Abstract

Projection moire interferometry (PMI) is an out-of-plane displacement measurement technique that consists of differencing reference and deformed images of a grid pattern projected onto the test object. In conventional PMI, a tedious process of computing the fringe sensitivity coefficient (FSC), which requires moving the test object or the reference plane to known displacements, is used. We present a new technique for computing the FSC values that is called virtually calibrated projection moire interferometry (VCPMI). VCPMI is based on computer simulations of the conventional PMI process and does not require moving the actual test object or reference plane. We validate the VCPMI approach by comparing results for a flat plate and an airfoil with those made by use of other measurement methods.

© 2005 Optical Society of America

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References

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  1. A. Mikheev, “Simultaneous velocity and temperature field measurement of high-temperature flows,” Deutsche schungsanstalt Luft und Raumfahrt Mitteilung 40, 377–381 (2001).
  2. G. M. Quenot, J. Pakleza, T. A. Kowalewski, “Particle image velocimetry with optical flow,” Exp. Fluids 25, 177–189 (1998).
    [CrossRef]
  3. F. Chen, G. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
    [CrossRef]
  4. R. Rodriguez-Vera, D. Kerr, “Displacement and shape information using electronic speckle contouring,” in Interferometry VI: Applications, R. J. Pryputniewicz, G. M. Brown, W. P. Jueptner, eds., Proc. SPIE2004, 52–62 (1994).
    [CrossRef]
  5. J. Kozlowski, P. Boccardi, M. Fiore, “Novel interferometric method for contour mapping of optically rough surfaces,” Opt. Lasers Eng. 31, 41–50 (1999).
    [CrossRef]
  6. B. F. Andresen, M. Strojnik, eds., “Infrared Technology XXI,” Proc. SPIE2552 (1995).
  7. A. Szwedowski, M. Lesniewski, “Hybrid analysis of optical elements by interferometry and thermography,” in Interferometry '99: Applications, W. P. Jueptner, K. Patorski, eds., Proc. SPIE3745, 78–85 (1999).
    [CrossRef]
  8. G. A. Fleming, H. L. Soto, B. W. South, S. M. Bartram, “Advances in projection moiré interferometry development for large wind tunnel applications,” presented at the World Aviation Conference, San Francisco, Calif., 19–21 October 1999.
  9. G. A. Fleming, S. A. Gorton, “Measurement of rotorcraft blade deformation using projection moiré interferometry,” J. Shock Vib. 7, 149–165 (2000).
    [CrossRef]
  10. L. Pirrodda, “Shadow and projection moiré techniques for absolute or relative mapping of surface shapes,” Opt. Eng. 21, 640–649 (1982).
  11. D. Mishra, J. Blotter, “Comparison of reference image generation techniques for projection moiré interferometry,” Appl. Opt. 40, 5624–5631 (2001).
    [CrossRef]
  12. D. Mishra, J. Blotter, “Image dewarping and region of interest detection for processing moiré images,” Opt. Commun. 213, 39–47 (2002).
    [CrossRef]
  13. J. Heikkila, “Geometric camera calibration using circular control points,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1066–1077 (2000).
    [CrossRef]
  14. Q. Long, “Self-calibration of an affine camera from multiple views,” Int. J. Comput. Vision 19, 93–105 (1996).
    [CrossRef]
  15. L. Robert, “Camera calibration without feature extraction,” Comput. Vis. Image Underst. 63, 314–325 (1996).
    [CrossRef]
  16. M. Ito, “Robot vision modeling. Camera modeling and camera calibration,” Advanced Robotics 5, 321–325 (1991).
    [CrossRef]
  17. J. Bouguet, Matlab camera calibration toolbox: http://www.vision.caltech.edu/bouguetj/calib_doc .
  18. D. Forsyth, J. Ponce, Computer Vision: A Modern Approach (Pearson, 2003).
  19. J. H. Matthews, K. D. Fink, Numerical Methods Using MATLAB (Pearson, 2004).
  20. Software developed by the Zemax Corporation, San Diego, Calif.
  21. User-defined scattering in Zemax User Manual (Zemax Corporation, San Diego, Calif., 12November2003), p. 334.

2002 (1)

D. Mishra, J. Blotter, “Image dewarping and region of interest detection for processing moiré images,” Opt. Commun. 213, 39–47 (2002).
[CrossRef]

2001 (2)

A. Mikheev, “Simultaneous velocity and temperature field measurement of high-temperature flows,” Deutsche schungsanstalt Luft und Raumfahrt Mitteilung 40, 377–381 (2001).

