Abstract

A new method for full field automatic 3-D surface reconstruction is proposed which makes use of multiple contourograms shifted in phase by object translation. The method is demonstrated for shadow moire topography. It is shown that surface reconstruction can be done fast and with a resolution at least 10 times higher than the fringe distance of the measuring setup. Convexity and concavity of the surface are automatically determined. Also shown is the possibility of measuring irregular surfaces with very sudden height jumps.

© 1988 Optical Society of America

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References

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  1. K. Andresen, “Das Phasenshiftverfahren zum Moire-Bildauswehrtung,” Optik 72, 115 (1986).
  2. H. Takasaki, “Moire Topography from Its Birth to Practical Application,” Opt. Lasers Eng. 3, 3 (1982).
    [CrossRef]
  3. D. M. Meadows, W. O. Johnson, J. B. Allen, “Generation of Surface Contours by Moire Patterns,” Appl. Opt. 9, 942 (1970).
    [CrossRef] [PubMed]
  4. J. L. Janssens, W. F. Decraemer, V. J. Vanhuyse, “Visibility Depth of Shadow Moire Fringes in Function of Extend of Light Source and Aperture of Recording System,” Optik 71, 45 (1985).
  5. M. Halioua, R. S. Krishnamurthy, H. Liu, F-P. Chiang, “Projection Moire with Moving Gratings for Automated 3-D Topography,” Appl. Opt. 33, 850 (1983).
    [CrossRef]
  6. W. R. J. Funnell, “Image Processing Applied to the Interactive Analysis of Interferometric Fringes,” Appl. Opt. 20, 3245 (1981).
    [CrossRef] [PubMed]

1986 (1)

K. Andresen, “Das Phasenshiftverfahren zum Moire-Bildauswehrtung,” Optik 72, 115 (1986).

1985 (1)

J. L. Janssens, W. F. Decraemer, V. J. Vanhuyse, “Visibility Depth of Shadow Moire Fringes in Function of Extend of Light Source and Aperture of Recording System,” Optik 71, 45 (1985).

1983 (1)

M. Halioua, R. S. Krishnamurthy, H. Liu, F-P. Chiang, “Projection Moire with Moving Gratings for Automated 3-D Topography,” Appl. Opt. 33, 850 (1983).
[CrossRef]

1982 (1)

H. Takasaki, “Moire Topography from Its Birth to Practical Application,” Opt. Lasers Eng. 3, 3 (1982).
[CrossRef]

1981 (1)

1970 (1)

Allen, J. B.

Andresen, K.

K. Andresen, “Das Phasenshiftverfahren zum Moire-Bildauswehrtung,” Optik 72, 115 (1986).

Chiang, F-P.

M. Halioua, R. S. Krishnamurthy, H. Liu, F-P. Chiang, “Projection Moire with Moving Gratings for Automated 3-D Topography,” Appl. Opt. 33, 850 (1983).
[CrossRef]

Decraemer, W. F.

J. L. Janssens, W. F. Decraemer, V. J. Vanhuyse, “Visibility Depth of Shadow Moire Fringes in Function of Extend of Light Source and Aperture of Recording System,” Optik 71, 45 (1985).

Funnell, W. R. J.

Halioua, M.

M. Halioua, R. S. Krishnamurthy, H. Liu, F-P. Chiang, “Projection Moire with Moving Gratings for Automated 3-D Topography,” Appl. Opt. 33, 850 (1983).
[CrossRef]

Janssens, J. L.

J. L. Janssens, W. F. Decraemer, V. J. Vanhuyse, “Visibility Depth of Shadow Moire Fringes in Function of Extend of Light Source and Aperture of Recording System,” Optik 71, 45 (1985).

Johnson, W. O.

Krishnamurthy, R. S.

M. Halioua, R. S. Krishnamurthy, H. Liu, F-P. Chiang, “Projection Moire with Moving Gratings for Automated 3-D Topography,” Appl. Opt. 33, 850 (1983).
[CrossRef]

Liu, H.

M. Halioua, R. S. Krishnamurthy, H. Liu, F-P. Chiang, “Projection Moire with Moving Gratings for Automated 3-D Topography,” Appl. Opt. 33, 850 (1983).
[CrossRef]

Meadows, D. M.

Takasaki, H.

H. Takasaki, “Moire Topography from Its Birth to Practical Application,” Opt. Lasers Eng. 3, 3 (1982).
[CrossRef]

Vanhuyse, V. J.

