Abstract

In this paper, we report on a laser fringe projection set-up, which can generate fringe patterns with multiple frequencies and phase shifts. Stationary fringe patterns with sinusoidal intensity distributions are produced by the interference of two laser beams, which are frequency modulated by a pair of acousto-optic modulators (AOMs). The AOMs are driven by two RF signals with the same frequency but a phase delay between them. By changing the RF frequency and the phase delay, the fringe spatial frequency and phase shift can be electronically controlled, which allows high-speed switching from one frequency or phase to another thus makes a dynamic 3D profiling possible.

©2005 Optical Society of America

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References

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  1. X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).
    [Crossref]
  2. V. Srinivasan, H. C. Liu, and M. Halioua, “Automated phase-measuring profilometry of 3-D diffuse objects,” Appl. Opt. 23, 3105–3108 (1984).
    [Crossref] [PubMed]
  3. X. Su, W. S. Zhou, V. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–73 (1992).
    [Crossref]
  4. M. Takeda, H. Ina, and S. Koboyashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [Crossref]
  5. M. Takeda and H. Motoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1983).
    [Crossref] [PubMed]
  6. C. A. Hobson, J. T. Atkinson, and F. Lilley, “The application of digital filtering to phase recovery when surface contouring using fringe projection techniques,” Opt. Lasers Eng. 27, 355–368 (1997).
    [Crossref]
  7. X. Su and W. Chen, Opt. “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
    [Crossref]
  8. J. M. Huntley and H. O. Saldner, “Temporal phase unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
    [Crossref] [PubMed]
  9. H. O. Saldner and J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36, 2770–2775 (1997).
    [Crossref] [PubMed]
  10. G. C. Jin, N.K. Bao, and P.S. Chung, “Applications of a novel phase-shift method using a computer-controlled polarization mechanism,” Opt. Eng. 33, 2733–2737 (1994).
    [Crossref]
  11. M. S. Mermeistein, D. L. Feldkhum, and L. G. Shirley, “Video-rate surface profiling with acousto-optic accordion fringe interferometry,” Opt. Eng. 39, 106–113 (2000).
    [Crossref]
  12. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
    [Crossref] [PubMed]

2004 (1)

X. Su and W. Chen, Opt. “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[Crossref]

2001 (1)

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).
[Crossref]

2000 (1)

M. S. Mermeistein, D. L. Feldkhum, and L. G. Shirley, “Video-rate surface profiling with acousto-optic accordion fringe interferometry,” Opt. Eng. 39, 106–113 (2000).
[Crossref]

1997 (2)

H. O. Saldner and J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36, 2770–2775 (1997).
[Crossref] [PubMed]

C. A. Hobson, J. T. Atkinson, and F. Lilley, “The application of digital filtering to phase recovery when surface contouring using fringe projection techniques,” Opt. Lasers Eng. 27, 355–368 (1997).
[Crossref]

1994 (1)

G. C. Jin, N.K. Bao, and P.S. Chung, “Applications of a novel phase-shift method using a computer-controlled polarization mechanism,” Opt. Eng. 33, 2733–2737 (1994).
[Crossref]

1993 (1)

1992 (1)

X. Su, W. S. Zhou, V. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–73 (1992).
[Crossref]

1984 (1)

1983 (1)

1982 (1)

1966 (1)

Atkinson, J. T.

C. A. Hobson, J. T. Atkinson, and F. Lilley, “The application of digital filtering to phase recovery when surface contouring using fringe projection techniques,” Opt. Lasers Eng. 27, 355–368 (1997).
[Crossref]

Bao, N.K.

G. C. Jin, N.K. Bao, and P.S. Chung, “Applications of a novel phase-shift method using a computer-controlled polarization mechanism,” Opt. Eng. 33, 2733–2737 (1994).
[Crossref]

Chen, W.

X. Su and W. Chen, Opt. “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[Crossref]

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).
[Crossref]

Chung, P.S.

G. C. Jin, N.K. Bao, and P.S. Chung, “Applications of a novel phase-shift method using a computer-controlled polarization mechanism,” Opt. Eng. 33, 2733–2737 (1994).
[Crossref]

Feldkhum, D. L.

M. S. Mermeistein, D. L. Feldkhum, and L. G. Shirley, “Video-rate surface profiling with acousto-optic accordion fringe interferometry,” Opt. Eng. 39, 106–113 (2000).
[Crossref]

Halioua, M.

Hobson, C. A.

C. A. Hobson, J. T. Atkinson, and F. Lilley, “The application of digital filtering to phase recovery when surface contouring using fringe projection techniques,” Opt. Lasers Eng. 27, 355–368 (1997).
[Crossref]

Huntley, J. M.

Ina, H.

Jin, G. C.

G. C. Jin, N.K. Bao, and P.S. Chung, “Applications of a novel phase-shift method using a computer-controlled polarization mechanism,” Opt. Eng. 33, 2733–2737 (1994).
[Crossref]

Koboyashi, S.

Kogelnik, H.

Li, T.

Lilley, F.