D. Mishra, J. Blotter, “Comparison of reference image generation techniques for projection moiré interferometry,” Appl. Opt. 40, 5624–5631 (2001).
[CrossRef]

2000 (3)

G. A. Fleming, S. A. Gorton, “Measurement of rotorcraft blade deformation using projection moiré interferometry,” J. Shock Vib. 7, 149–165 (2000).
[CrossRef]

F. Chen, G. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

J. Heikkila, “Geometric camera calibration using circular control points,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1066–1077 (2000).
[CrossRef]

1999 (1)

J. Kozlowski, P. Boccardi, M. Fiore, “Novel interferometric method for contour mapping of optically rough surfaces,” Opt. Lasers Eng. 31, 41–50 (1999).
[CrossRef]

1998 (1)

G. M. Quenot, J. Pakleza, T. A. Kowalewski, “Particle image velocimetry with optical flow,” Exp. Fluids 25, 177–189 (1998).
[CrossRef]

1996 (2)

Q. Long, “Self-calibration of an affine camera from multiple views,” Int. J. Comput. Vision 19, 93–105 (1996).
[CrossRef]

L. Robert, “Camera calibration without feature extraction,” Comput. Vis. Image Underst. 63, 314–325 (1996).
[CrossRef]

1991 (1)

M. Ito, “Robot vision modeling. Camera modeling and camera calibration,” Advanced Robotics 5, 321–325 (1991).
[CrossRef]

1982 (1)

L. Pirrodda, “Shadow and projection moiré techniques for absolute or relative mapping of surface shapes,” Opt. Eng. 21, 640–649 (1982).

Bartram, S. M.

G. A. Fleming, H. L. Soto, B. W. South, S. M. Bartram, “Advances in projection moiré interferometry development for large wind tunnel applications,” presented at the World Aviation Conference, San Francisco, Calif., 19–21 October 1999.

Blotter, J.

D. Mishra, J. Blotter, “Image dewarping and region of interest detection for processing moiré images,” Opt. Commun. 213, 39–47 (2002).
[CrossRef]

D. Mishra, J. Blotter, “Comparison of reference image generation techniques for projection moiré interferometry,” Appl. Opt. 40, 5624–5631 (2001).
[CrossRef]

Boccardi, P.

J. Kozlowski, P. Boccardi, M. Fiore, “Novel interferometric method for contour mapping of optically rough surfaces,” Opt. Lasers Eng. 31, 41–50 (1999).
[CrossRef]

Bouguet, J.

J. Bouguet, Matlab camera calibration toolbox: http://www.vision.caltech.edu/bouguetj/calib_doc .

Brown, G.

F. Chen, G. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Chen, F.

F. Chen, G. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Fink, K. D.

J. H. Matthews, K. D. Fink, Numerical Methods Using MATLAB (Pearson, 2004).

Fiore, M.

J. Kozlowski, P. Boccardi, M. Fiore, “Novel interferometric method for contour mapping of optically rough surfaces,” Opt. Lasers Eng. 31, 41–50 (1999).
[CrossRef]

Fleming, G. A.

G. A. Fleming, S. A. Gorton, “Measurement of rotorcraft blade deformation using projection moiré interferometry,” J. Shock Vib. 7, 149–165 (2000).
[CrossRef]

G. A. Fleming, H. L. Soto, B. W. South, S. M. Bartram, “Advances in projection moiré interferometry development for large wind tunnel applications,” presented at the World Aviation Conference, San Francisco, Calif., 19–21 October 1999.

Forsyth, D.

D. Forsyth, J. Ponce, Computer Vision: A Modern Approach (Pearson, 2003).

Gorton, S. A.

G. A. Fleming, S. A. Gorton, “Measurement of rotorcraft blade deformation using projection moiré interferometry,” J. Shock Vib. 7, 149–165 (2000).
[CrossRef]

Heikkila, J.

J. Heikkila, “Geometric camera calibration using circular control points,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1066–1077 (2000).
[CrossRef]

Ito, M.

M. Ito, “Robot vision modeling. Camera modeling and camera calibration,” Advanced Robotics 5, 321–325 (1991).
[CrossRef]

Kerr, D.

R. Rodriguez-Vera, D. Kerr, “Displacement and shape information using electronic speckle contouring,” in Interferometry VI: Applications, R. J. Pryputniewicz, G. M. Brown, W. P. Jueptner, eds., Proc. SPIE2004, 52–62 (1994).
[CrossRef]

Kowalewski, T. A.

G. M. Quenot, J. Pakleza, T. A. Kowalewski, “Particle image velocimetry with optical flow,” Exp. Fluids 25, 177–189 (1998).
[CrossRef]

Kozlowski, J.

J. Kozlowski, P. Boccardi, M. Fiore, “Novel interferometric method for contour mapping of optically rough surfaces,” Opt. Lasers Eng. 31, 41–50 (1999).
[CrossRef]

Lesniewski, M.

