Abstract

The recently proposed technique of temporal phase unwrapping has been used to analyze the phase maps from a projected-fringe phase-shifting surface profilometer. A sequence of maps is acquired while the fringe pitch is changed; the phase at each pixel is then unwrapped over time independently of the other pixels in the image to provide an absolute measure of surface height. The main advantage is that objects containing height discontinuities are profiled as easily as smooth ones. This contrasts with the conventional spatial phase-unwrapping approach for which the phase jump across a height discontinuity is indeterminate to an integral multiple of 2π. The error in height is shown to decrease inversely with the number of phase maps used.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. E. Brooks, L. O. Heflinger, “Moiré gauging using optical interference patterns,” Appl. Opt. 8, 935–939 (1969).
    [CrossRef] [PubMed]
  2. G. Indebetouw, “Profile measurement using projection of running fringes,” Appl. Opt. 17, 2930–2933 (1978).
    [CrossRef] [PubMed]
  3. V. Srinivasan, H. C. Liu, M. Halioua, “Automated phase-measuring profilometry of 3-D diffuse objects,” Appl. Opt. 23, 3105–3108 (1984).
    [CrossRef] [PubMed]
  4. D. R. Burton, A. J. Goodall, J. T. Atkinson, M. J. Lalor, “The use of carrier frequency shifting for the elimination of phase discontinuities in Fourier transform profilometry,” Opt. Lasers Eng. 23, 245–257 (1995).
    [CrossRef]
  5. H. Zhao, W. Chen, Y. Tan, “Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,” Appl.Opt. 33, 4497–4500 (1994).
  6. G. T. Reid, R. C. Rixon, H. Stewart, “Moiré topography with large contour intervals,” in International Conference on Photomechanics and Speckle Metrology, F.-P. Chiang, ed., Proc. SPIE814, 307–313 (1987).
    [CrossRef]
  7. K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, 1993), pp. 94–140.
  8. P. J. Caber, “Interferometric profiler for rough surfaces,” Appl. Opt. 32, 3438–3441 (1993).
    [CrossRef] [PubMed]
  9. J. M. Huntley, H. O. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
    [CrossRef] [PubMed]
  10. K. A. Stetson, “Theory and applications of electronic holography,” in Proceedings of the International Conference on Hologram Interferometry and Speckle Metrology, K. A. Stetson, R. J. Pryputniewicz, eds. (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 294–300.
  11. K. Creath, “Averaging double-exposure speckle interferograms,” Opt. Lett. 10, 582–584 (1985).
    [CrossRef] [PubMed]

1995 (1)

D. R. Burton, A. J. Goodall, J. T. Atkinson, M. J. Lalor, “The use of carrier frequency shifting for the elimination of phase discontinuities in Fourier transform profilometry,” Opt. Lasers Eng. 23, 245–257 (1995).
[CrossRef]

1994 (1)

H. Zhao, W. Chen, Y. Tan, “Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,” Appl.Opt. 33, 4497–4500 (1994).

1993 (2)

1985 (1)

1984 (1)

1978 (1)

1969 (1)

Atkinson, J. T.

D. R. Burton, A. J. Goodall, J. T. Atkinson, M. J. Lalor, “The use of carrier frequency shifting for the elimination of phase discontinuities in Fourier transform profilometry,” Opt. Lasers Eng. 23, 245–257 (1995).
[CrossRef]

Brooks, R. E.

Burton, D. R.

D. R. Burton, A. J. Goodall, J. T. Atkinson, M. J. Lalor, “The use of carrier frequency shifting for the elimination of phase discontinuities in Fourier transform profilometry,” Opt. Lasers Eng. 23, 245–257 (1995).
[CrossRef]

Caber, P. J.

Chen, W.

H. Zhao, W. Chen, Y. Tan, “Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,” Appl.Opt. 33, 4497–4500 (1994).

Creath, K.

K. Creath, “Averaging double-exposure speckle interferograms,” Opt. Lett. 10, 582–584 (1985).
[CrossRef] [PubMed]

K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, 1993), pp. 94–140.

Goodall, A. J.

D. R. Burton, A. J. Goodall, J. T. Atkinson, M. J. Lalor, “The use of carrier frequency shifting for the elimination of phase discontinuities in Fourier transform profilometry,” Opt. Lasers Eng. 23, 245–257 (1995).
[CrossRef]

Halioua, M.

Heflinger, L. O.

Huntley, J. M.

Indebetouw, G.

Lalor, M. J.

D. R. Burton, A. J. Goodall, J. T. Atkinson, M. J. Lalor, “The use of carrier frequency shifting for the elimination of phase discontinuities in Fourier transform profilometry,” Opt. Lasers Eng. 23, 245–257 (1995).
[CrossRef]

Liu, H. C.