C. A. Hobson, J. T. Atkinson, and F. Lilley, “The application of digital filtering to phase recovery when surface contouring using fringe projection techniques,” Opt. Lasers Eng. 27, 355–368 (1997).
[Crossref]

Liu, H. C.

Mermeistein, M. S.

M. S. Mermeistein, D. L. Feldkhum, and L. G. Shirley, “Video-rate surface profiling with acousto-optic accordion fringe interferometry,” Opt. Eng. 39, 106–113 (2000).
[Crossref]

Motoh, H.

Saldner, H. O.

Shirley, L. G.

M. S. Mermeistein, D. L. Feldkhum, and L. G. Shirley, “Video-rate surface profiling with acousto-optic accordion fringe interferometry,” Opt. Eng. 39, 106–113 (2000).
[Crossref]

Srinivasan, V.

Su, X.

X. Su and W. Chen, Opt. “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[Crossref]

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).
[Crossref]

X. Su, W. S. Zhou, V. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–73 (1992).
[Crossref]

Takeda, M.

von Bally, V.

X. Su, W. S. Zhou, V. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–73 (1992).
[Crossref]

Vukicevic, D.

X. Su, W. S. Zhou, V. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–73 (1992).
[Crossref]

Zhou, W. S.

X. Su, W. S. Zhou, V. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–73 (1992).
[Crossref]

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

X. Su, W. S. Zhou, V. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–73 (1992).
[Crossref]

Opt. Eng. (2)

G. C. Jin, N.K. Bao, and P.S. Chung, “Applications of a novel phase-shift method using a computer-controlled polarization mechanism,” Opt. Eng. 33, 2733–2737 (1994).
[Crossref]

M. S. Mermeistein, D. L. Feldkhum, and L. G. Shirley, “Video-rate surface profiling with acousto-optic accordion fringe interferometry,” Opt. Eng. 39, 106–113 (2000).
[Crossref]

Opt. Lasers Eng. (3)

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).
[Crossref]

C. A. Hobson, J. T. Atkinson, and F. Lilley, “The application of digital filtering to phase recovery when surface contouring using fringe projection techniques,” Opt. Lasers Eng. 27, 355–368 (1997).
[Crossref]

X. Su and W. Chen, Opt. “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. Schematic diagram of the proposed fringe projector. BS - beam splitter; AOM - acousto-optic modulator; WP- wedge prism, PH - pinholes; BC - beam combiner; MO - microscope objective.

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Fig. 2.
Fig. 2. Simulated fringe pattern projected on a convex surface with a plane as reference.

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Fig. 3.
Fig. 3. Schematic diagram of the electronics developed for driving the AOMs, and for controlling the fringe spacing and the phase shift.

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Fig. 4.
Fig. 4. Image recorded by a CCD camera when the fringe pattern was projected on a dome-shaped object with a reference plane.

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Fig. 5.
Fig. 5. Fringes recorded with a nominal phase shift of 180 degrees.

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Fig. 6.
Fig. 6. Recorded fringe patterns with three different periods projected on a rectangle block

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Fig. 7.
Fig. 7. Reconstructed 3D surface plot of the rectangle block

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Equations (12)

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E ( x , y , z , t ) = E 0 w o w ( z ) exp { − x 2 + y 2 w 2 ( z ) } exp { − i [ k z − ω t − tan − 1 ( z z 0 ) + k x 2 + y 2 2 R ( z ) ] } ,
z 0 = π w 0 2 ⁄ λ ,
w ( z ) = w 0 [ 1 + ( z ⁄ z 0 ) 2 ] 1 ⁄ 2 ,
R ( z ) = z [ 1 + ( z 0 + z ) 2 ] .
E ( x , y , z , t ) = E 0 exp { − x 2 + y 2 w 0 2 } exp { − i [ k z − ω t ] } .
A 1 = A 10 exp [ − i ( K 1 X 1 − Ω t + Φ 1 ) ] ,
A 2 = A 20 exp [ − i ( K 2 X 2 − Ω t + Φ 2 ) ] .
E ′ 1 ( x 1 , y 1 , z 1 , t ) = E 10 exp { − x 1 2 + y 1 2 w 0 2 } exp { − i [ k 1 z 1 − ( ω 0 + Ω ) t + Φ 1 ] } ,
E 2 ′ ( x 2 , y 2 , z 2 , t ) = E 20 exp { − x 2 2 + y 2 2 w 0 2 } exp { − i [ k 2 z 2 − ( ω 0 + Ω ) t + Φ 2 ] } ,
E ( x , y , z , t ) = E ′ 10 w ′ 0 w ′ ( z ) exp { − r 2 w ′ 2 ( z ) } exp { − i [ k z + r 2 2 R 1 − ( ω 0 + Ω ) t + Φ 1 ] }
+ E ′ 20 w ′ 0 w ′ ( z ) exp { − r 2 w ′ 2 ( z ) } exp { − i [ k z + r 2 2 R 2 − ( ω 0 + Ω ) t + Φ 2 ] } ,
I ( x , y , z ) = [ E ( x , y , z , t ) · E ( x , y , z , t ) * ] .

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