A. Szwedowski, M. Lesniewski, “Hybrid analysis of optical elements by interferometry and thermography,” in Interferometry '99: Applications, W. P. Jueptner, K. Patorski, eds., Proc. SPIE3745, 78–85 (1999).
[CrossRef]

Long, Q.

Q. Long, “Self-calibration of an affine camera from multiple views,” Int. J. Comput. Vision 19, 93–105 (1996).
[CrossRef]

Matthews, J. H.

J. H. Matthews, K. D. Fink, Numerical Methods Using MATLAB (Pearson, 2004).

Mikheev, A.

A. Mikheev, “Simultaneous velocity and temperature field measurement of high-temperature flows,” Deutsche schungsanstalt Luft und Raumfahrt Mitteilung 40, 377–381 (2001).

Mishra, D.

D. Mishra, J. Blotter, “Image dewarping and region of interest detection for processing moiré images,” Opt. Commun. 213, 39–47 (2002).
[CrossRef]

D. Mishra, J. Blotter, “Comparison of reference image generation techniques for projection moiré interferometry,” Appl. Opt. 40, 5624–5631 (2001).
[CrossRef]

Pakleza, J.

G. M. Quenot, J. Pakleza, T. A. Kowalewski, “Particle image velocimetry with optical flow,” Exp. Fluids 25, 177–189 (1998).
[CrossRef]

Pirrodda, L.

L. Pirrodda, “Shadow and projection moiré techniques for absolute or relative mapping of surface shapes,” Opt. Eng. 21, 640–649 (1982).

Ponce, J.

D. Forsyth, J. Ponce, Computer Vision: A Modern Approach (Pearson, 2003).

Quenot, G. M.

G. M. Quenot, J. Pakleza, T. A. Kowalewski, “Particle image velocimetry with optical flow,” Exp. Fluids 25, 177–189 (1998).
[CrossRef]

Robert, L.

L. Robert, “Camera calibration without feature extraction,” Comput. Vis. Image Underst. 63, 314–325 (1996).
[CrossRef]

Rodriguez-Vera, R.

R. Rodriguez-Vera, D. Kerr, “Displacement and shape information using electronic speckle contouring,” in Interferometry VI: Applications, R. J. Pryputniewicz, G. M. Brown, W. P. Jueptner, eds., Proc. SPIE2004, 52–62 (1994).
[CrossRef]

Song, M.

F. Chen, G. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Soto, H. L.

G. A. Fleming, H. L. Soto, B. W. South, S. M. Bartram, “Advances in projection moiré interferometry development for large wind tunnel applications,” presented at the World Aviation Conference, San Francisco, Calif., 19–21 October 1999.

South, B. W.

G. A. Fleming, H. L. Soto, B. W. South, S. M. Bartram, “Advances in projection moiré interferometry development for large wind tunnel applications,” presented at the World Aviation Conference, San Francisco, Calif., 19–21 October 1999.

Szwedowski, A.

A. Szwedowski, M. Lesniewski, “Hybrid analysis of optical elements by interferometry and thermography,” in Interferometry '99: Applications, W. P. Jueptner, K. Patorski, eds., Proc. SPIE3745, 78–85 (1999).
[CrossRef]

Advanced Robotics (1)

M. Ito, “Robot vision modeling. Camera modeling and camera calibration,” Advanced Robotics 5, 321–325 (1991).
[CrossRef]

Appl. Opt. (1)

Comput. Vis. Image Underst. (1)

L. Robert, “Camera calibration without feature extraction,” Comput. Vis. Image Underst. 63, 314–325 (1996).
[CrossRef]

Deutsche schungsanstalt Luft und Raumfahrt Mitteilung (1)

A. Mikheev, “Simultaneous velocity and temperature field measurement of high-temperature flows,” Deutsche schungsanstalt Luft und Raumfahrt Mitteilung 40, 377–381 (2001).

Exp. Fluids (1)

G. M. Quenot, J. Pakleza, T. A. Kowalewski, “Particle image velocimetry with optical flow,” Exp. Fluids 25, 177–189 (1998).
[CrossRef]

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

J. Heikkila, “Geometric camera calibration using circular control points,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1066–1077 (2000).
[CrossRef]

Int. J. Comput. Vision (1)

Q. Long, “Self-calibration of an affine camera from multiple views,” Int. J. Comput. Vision 19, 93–105 (1996).
[CrossRef]

J. Shock Vib. (1)

G. A. Fleming, S. A. Gorton, “Measurement of rotorcraft blade deformation using projection moiré interferometry,” J. Shock Vib. 7, 149–165 (2000).
[CrossRef]

Opt. Commun. (1)

D. Mishra, J. Blotter, “Image dewarping and region of interest detection for processing moiré images,” Opt. Commun. 213, 39–47 (2002).
[CrossRef]

Opt. Eng. (2)

L. Pirrodda, “Shadow and projection moiré techniques for absolute or relative mapping of surface shapes,” Opt. Eng. 21, 640–649 (1982).

