Abstract

Our aim is to describe a method for detecting small deformations from a three-dimensional (3D) shape of large lateral dimensions. For this purpose the measurement method is based on the simultaneous utilization of several 3D optical systems and the phase-shifting technique. In this way, the following problems appear: optical distortion due to the large field observed, nonlinear phase-to-height conversion, conversion of image coordinates into object coordinates for each 3D optical system, and coordinate unification of all optical systems. The resolution is 50 µm with a field of view of 320 mm × 150 mm. We used this system to study the 3D human foot arch deformation under low loads in vivo. First results indicate the hysteresis behavior of the human foot under a low load (50 to 450 N).

© 2002 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2001 (2)

2000 (3)

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

H. Tiziani, M. Wegner, D. Steudle, “Confocal principle for macro- and microscopic surface and defect analysis,” Opt. Eng. 39, 32–39 (2000).
[CrossRef]

C. R. Coggrave, J. M. Huntley, “Optimization of a shape measurement system based on spatial light modulators,” Opt. Eng. 39, 91–98 (2000).
[CrossRef]

1998 (1)

J. S. Massa, G. S. Buller, A. C. Walker, S. Cova, M. Umasuthan, A. Wallace, “Time of flight optical ranging system based on time correlated single photon counting,” Appl. Opt. 31, 7298–7304 (1998).
[CrossRef]

1995 (1)

1994 (3)

1992 (2)

S. Xian-Yu, Z. Wen-Se, G. Bally, D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[CrossRef]

J. Cheng, P. Cohen, M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–979 (1992).
[CrossRef]

1991 (1)

1988 (1)

1987 (1)

R. Ker, M. Bennet, S. Bibby, R. Kester, R. M. Alexander, “The spring in the arch of the human foot,” Nature (London) 325, 147–149 (1987).
[CrossRef]

1985 (2)

1983 (1)

Ai, C.

Alexander, R. M.

R. Ker, M. Bennet, S. Bibby, R. Kester, R. M. Alexander, “The spring in the arch of the human foot,” Nature (London) 325, 147–149 (1987).
[CrossRef]

Andra, P.

P. Andra, E. Ivanov, W. Osten, “Scaled topometry—an active measurement approach for wide scale 3D surface inspection,” in Fringe ’97 Automatic Processing of Fringe Patterns, W. Juptner, W. Osten, eds. (Akademie Verlag, Germany, 1997), pp. 179–189.

Bally, G.

S. Xian-Yu, Z. Wen-Se, G. Bally, D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[CrossRef]

Bally, G. V.

D. Dirkesen, X. Su, D. Vukicevic, G. V. Bally, “Optimized phase shifting and use of fringe modulation function for high resolution phase evaluation,” in FRINGE ’93 Proceedings of the Second International Workshop on Automatic Processing of Fringe Patterns, W. Juptner, W. Osten, eds. (Akademie, Berlin, 1993), pp. 72–77.

Bennet, M.

R. Ker, M. Bennet, S. Bibby, R. Kester, R. M. Alexander, “The spring in the arch of the human foot,” Nature (London) 325, 147–149 (1987).
[CrossRef]

Bernabeu, E.

Bibby, S.

R. Ker, M. Bennet, S. Bibby, R. Kester, R. M. Alexander, “The spring in the arch of the human foot,” Nature (London) 325, 147–149 (1987).
[CrossRef]

Breuckmann, B.

B. Breuckmann, F. Halbauer, E. Klaas, M. Kube, “3D-measurement for industrial applications,” in Rapid Prototyping and Flexible Manufacturing, R. Ahlers, G. Reinhart, eds., Proc. SPIE3102, 20–29 (1997).
[CrossRef]

Brohinsky, W. R.

Brown, G. M.

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

Bryanston-Cross, P.

T. Judge, P. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199–239 (1994).
[CrossRef]

Buller, G. S.

J. S. Massa, G. S. Buller, A. C. Walker, S. Cova, M. Umasuthan, A. Wallace, “Time of flight optical ranging system based on time correlated single photon counting,” Appl. Opt. 31, 7298–7304 (1998).
[CrossRef]

Burow, R.

Chen, F.

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

Cheng, J.

J. Cheng, P. Cohen, M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–979 (1992).
[CrossRef]

Coggrave, C. R.

C. R. Coggrave, J. M. Huntley, “Optimization of a shape measurement system based on spatial light modulators,” Opt. Eng. 39, 91–98 (2000).
[CrossRef]

Cohen, P.

J. Cheng, P. Cohen, M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–979 (1992).
[CrossRef]

Cova, S.

