinska, J. M. Woznicki, “Digital fringe projection system for large-volume 360-deg shape measurement,” Opt. Eng. 41, 443-449 (2002).
[CrossRef]

Longet-Higgins, H. C.

H. C. Longet-Higgins, “A computer algorithm for reconstructing a scene from two projections,” Nature 293, 133-135 (1981).
[CrossRef]

Luong, Q. T.

Q. T. Luong and O. D. Faugeras, “The fundamental matrix: theory, algorithms, and stability analysis,” Int. J. Comput. Vis. 17, 43-75 (1996).
[CrossRef]

Marklund, O.

O. Marklund, J. M. Huntley, and R. Cusack, “Robust unwrapping algorithm for three-dimensional phase volumes of arbitrary shape containing knotted phase singularity loops,” Opt. Eng. 46, 085601 (2007).
[CrossRef]

Pinto, T. L.

A. V. Fantin, A. Albertazzi, and T. L. Pinto, “Efficient mesh oriented algorithm for 3D measurement in multiple camera fringe projection,” Proc. SPIE 6616, 66161B (2007).
[CrossRef]

Ritter, R.

R. Carsten, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224-231 (2000).
[CrossRef]

Saldner, H. O.

H. O. Saldner and J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator based fringe projector,” Opt. Eng. 36, 610-615 (1997).
[CrossRef]

J. M. Huntley and H. O. Saldner, “Shape measurement by temporal phase unwrapping and spatial light modulator-based fringe projector,” in Proceedings of Sensors, Sensor Systems, and Sensor Data Processing, O. Loffeld, ed. (SPIE, 1997), pp. 185-192

Santos, J. M. C.

A. C. Hofmann, A. G. Albertazzi, Jr., J. M. C. Santos, E. Valim, and R. S. Gondo, “A stereoscopic endoscopic optical system for measurement of the 3D weld geometry of pipes: concepts and preliminary results,” in Proceedings of The 25th International Conference on Offshore Mechanics and Arctic Engineering (American Society of Mechanical Engineers, 2006).

A. C. Hofmann, A. G. AlbertazziJr., J. M. C. Santos, E. Valim, and R. S. Gondo, “Sistema óptico endoscópico estereoscópico para medida 3D da geometria da solda de dutos--conceitos e resultados preliminares,” in Proceedings of 9a COTEQ-Conferência Internacional sobre Tecnologia de Equipamentos (Abende, 2007), pp. 1-10.

Sitnik, R.

R. Sitnik, M. Kujawinska, J. M. Woznicki, “Digital fringe projection system for large-volume 360-deg shape measurement,” Opt. Eng. 41, 443-449 (2002).
[CrossRef]

Thesing, J.

R. Carsten, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224-231 (2000).
[CrossRef]

Valim, E.

A. C. Hofmann, A. G. AlbertazziJr., J. M. C. Santos, E. Valim, and R. S. Gondo, “Sistema óptico endoscópico estereoscópico para medida 3D da geometria da solda de dutos--conceitos e resultados preliminares,” in Proceedings of 9a COTEQ-Conferência Internacional sobre Tecnologia de Equipamentos (Abende, 2007), pp. 1-10.

A. C. Hofmann, A. G. Albertazzi, Jr., J. M. C. Santos, E. Valim, and R. S. Gondo, “A stereoscopic endoscopic optical system for measurement of the 3D weld geometry of pipes: concepts and preliminary results,” in Proceedings of The 25th International Conference on Offshore Mechanics and Arctic Engineering (American Society of Mechanical Engineers, 2006).

Veit, K.

K. Veit, “Verringerung systematischer meßfehler bei der phasenmessenden triangulation durch kalibration,” Ph.D. dissertation (University of Erlangen-Nuremberg, 2003).

Woznicki, J. M.

R. Sitnik, M. Kujawinska, J. M. Woznicki, “Digital fringe projection system for large-volume 360-deg shape measurement,” Opt. Eng. 41, 443-449 (2002).
[CrossRef]

Zisserman, A.

R. Hartley and A. Zisserman, Multiple View Geometry (Cambrige University, 2003).

Zumbrunn, R.

R. Zumbrunn, “Automated fast shape determination of diffuse reflecting objects at close range by means of structured light and digital phase measurement,” in Proceedings of ISPRS Intercomission Conference on Fast Processing of Photogrammetric Data (Elsevier, 1987), pp. 363-379.

Int. J. Comput. Vis.

Q. T. Luong and O. D. Faugeras, “The fundamental matrix: theory, algorithms, and stability analysis,” Int. J. Comput. Vis. 17, 43-75 (1996).
[CrossRef]

Nature

H. C. Longet-Higgins, “A computer algorithm for reconstructing a scene from two projections,” Nature 293, 133-135 (1981).
[CrossRef]

Opt. Eng.

