Abstract

When a sinusoidal grating is projected on either a reference plane or a diffuse object to be measured, every point along a line normal to the grating lines, on the reference plane as well as the object, can be characterized by a unique phase value. By measuring this phase accurately using phase modulation methods and by determining points on the reference plane and the object having identical phases, it is shown that the object height can be computed. A working system requires a projector, a translatable sinusoidal grating, and a detector array interfaced to a microcomputer. Results of measurements on diffuse test objects are described and errors are analyzed.

© 1985 Optical Society of America

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References

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1984 (1)

1983 (1)

1982 (1)

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

1979 (1)

1978 (1)

G. Indebetouw, “Profile Measurement Using Projection of Running Fringes,” Appl Opt. 17, 2930 (1978).
[CrossRef] [PubMed]

1975 (1)

P. Benoit, E. Mathieu, J. Hormiere, A. Thomas, “Characterization and Control of Three Dimensional Objects Using Fringe Rejection Techniques,” Nouv. Rev. Opt. 6, 67 (1975).
[CrossRef]

1974 (1)

1970 (2)

Allen, J. B.

Benoit, P.

P. Benoit, E. Mathieu, J. Hormiere, A. Thomas, “Characterization and Control of Three Dimensional Objects Using Fringe Rejection Techniques,” Nouv. Rev. Opt. 6, 67 (1975).
[CrossRef]

Brangaccio, D. J.

Bruning, J. H.

Gallagher, J. E.

Halioua, M.

Herriott, D. R.

Hormiere, J.

P. Benoit, E. Mathieu, J. Hormiere, A. Thomas, “Characterization and Control of Three Dimensional Objects Using Fringe Rejection Techniques,” Nouv. Rev. Opt. 6, 67 (1975).
[CrossRef]

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).

Indebetouw, G.

G. Indebetouw, “Profile Measurement Using Projection of Running Fringes,” Appl Opt. 17, 2930 (1978).
[CrossRef] [PubMed]

Johnson, W. O.

Liu, H. C.

Mathieu, E.

P. Benoit, E. Mathieu, J. Hormiere, A. Thomas, “Characterization and Control of Three Dimensional Objects Using Fringe Rejection Techniques,” Nouv. Rev. Opt. 6, 67 (1975).
[CrossRef]

Meadows, D. M.

Moore, D. T.

Mutoh, K.

Rosenfeld, D. P.

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).

Srinivasan, V.

Takasaki, H.

Takeda, M.

Thomas, A.

P. Benoit, E. Mathieu, J. Hormiere, A. Thomas, “Characterization and Control of Three Dimensional Objects Using Fringe Rejection Techniques,” Nouv. Rev. Opt. 6, 67 (1975).
[CrossRef]

Truax, B. E.

White, A. D.

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).

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Figures (4)

Fig. 1
Fig. 1

Ray diagram for the analysis of the deformed grating image in the case of general projection geometry.

Fig. 2
Fig. 2

Profile of a cylindrical test object: comparison between optical (line) and contact (×) measurements.

Fig. 3
Fig. 3

View of the mannequin face with a projected sinusoidal grating of 15-mm period. The phase measuring technique requires three such interferograms with one-third period phase shift between interferograms.

Fig. 4
Fig. 4

Perspective profile plot of the mannequin face with respect to a given reference plane.

Equations (7)

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I R = a ( x , y ) + b ( x , y ) cos ϕ ( x ) ,
ϕ C = 2 π n + ϕ C ,
tan ϕ C = 1 N I n sin ( 2 π n / N ) / 1 N I n cos ( 2 π n / N ) .
h ( x , y ) = ( A C / d ) l 0 ( l + A C / d ) 1 ,
h ( x , y ) = ( A C / d ) l 0 ,
I 1 = a + b ± b / Q , I 2 = a ( b / 2 ) ± b / Q , I 3 = a ( b / 2 ) ± b / Q .
ϕ E max = 1 / 0.866 Q .

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