J. S. Massa, G. S. Buller, A. C. Walker, S. Cova, M. Umasuthan, A. Wallace, “Time of flight optical ranging system based on time correlated single photon counting,” Appl. Opt. 31, 7298–7304 (1998).
[CrossRef]

Devernay, F.

F. Devernay, O. Faugeras, “Automatic calibration and removal of distortion from scenes of structured environments,” in Investigative and Trial Image Processing, L. I. Rudin, S. K. Bramble, eds., Proc. SPIE2567, 62–72 (1995).
[CrossRef]

Dirkesen, D.

D. Dirkesen, X. Su, D. Vukicevic, G. V. Bally, “Optimized phase shifting and use of fringe modulation function for high resolution phase evaluation,” in FRINGE ’93 Proceedings of the Second International Workshop on Automatic Processing of Fringe Patterns, W. Juptner, W. Osten, eds. (Akademie, Berlin, 1993), pp. 72–77.

Elssner, K. E.

Farid, H.

Farrant, D. I.

Faugeras, O.

F. Devernay, O. Faugeras, “Automatic calibration and removal of distortion from scenes of structured environments,” in Investigative and Trial Image Processing, L. I. Rudin, S. K. Bramble, eds., Proc. SPIE2567, 62–72 (1995).
[CrossRef]

Ghiglia, D. C.

D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley, New York, 1998).

Grzanna, J.

Halbauer, F.

B. Breuckmann, F. Halbauer, E. Klaas, M. Kube, “3D-measurement for industrial applications,” in Rapid Prototyping and Flexible Manufacturing, R. Ahlers, G. Reinhart, eds., Proc. SPIE3102, 20–29 (1997).
[CrossRef]

Herniou, M.

J. Cheng, P. Cohen, M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–979 (1992).
[CrossRef]

Hibino, K.

Huntley, J. M.

J. M. Huntley, “Three-dimensional noise-immune phase-unwrapping algorithm,” Appl. Opt. 40, 3901–3908 (2001).
[CrossRef]

C. R. Coggrave, J. M. Huntley, “Optimization of a shape measurement system based on spatial light modulators,” Opt. Eng. 39, 91–98 (2000).
[CrossRef]

Ivanov, E.

P. Andra, E. Ivanov, W. Osten, “Scaled topometry—an active measurement approach for wide scale 3D surface inspection,” in Fringe ’97 Automatic Processing of Fringe Patterns, W. Juptner, W. Osten, eds. (Akademie Verlag, Germany, 1997), pp. 179–189.

Judge, T.

T. Judge, P. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199–239 (1994).
[CrossRef]

Ker, R.

R. Ker, M. Bennet, S. Bibby, R. Kester, R. M. Alexander, “The spring in the arch of the human foot,” Nature (London) 325, 147–149 (1987).
[CrossRef]

Kester, R.

R. Ker, M. Bennet, S. Bibby, R. Kester, R. M. Alexander, “The spring in the arch of the human foot,” Nature (London) 325, 147–149 (1987).
[CrossRef]

Klaas, E.

B. Breuckmann, F. Halbauer, E. Klaas, M. Kube, “3D-measurement for industrial applications,” in Rapid Prototyping and Flexible Manufacturing, R. Ahlers, G. Reinhart, eds., Proc. SPIE3102, 20–29 (1997).
[CrossRef]

Kontsevich, L. L.

Kube, M.

B. Breuckmann, F. Halbauer, E. Klaas, M. Kube, “3D-measurement for industrial applications,” in Rapid Prototyping and Flexible Manufacturing, R. Ahlers, G. Reinhart, eds., Proc. SPIE3102, 20–29 (1997).
[CrossRef]

Larkin, K.

Maas, A. M.

Massa, J. S.

J. S. Massa, G. S. Buller, A. C. Walker, S. Cova, M. Umasuthan, A. Wallace, “Time of flight optical ranging system based on time correlated single photon counting,” Appl. Opt. 31, 7298–7304 (1998).
[CrossRef]

Merkel, K.

Nayar, S. K.

R. Swaminatha, S. K. Nayar, “Non-metric calibration of wide-angle lenses and polycameras,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 413–419.

Oreb, B. F.

Osten, W.

P. Andra, E. Ivanov, W. Osten, “Scaled topometry—an active measurement approach for wide scale 3D surface inspection,” in Fringe ’97 Automatic Processing of Fringe Patterns, W. Juptner, W. Osten, eds. (Akademie Verlag, Germany, 1997), pp. 179–189.

