Abstract

A method of automatically reconstructing the 3-D surface of an object from a 2-D moire pattern has been extended to interpret ambiguous fringe patterns by displacing the object. Potential applications of the surface reconstruction technique include inspection, cad/cam, microscopy, and robot vision. The digitized binary image was segmented into labeled fringes, the contours were detected, and the surface was reconstructed. A coin was used as an example to illustrate the procedure. The feasibility of using automatic moire contouring to inspect surfaces is discussed.

© 1984 Optical Society of America

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References

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  1. W. R. J. Funnell, “Image processing applied to the interactive analysis of interferometric fringes,” Appl. Opt. 20, 3245 (1981).
    [CrossRef] [PubMed]
  2. M. Kamegai, G. T. Carpluk, “Data Reduction Scheme for Laser Doppler Interferometers,” NTIS Report UCID-16621, U. California, Livermore (1974).
  3. J. J. Snyder, “Algorithm for fast digital analysis of interference fringes,” Appl. Opt. 19, 1223 (1980).
    [CrossRef] [PubMed]
  4. G. H. Kaufmann, “On the Numerical Processing of Speckle Fringes,” Opt. Laser Technol. 12, 209 (1980).
    [CrossRef]
  5. B. Ineichen, P. Eglin, R. Daendliker, “Hybrid optical and electronic image processing for strain measurements by speckle photography,” Appl. Opt. 19, 2191 (1980).
    [CrossRef] [PubMed]
  6. T. M. Kries, H. Kreitlow, “Quantitative Evaluation of Holographic Interference Patterns Under Image Processing Aspects,” Proc. Soc. Photo-Opt. Instrum. Eng. 210, 196 (1980).
  7. H. Takasaki, “Moire topography,” Appl. Opt. 9, 1467 (1970).
    [CrossRef] [PubMed]
  8. D. M. Meadows, W. O. Johnson, J. B. Allan, “Generation of surface contours by moire patterns,” Appl. Opt. 9, 942 (1970).
    [CrossRef] [PubMed]
  9. T. Yatagai, M. Idesawa, S. Saito, “Automatic Topography Using High Precision Digital Moire Methods,” Proc. Soc. Photo-Opt. Instrum. Eng. 361, 81 (1982).
  10. H. E. Cline, A. S. Holik, W. E. Lorensen, “Computer-aided surface reconstruction of interference contours,” Appl. Opt. 21, 4481 (1982).
    [CrossRef] [PubMed]
  11. P. H. Winston, B. K. P. Horn, LISP (Addison-Wesley, Reading, Mass., 1981).
  12. H. N. Christiansen, M. B. Stephenson, “movie.byu—A General Purpose Computer Graphics Display System,” in Proceedings, Symposium on Applications of Computer Methods in Engineering (U. Southern California, Los Angeles, 1977), Vol. 2, p. 759.
  13. H. W. Christiansen, W. Sederberg, Comput. Graphics 12, 187 (1978).
    [CrossRef]

1982 (2)

T. Yatagai, M. Idesawa, S. Saito, “Automatic Topography Using High Precision Digital Moire Methods,” Proc. Soc. Photo-Opt. Instrum. Eng. 361, 81 (1982).

H. E. Cline, A. S. Holik, W. E. Lorensen, “Computer-aided surface reconstruction of interference contours,” Appl. Opt. 21, 4481 (1982).
[CrossRef] [PubMed]

1981 (1)

1980 (4)

J. J. Snyder, “Algorithm for fast digital analysis of interference fringes,” Appl. Opt. 19, 1223 (1980).
[CrossRef] [PubMed]

G. H. Kaufmann, “On the Numerical Processing of Speckle Fringes,” Opt. Laser Technol. 12, 209 (1980).
[CrossRef]

B. Ineichen, P. Eglin, R. Daendliker, “Hybrid optical and electronic image processing for strain measurements by speckle photography,” Appl. Opt. 19, 2191 (1980).
[CrossRef] [PubMed]

T. M. Kries, H. Kreitlow, “Quantitative Evaluation of Holographic Interference Patterns Under Image Processing Aspects,” Proc. Soc. Photo-Opt. Instrum. Eng. 210, 196 (1980).

1978 (1)

H. W. Christiansen, W. Sederberg, Comput. Graphics 12, 187 (1978).
[CrossRef]

1970 (2)

Allan, J. B.

Carpluk, G. T.

M. Kamegai, G. T. Carpluk, “Data Reduction Scheme for Laser Doppler Interferometers,” NTIS Report UCID-16621, U. California, Livermore (1974).

Christiansen, H. N.

H. N. Christiansen, M. B. Stephenson, “movie.byu—A General Purpose Computer Graphics Display System,” in Proceedings, Symposium on Applications of Computer Methods in Engineering (U. Southern California, Los Angeles, 1977), Vol. 2, p. 759.

Christiansen, H. W.

H. W. Christiansen, W. Sederberg, Comput. Graphics 12, 187 (1978).
[CrossRef]

Cline, H. E.

Daendliker, R.

Eglin, P.

Funnell, W. R. J.

Holik, A. S.

Horn, B. K. P.

P. H. Winston, B. K. P. Horn, LISP (Addison-Wesley, Reading, Mass., 1981).

Idesawa, M.

T. Yatagai, M. Idesawa, S. Saito, “Automatic Topography Using High Precision Digital Moire Methods,” Proc. Soc. Photo-Opt. Instrum. Eng. 361, 81 (1982).