O. Marklund, J. M. Huntley, and R. Cusack, “Robust unwrapping algorithm for three-dimensional phase volumes of arbitrary shape containing knotted phase singularity loops,” Opt. Eng. 46, 085601 (2007).
[CrossRef]

H. O. Saldner and J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator based fringe projector,” Opt. Eng. 36, 610-615 (1997).
[CrossRef]

R. Carsten, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224-231 (2000).
[CrossRef]

R. Sitnik, M. Kujawinska, J. M. Woznicki, “Digital fringe projection system for large-volume 360-deg shape measurement,” Opt. Eng. 41, 443-449 (2002).
[CrossRef]

Proc. SPIE

A. V. Fantin, A. Albertazzi, and T. L. Pinto, “Efficient mesh oriented algorithm for 3D measurement in multiple camera fringe projection,” Proc. SPIE 6616, 66161B (2007).
[CrossRef]

Other

K. Veit, “Verringerung systematischer meßfehler bei der phasenmessenden triangulation durch kalibration,” Ph.D. dissertation (University of Erlangen-Nuremberg, 2003).

R. Zumbrunn, “Automated fast shape determination of diffuse reflecting objects at close range by means of structured light and digital phase measurement,” in Proceedings of ISPRS Intercomission Conference on Fast Processing of Photogrammetric Data (Elsevier, 1987), pp. 363-379.

O. D. Faugeras, Three Dimensional Computer Vision (MIT, 1993).

R. Hartley and A. Zisserman, Multiple View Geometry (Cambrige University, 2003).

A. C. Hofmann, A. G. Albertazzi, Jr., J. M. C. Santos, E. Valim, and R. S. Gondo, “A stereoscopic endoscopic optical system for measurement of the 3D weld geometry of pipes: concepts and preliminary results,” in Proceedings of The 25th International Conference on Offshore Mechanics and Arctic Engineering (American Society of Mechanical Engineers, 2006).

A. C. Hofmann, “Stereoscopic endoscopic system for geometric measurement of welded joints in pipelines” (in Portuguese). Masters thesis (Universidade Federal de Santa Catarina, 2004).

A. C. Hofmann, A. G. AlbertazziJr., J. M. C. Santos, E. Valim, and R. S. Gondo, “Sistema óptico endoscópico estereoscópico para medida 3D da geometria da solda de dutos--conceitos e resultados preliminares,” in Proceedings of 9a COTEQ-Conferência Internacional sobre Tecnologia de Equipamentos (Abende, 2007), pp. 1-10.

J. M. Huntley and H. O. Saldner, “Shape measurement by temporal phase unwrapping and spatial light modulator-based fringe projector,” in Proceedings of Sensors, Sensor Systems, and Sensor Data Processing, O. Loffeld, ed. (SPIE, 1997), pp. 185-192

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Figures (14)

Fig. 1
Fig. 1

Pinhole camera model. The image q of point Q is determined by extending the line that connects Q to the projection center C.

Fig. 2
Fig. 2

Fringe projection on the surface to be measured. The same fringe pattern is viewed by both cameras from different angles.

Fig. 3
Fig. 3

Approach to locate corresponding points using phase information. Only the point on the surface has the same phase value in both images.

Fig. 4
Fig. 4

Basic configuration of the photogrammetric endoscope formed by two cameras, a helical fringe projector and a structural transparent tube.

Fig. 5
Fig. 5

Helical fringe projector formed by a halogen lamp, a glass cylinder with a printed fringe patterns and a step motor.

Fig. 6
Fig. 6

Use of a conical lens to improve radial resolution

Fig. 7
Fig. 7

The effect of a conical lens. The left image was acquired without the conical lens. The right one was done using a conical lens.

Fig. 8
Fig. 8

Actual view of the built prototype

Fig. 9
Fig. 9

Actual view of the camera before and after rotation. The V-shaped artifact in the upper part of both images is the connecting rod that hides the electric wiring.

Fig. 10
Fig. 10

Sequence of eight 45 ° rotated images to produce two 90 ° phase shifted fringe patterns with four and five spiral fringes.

Fig. 11
Fig. 11

Wrapped phase patters for three spiral fringes. Left image is the natural wrapped phase pattern. Central image is the synthetic phase ramp. Right image is the phase pattern after removing the singularity by subtracting the synthetic ramp.

Fig. 12
Fig. 12

Finding corresponding points using unwrapped phase information from images A (left) and B (right). The right choice is made when the radial values r a and r b produces a phase difference Δ Φ = 0 .

Fig. 13
Fig. 13

Reconstruction of the measured cylindrical surface moving a virtual cursor along radial lines.

Fig. 14
Fig. 14

Measurement of a junction with a welding seam. The upper right part shows a region where the weld seam is thicker. The lower right part shows a region where it is thinner.

Tables (2)

Tables Icon

Table 1 Measurement Performance of the Photogrammetric Endoscope

Tables Icon

Table 2 Results of the Transverse Displacement Experiment

Equations (4)

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

q x im = p 0 x c Q x Q z , q y im = p 0 y c Q y Q z ,
{ x y h } = [ p 1 p 5 p 9 p 2 p 6 p 10 p 3 p 7 p 11 p 4 p 8 p 12 ] { X Y Z 1 } ,
x im = x h , y im = y h .
φ ( r , θ ) = f ( r ) + k θ .

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