Petrov, P.

Popescu, A. C.

Pritt, M. D.

D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley, New York, 1998).

Quiroga, J. A.

Schwider, J.

Song, M.

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

Spolaczyk, R.

Stetson, K. A.

Steudle, D.

H. Tiziani, M. Wegner, D. Steudle, “Confocal principle for macro- and microscopic surface and defect analysis,” Opt. Eng. 39, 32–39 (2000).
[CrossRef]

Strand, T.

T. Strand, “Optical three-dimensional sensing for machine vision,” Opt. Eng. 24, 33–40 (1985).
[CrossRef]

Su, X.

D. Dirkesen, X. Su, D. Vukicevic, G. V. Bally, “Optimized phase shifting and use of fringe modulation function for high resolution phase evaluation,” in FRINGE ’93 Proceedings of the Second International Workshop on Automatic Processing of Fringe Patterns, W. Juptner, W. Osten, eds. (Akademie, Berlin, 1993), pp. 72–77.

Swaminatha, R.

R. Swaminatha, S. K. Nayar, “Non-metric calibration of wide-angle lenses and polycameras,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 413–419.

Tiziani, H.

H. Tiziani, M. Wegner, D. Steudle, “Confocal principle for macro- and microscopic surface and defect analysis,” Opt. Eng. 39, 32–39 (2000).
[CrossRef]

Tiziani, H. J.

H. J. Tiziani, “Optical metrology of engineering surfaces: scope and trends,” in Optical Measurement Techniques and Applications, A. House, ed. (P. K. Rasgoti, Boston, 1997).

Umasuthan, M.

J. S. Massa, G. S. Buller, A. C. Walker, S. Cova, M. Umasuthan, A. Wallace, “Time of flight optical ranging system based on time correlated single photon counting,” Appl. Opt. 31, 7298–7304 (1998).
[CrossRef]

Vergelskaya, L. S.

Vrooman, H. A.

Vukicevic, D.

S. Xian-Yu, Z. Wen-Se, G. Bally, D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[CrossRef]

D. Dirkesen, X. Su, D. Vukicevic, G. V. Bally, “Optimized phase shifting and use of fringe modulation function for high resolution phase evaluation,” in FRINGE ’93 Proceedings of the Second International Workshop on Automatic Processing of Fringe Patterns, W. Juptner, W. Osten, eds. (Akademie, Berlin, 1993), pp. 72–77.

Walker, A. C.

J. S. Massa, G. S. Buller, A. C. Walker, S. Cova, M. Umasuthan, A. Wallace, “Time of flight optical ranging system based on time correlated single photon counting,” Appl. Opt. 31, 7298–7304 (1998).
[CrossRef]

Wallace, A.

J. S. Massa, G. S. Buller, A. C. Walker, S. Cova, M. Umasuthan, A. Wallace, “Time of flight optical ranging system based on time correlated single photon counting,” Appl. Opt. 31, 7298–7304 (1998).
[CrossRef]

Wegner, M.

H. Tiziani, M. Wegner, D. Steudle, “Confocal principle for macro- and microscopic surface and defect analysis,” Opt. Eng. 39, 32–39 (2000).
[CrossRef]

Wen-Se, Z.

S. Xian-Yu, Z. Wen-Se, G. Bally, D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[CrossRef]

Wyant, J.

Xian-Yu, S.

S. Xian-Yu, Z. Wen-Se, G. Bally, D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[CrossRef]

Appl. Opt. (7)

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

J. Cheng, P. Cohen, M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–979 (1992).
[CrossRef]

J. Opt. Soc. Am. A (3)

Nature (London) (1)

R. Ker, M. Bennet, S. Bibby, R. Kester, R. M. Alexander, “The spring in the arch of the human foot,” Nature (London) 325, 147–149 (1987).
[CrossRef]

Opt. Commun. (1)

S. Xian-Yu, Z. Wen-Se, G. Bally, D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[CrossRef]

Opt. Eng. (4)

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

T. Strand, “Optical three-dimensional sensing for machine vision,” Opt. Eng. 24, 33–40 (1985).
[CrossRef]

H. Tiziani, M. Wegner, D. Steudle, “Confocal principle for macro- and microscopic surface and defect analysis,” Opt. Eng. 39, 32–39 (2000).
[CrossRef]

C. R. Coggrave, J. M. Huntley, “Optimization of a shape measurement system based on spatial light modulators,” Opt. Eng. 39, 91–98 (2000).
[CrossRef]

Opt. Lasers Eng. (1)

T. Judge, P. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199–239 (1994).
[CrossRef]

Other (7)

H. J. Tiziani, “Optical metrology of engineering surfaces: scope and trends,” in Optical Measurement Techniques and Applications, A. House, ed. (P. K. Rasgoti, Boston, 1997).