J. L. Janssens, W. F. Decraemer, V. J. Vanhuyse, “Visibility Depth of Shadow Moire Fringes in Function of Extend of Light Source and Aperture of Recording System,” Optik 71, 45 (1985).

Appl. Opt. (3)

Opt. Lasers Eng. (1)

H. Takasaki, “Moire Topography from Its Birth to Practical Application,” Opt. Lasers Eng. 3, 3 (1982).
[CrossRef]

Optik (2)

K. Andresen, “Das Phasenshiftverfahren zum Moire-Bildauswehrtung,” Optik 72, 115 (1986).

J. L. Janssens, W. F. Decraemer, V. J. Vanhuyse, “Visibility Depth of Shadow Moire Fringes in Function of Extend of Light Source and Aperture of Recording System,” Optik 71, 45 (1985).

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Figures (9)

Fig. 1
Fig. 1

Experimental setup: 1,1′, light sources; 2, grating on a translation stage; 3, miniature motor; 4, object; 5, translation stage; 6, stepper motor; 7, video camera.

Fig. 2
Fig. 2

Intensity distributions of one image line passing through the center of the cone surface for object positions 0 and 2π/S behind the grating. The intensity is given in arbitrary units; the position on the x axis is given in pixel numbers.

Fig. 3
Fig. 3

Intensity distributions of one image line passing through the center of the cone surface for object positions 0 and π/S behind the grating.

Fig. 4
Fig. 4

Result obtained by subtraction of the distributions of Fig. 3.

Fig. 5
Fig. 5

Reconstruction of one surface line passing through the center of the cone. The 512 measured points take the form of a continuous line, the dots represent ten theoretical points. The vertical axis is extended four times with respect to that of the horizontal axis.

Fig. 6
Fig. 6

Moire topogram of a cast of a cat tympanic membrane.

Fig. 7
Fig. 7

Image obtained by subtracting pictures as in Eq. (9).

Fig. 8
Fig. 8

Three-dimensional plot of the surface of the cat tympanic membrane, reconstructed on a 240 × 300 points matrix.

Fig. 9
Fig. 9

Three-dimensional plot of the reconstructed surface of a half-relief sculpture.

Equations (14)

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I ( x , y ) = A ( x , y ) { sin [ S · O ( x , y ) ] + B ( x , y ) } ,
I 0 ( x , y ) = A ( x , y ) { sin [ S · O ( x , y ) ] + B ( x , y ) } ,
I 1 ( x , y ) = A ( x , y ) [ sin { S [ O ( x , y ) + δ 1 ] } + B ( x , y ) ] ,
I 2 ( x , y ) = A ( x , y ) [ sin { S [ O ( x , y ) + δ 2 ] } + B ( x , y ) ] .
I 1 ( x , y ) I 0 ( x , y ) I 2 ( x , y ) I 0 ( x , y ) = sin { S [ O ( x , y ) + δ 2 ] } sin [ S · O ( x , y ) ] sin { S [ O ( x , y ) + δ 2 ] } sin [ S · O ( x , y ) ] .
O ( x , y ) = 1 S arctan sin δ 1 + I 1 ( x , y ) I 0 ( x , y ) I 2 ( x , y ) I 0 ( x , y ) sin δ 2 ( cos δ 1 1 ) I 1 ( x , y ) I 0 ( x , y ) I 2 ( x , y ) I 0 ( x , y ) ( cos δ 2 1 ) .
I 0 ( x , y ) = A ( x , y ) { sin [ S · O ( x , y ) ] + B ( x , y ) } ,
I π ( x , y ) = A ( x , y ) { sin [ S · O ( x , y ) + π ] + B ( x , y ) } .
I 0 ( x , y ) = A ( x , y ) sin [ S · O ( x , y ) ] .
I δ ( x , y ) = A ( x , y ) sin { S [ O ( x , y ) + δ ] } .
O ( x , y ) = 1 S arctan I δ ( x , y ) sin δ I 0 ( x , y ) I δ ( x , y ) cos δ .
F ( z ) = C · ( 1 + M ( z ) cos { 2 π z D / [ p ( H + z ) ] } ) ,
C = c · A 2 S 2 / 4 ,
M ( z ) = 1 + ( 1 / 2 ) [ 2 p ( H + z ) / ( π z S ) ] · J 1 { π z S / [ p ( H + z ) ] } · [ 2 p ( H + z ) / ( π z A ) ] · J 1 { π z A / [ p ( H + z ) ] } ,

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