Ineichen, B.

Johnson, W. O.

Kamegai, M.

M. Kamegai, G. T. Carpluk, “Data Reduction Scheme for Laser Doppler Interferometers,” NTIS Report UCID-16621, U. California, Livermore (1974).

Kaufmann, G. H.

G. H. Kaufmann, “On the Numerical Processing of Speckle Fringes,” Opt. Laser Technol. 12, 209 (1980).
[CrossRef]

Kreitlow, H.

T. M. Kries, H. Kreitlow, “Quantitative Evaluation of Holographic Interference Patterns Under Image Processing Aspects,” Proc. Soc. Photo-Opt. Instrum. Eng. 210, 196 (1980).

Kries, T. M.

T. M. Kries, H. Kreitlow, “Quantitative Evaluation of Holographic Interference Patterns Under Image Processing Aspects,” Proc. Soc. Photo-Opt. Instrum. Eng. 210, 196 (1980).

Lorensen, W. E.

Meadows, D. M.

Saito, S.

T. Yatagai, M. Idesawa, S. Saito, “Automatic Topography Using High Precision Digital Moire Methods,” Proc. Soc. Photo-Opt. Instrum. Eng. 361, 81 (1982).

Sederberg, W.

H. W. Christiansen, W. Sederberg, Comput. Graphics 12, 187 (1978).
[CrossRef]

Snyder, J. J.

Stephenson, M. B.

H. N. Christiansen, M. B. Stephenson, “movie.byu—A General Purpose Computer Graphics Display System,” in Proceedings, Symposium on Applications of Computer Methods in Engineering (U. Southern California, Los Angeles, 1977), Vol. 2, p. 759.

Takasaki, H.

Winston, P. H.

P. H. Winston, B. K. P. Horn, LISP (Addison-Wesley, Reading, Mass., 1981).

Yatagai, T.

T. Yatagai, M. Idesawa, S. Saito, “Automatic Topography Using High Precision Digital Moire Methods,” Proc. Soc. Photo-Opt. Instrum. Eng. 361, 81 (1982).

Appl. Opt. (6)

Comput. Graphics (1)

H. W. Christiansen, W. Sederberg, Comput. Graphics 12, 187 (1978).
[CrossRef]

Opt. Laser Technol. (1)

G. H. Kaufmann, “On the Numerical Processing of Speckle Fringes,” Opt. Laser Technol. 12, 209 (1980).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

T. M. Kries, H. Kreitlow, “Quantitative Evaluation of Holographic Interference Patterns Under Image Processing Aspects,” Proc. Soc. Photo-Opt. Instrum. Eng. 210, 196 (1980).

T. Yatagai, M. Idesawa, S. Saito, “Automatic Topography Using High Precision Digital Moire Methods,” Proc. Soc. Photo-Opt. Instrum. Eng. 361, 81 (1982).

Other (3)

P. H. Winston, B. K. P. Horn, LISP (Addison-Wesley, Reading, Mass., 1981).

H. N. Christiansen, M. B. Stephenson, “movie.byu—A General Purpose Computer Graphics Display System,” in Proceedings, Symposium on Applications of Computer Methods in Engineering (U. Southern California, Los Angeles, 1977), Vol. 2, p. 759.

M. Kamegai, G. T. Carpluk, “Data Reduction Scheme for Laser Doppler Interferometers,” NTIS Report UCID-16621, U. California, Livermore (1974).

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Figures (12)

Fig. 1
Fig. 1

Simulated fringe pattern from an analytical expression of the surface having both linear and and Gaussian terms.

Fig. 2
Fig. 2

Calculated fringe pattern of the surface shown in Fig. after a displacement vertically of a quarter fringe.

Fig. 3
Fig. 3

Profile of a surface maxima is reconstructed from two fringe patterns displaced by h/4 by comparing the intensity traces across the fringes.

Fig. 4
Fig. 4

Example of a fringe pattern illustrating the relationships between the binary pixels, the labeled fringes, and the contours between the fringes.

Fig. 5
Fig. 5

Connectivity tree where the nodes are the n fringes and the branches are the n − 1 contours between the fringes. Arrows indicate the relative height of adjacent fringes.

Fig. 6
Fig. 6

Schematic diagram of the automatic moire contouring apparatus comprising of a collimated light source, Ronchi grating, TV camera, computer, and graphics display.

Fig. 7
Fig. 7

Depth of moire contouring measured for different Ronchi gratings approaches the limit calculated by diffraction.

Fig. 8
Fig. 8

Fringe pattern of a quarter using a Ronchi grating with 84-μm wide lines. The vertical spacing between white fringes is calculated to be 144 μm.

Fig. 9
Fig. 9

Binary image of the fringe pattern where each pixel is set to one of two values depending on the threshold value.

Fig. 10
Fig. 10

Segmented fringe pattern where each labeled fringe is shown by a different gray level.

Fig. 11
Fig. 11

Wire frame representation of the surface obtained using the cad/cam software movie.byu.

Fig. 12
Fig. 12

Shaded and smoothed 3-D image of the surface of a quarter reconstructed from a moire fringe pattern of the quarter using the method described in the text.

Equations (8)

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

z = σ ( x , y )
I ( x , y ) = f ( z ) ,
f ( z ) = f ( z + h ) .
z = z + ϕ ,
I ( x , y ) = f ( z + ϕ ) .
fringes = [ A B C D E F G ] .
contours = [ AB AC BD DE DF FG ] .
h = d / tan θ .

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