F. Chen, G. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Opt. Lasers Eng. (1)

J. Kozlowski, P. Boccardi, M. Fiore, “Novel interferometric method for contour mapping of optically rough surfaces,” Opt. Lasers Eng. 31, 41–50 (1999).
[CrossRef]

Other (9)

B. F. Andresen, M. Strojnik, eds., “Infrared Technology XXI,” Proc. SPIE2552 (1995).

A. Szwedowski, M. Lesniewski, “Hybrid analysis of optical elements by interferometry and thermography,” in Interferometry '99: Applications, W. P. Jueptner, K. Patorski, eds., Proc. SPIE3745, 78–85 (1999).
[CrossRef]

G. A. Fleming, H. L. Soto, B. W. South, S. M. Bartram, “Advances in projection moiré interferometry development for large wind tunnel applications,” presented at the World Aviation Conference, San Francisco, Calif., 19–21 October 1999.

R. Rodriguez-Vera, D. Kerr, “Displacement and shape information using electronic speckle contouring,” in Interferometry VI: Applications, R. J. Pryputniewicz, G. M. Brown, W. P. Jueptner, eds., Proc. SPIE2004, 52–62 (1994).
[CrossRef]

J. Bouguet, Matlab camera calibration toolbox: http://www.vision.caltech.edu/bouguetj/calib_doc .

D. Forsyth, J. Ponce, Computer Vision: A Modern Approach (Pearson, 2003).

J. H. Matthews, K. D. Fink, Numerical Methods Using MATLAB (Pearson, 2004).

Software developed by the Zemax Corporation, San Diego, Calif.

User-defined scattering in Zemax User Manual (Zemax Corporation, San Diego, Calif., 12November2003), p. 334.

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Figures (20)

Fig. 1
Fig. 1

Typical PMI setup.

Fig. 2
Fig. 2

Illustration of intrinsic parameters.

Fig. 3
Fig. 3

Simulated PMI setup.

Fig. 4
Fig. 4

Virtual camera schematic.

Fig. 5
Fig. 5

Virtual projector schematic.

Fig. 6
Fig. 6

Checkerboard plane used for camera calibration.

Fig. 7
Fig. 7

Checkerboard image used for projector calibration.

Fig. 8
Fig. 8

Checkerboard images in the reference plane: (a) actual undistorted (b) virtual and (c) differenced (actual – virtual).

Fig. 9
Fig. 9

Projected checkerboard images: (a) actual undistorted (b) virtual and (c) differenced (actual – virtual).

Fig. 10
Fig. 10

Actual versus virtual FSC percent difference: quadratic coefficient.

Fig. 11
Fig. 11

Actual versus virtual FSC difference: linear coefficient.

Fig. 12
Fig. 12

Actual versus virtual FSC difference: constant coefficient.

Fig. 13
Fig. 13

Percent displacement error introduced from virtual calibration.

Fig. 14
Fig. 14

Displacement with average errors and error bars.

Fig. 15
Fig. 15

Position for airfoil insertion in the PMI setup.

Fig. 16
Fig. 16

PMI displacement field.

Fig. 17
Fig. 17

PMI versus fixture displacements.

Fig. 18
Fig. 18

CMM displacement field.

Fig. 19
Fig. 19

VCPMI percent difference.

Fig. 20
Fig. 20

Cross-sectional slice of displacement data.

Tables (2)

Tables Icon

Table 1 Camera Calibration Results

Tables Icon

Table 2 Projector Calibration Resultsa

Equations (5)

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

[ U V 1 ] = [ f x a f y c x 0 f y c y 0 0 1 ] Intrinsic Transformation [ 1 0 0 0 0 1 0 0 0 0 1 0 ] × [ R T [ 3 × 3 ] [ 3 × 1 ] 0 1 ] Extrinsic Transformation [ X Y Z 1 ] .
P n = [ x n y n 1 ] = [ 1 0 0 0 0 1 0 0 0 0 1 0 ] [ R T 0 1 ] [ X Y Z 1 ] ,
P d = ( 1 + D 1 r 2 + D 2 r 4 + D 3 r 6 ) Radial Distortion [ x n y n ] + [ 2 D 4 x n y n + D 5 ( r 2 + 2 x n 2 ) D 4 ( r 2 + 2 y n 2 ) + 2 D 5 x n y n ] Tangential Distortion ,
P p = [ f x α f y c x 0 f y c y 0 0 1 ] [ P d 1 ] .
D ( x ) = Δ phase ( x ) FSC ( x ) .

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