Reid, G. T.

G. T. Reid, R. C. Rixon, H. Stewart, “Moiré topography with large contour intervals,” in International Conference on Photomechanics and Speckle Metrology, F.-P. Chiang, ed., Proc. SPIE814, 307–313 (1987).
[CrossRef]

Rixon, R. C.

G. T. Reid, R. C. Rixon, H. Stewart, “Moiré topography with large contour intervals,” in International Conference on Photomechanics and Speckle Metrology, F.-P. Chiang, ed., Proc. SPIE814, 307–313 (1987).
[CrossRef]

Saldner, H. O.

Srinivasan, V.

Stetson, K. A.

K. A. Stetson, “Theory and applications of electronic holography,” in Proceedings of the International Conference on Hologram Interferometry and Speckle Metrology, K. A. Stetson, R. J. Pryputniewicz, eds. (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 294–300.

Stewart, H.

G. T. Reid, R. C. Rixon, H. Stewart, “Moiré topography with large contour intervals,” in International Conference on Photomechanics and Speckle Metrology, F.-P. Chiang, ed., Proc. SPIE814, 307–313 (1987).
[CrossRef]

Tan, Y.

H. Zhao, W. Chen, Y. Tan, “Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,” Appl.Opt. 33, 4497–4500 (1994).

Zhao, H.

H. Zhao, W. Chen, Y. Tan, “Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,” Appl.Opt. 33, 4497–4500 (1994).

Appl. Opt. (5)

Appl.Opt. (1)

H. Zhao, W. Chen, Y. Tan, “Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,” Appl.Opt. 33, 4497–4500 (1994).

Opt. Lasers Eng. (1)

D. R. Burton, A. J. Goodall, J. T. Atkinson, M. J. Lalor, “The use of carrier frequency shifting for the elimination of phase discontinuities in Fourier transform profilometry,” Opt. Lasers Eng. 23, 245–257 (1995).
[CrossRef]

Opt. Lett. (1)

Other (3)

G. T. Reid, R. C. Rixon, H. Stewart, “Moiré topography with large contour intervals,” in International Conference on Photomechanics and Speckle Metrology, F.-P. Chiang, ed., Proc. SPIE814, 307–313 (1987).
[CrossRef]

K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, 1993), pp. 94–140.

K. A. Stetson, “Theory and applications of electronic holography,” in Proceedings of the International Conference on Hologram Interferometry and Speckle Metrology, K. A. Stetson, R. J. Pryputniewicz, eds. (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 294–300.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Optical arrangement for shape measurement by projected fringes: SF, spatial filter; OL1, objective lens (collimator); OL2, objective lens (image formation); BS, beam splitter; M’s, mirrors; PZT, piezoelectric translation stage; CCD, video camera.

Fig. 2
Fig. 2

Wrapped phase maps, showing shapes of discontinuous objects: (a) test plate containing vertical grooves of varying depths, (b) six-pin integrated circuit on circuit board, (c) two adjacent teeth from a replica of a human jaw. Black and white represent phases of -π and +π, respectively.

Fig. 3
Fig. 3

Phase map from Fig. 2(a) unwrapped by the temporal phase-unwrapping algorithm, using 22 incremental maps.

Fig. 4
Fig. 4

Cross sections of a test object surface profile (central row of Fig. 3) obtained by unwrapping through (a) 1, (b) 6, (c) 22 incremental maps.

Fig. 5
Fig. 5

Standard deviation in surface height as a function of the total phase range across the image. The circles correspond to the results shown in Fig.4.

Fig. 6
Fig. 6

Phase map of the integrated circuit from Fig. 2(b) unwrapped by the temporal phase-unwrapping algorithm, using 22 incremental maps.

Fig. 7
Fig. 7

Phase map of molar teeth from Fig. 2(c) unwrapped by the temporal phase-unwrapping algorithm, using ten incremental maps.

Equations (10)

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

aAx, y, z, t=a0 expikxtx+kyty+kzz+ϕAx, y,
aBx, y, z=a0 expikzz+ϕBx, y,
Φt=ΦBx, y-ΦAx, y-kxtx-kyty.
Φs-Φ0=-kxsx-kysy.
Φs-Φ0=-kxsx+kysy sin α+z cos α,
kyt-kyt-1<π/Y sin α+Z cos α.
ΔΦt=Φt-Φt-1
ΔΦt=tan-1ΔI42tΔI13t-1-ΔI13tΔI42t-1ΔI13tΔI13t-1+ΔI42tΔI42t-1,
ΔIijt=Iit-Ijt.
Φs-Φ0=t=1sΔΦt.

Metrics