P. Andra, E. Ivanov, W. Osten, “Scaled topometry—an active measurement approach for wide scale 3D surface inspection,” in Fringe ’97 Automatic Processing of Fringe Patterns, W. Juptner, W. Osten, eds. (Akademie Verlag, Germany, 1997), pp. 179–189.

B. Breuckmann, F. Halbauer, E. Klaas, M. Kube, “3D-measurement for industrial applications,” in Rapid Prototyping and Flexible Manufacturing, R. Ahlers, G. Reinhart, eds., Proc. SPIE3102, 20–29 (1997).
[CrossRef]

F. Devernay, O. Faugeras, “Automatic calibration and removal of distortion from scenes of structured environments,” in Investigative and Trial Image Processing, L. I. Rudin, S. K. Bramble, eds., Proc. SPIE2567, 62–72 (1995).
[CrossRef]

R. Swaminatha, S. K. Nayar, “Non-metric calibration of wide-angle lenses and polycameras,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 413–419.

D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley, New York, 1998).

D. Dirkesen, X. Su, D. Vukicevic, G. V. Bally, “Optimized phase shifting and use of fringe modulation function for high resolution phase evaluation,” in FRINGE ’93 Proceedings of the Second International Workshop on Automatic Processing of Fringe Patterns, W. Juptner, W. Osten, eds. (Akademie, Berlin, 1993), pp. 72–77.

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Figures (12)

Fig. 1
Fig. 1

Optical system for measurement of the foot’s median arch deformation.

Fig. 2
Fig. 2

Schematic of the 3D reconstruction process.

Fig. 3
Fig. 3

Optical diagram of the phase-to-height conversion.

Fig. 4
Fig. 4

Image of a rectangular grid located in the reference plane.

Fig. 5
Fig. 5

Variation of (a) quadratic, (b) linear, and (c) intercept coefficients of vertical lines.

Fig. 6
Fig. 6

Corrected image of the deformed rectangular grid showed in Fig. 4.

Fig. 7
Fig. 7

Coordinate system of the reference plane and the CCD sensor camera.

Fig. 8
Fig. 8

Coordinate system unification: (a) a 2D pattern image from CCD camera 1, (b) the image from CCD camera 2 of the same pattern, and (c) the unified image of the 2D pattern.

Fig. 9
Fig. 9

3D reconstruction of the test object of 30-mm height.

Fig. 10
Fig. 10

Three-dimensional reconstruction of the thickness of a sheet paper.

Fig. 11
Fig. 11

(a) Steps of the loading process. (b) Foot arch behavior under load.

Fig. 12
Fig. 12

3D foot profile.

Equations (21)

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

Ixi, yi=I0xi, yi+γxi, yi×n=1 An cosnΦzxi, yi,
Φzxi, yi=2πf0n · ri+ϕ0xi, yi+ΔΦzxi, yi,
Ijxi, yi=I0xi, yi+γxi, yin=1 An cos×nΦzxi, yi+φj,
Φzxi, yi=arctanj=1N Ijxi, yisin φjj=1N Ijxi, yicos φj.
Φzxi, yi=arctanI4-I2I1-I3,
ΔΦ=Φz-ΦzA3A1sin4Φz,
ΔΦz=Φz-Φ0,
Φz=2πp0x+zx0d0+z tan θ1-x0 sin θdp-zx0 sin θdpd0+z cos θdp,
ΔΦzx, y=Ax, yzx, y+Bx, yzx, y2+Cx, yzx, y3.
X0C=MXiC
ΔXiC=Cr03 expiθ0,
Ux=x0Δx0, Uy=y0Δy0,
yi=ahxi2+bhxi+ch,
xi=avyi2+bvyi+cv.
av=mavIx+bav, bv=mbvIx+bbv, cv=Ix,
ah=mahIy+bah, bh=mbhIy+bbh, ch=Iy.
Ux=aUxIx3+bUxIx2+cUxIx+dUx, Uy=aUyIy3+bUyIy2+cUyIy+dUy.
Ix=xi-bavyi2-bbvyimavyi2+mbvyi+1, Iy=yi-bahxi2-bbhximahxi2+mbvxi+1.
Z=-B2A+B2+4AΔΦ2A.
x=x01+zz0, y=y01+zz0,
AVI=v0-vxv0,

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