Abstract

The high resolution surface profile of a 3-D diffuse object is obtained by measurement of the phase distribution across the image of a projected sinusoidal grating deformed by the surface. A shearing polarization interferometer is used for projection. Deformed grating images are detected by an array camera and processed by a microcomputer. Surface height resolutions of better than 10 μm have been attained, limited essentially by electronic quantization noise. In contrast to direct deformed grating analysis, this method, based on phase-shifting interferometric techniques, is capable of accurate measurement even with coarse projected gratings and low density image sensing arrays. Areas of application include industrial quality control, biostereometrics, robotics, and solid modeling for computer graphics.

© 1984 Optical Society of America

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References

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    [CrossRef]
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1983

1982

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

1979

1978

1975

J. C. Wyant, “Use of an ac Heterodyne Lateral Shear Interferometer with Real-Time Wave Front Correction Systems,” Appl. Opt. 14, 2622 (1975).
[CrossRef] [PubMed]

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

1974

1970

1840

H. De Senarmont, Ann. Chim. Phys. 73, 337 (1840).

Allen, J. B.

Benoit, P.

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

Brangaccio, D. J.

Bruning, J. H.

De Senarmont, H.

H. De Senarmont, Ann. Chim. Phys. 73, 337 (1840).

Gallagher, J. E.

Halioua, M.

V. Srinivasan, H. C. Liu, M. Halioua, submitted to Applied Optics, June1984.

Herriott, D. R.

Hormiere, J.

P. Benoit, E. Mathieu, J. Hormiere, A. Thomas, “Characterization and Control of Three Dimensional Objects Using Fringe Projection 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.

Johnson, W. O.

Liu, H. C.

V. Srinivasan, H. C. Liu, M. Halioua, submitted to Applied Optics, June1984.

Mathieu, E.

P. Benoit, E. Mathieu, J. Hormiere, A. Thomas, “Characterization and Control of Three Dimensional Objects Using Fringe Projection 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.

V. Srinivasan, H. C. Liu, M. Halioua, submitted to Applied Optics, June1984.

Takasaki, H.

Takeda, M.

Thomas, A.

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

Truax, B. E.

White, A. D.

Wyant, J. C.

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).

Ann. Chim. Phys.

H. De Senarmont, Ann. Chim. Phys. 73, 337 (1840).

Appl. Opt.

Nouv. Rev. Opt.

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

Proc. Soc. Photo-Opt. Instrum. Eng.

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

Other

V. Srinivasan, H. C. Liu, M. Halioua, submitted to Applied Optics, June1984.

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the phase-measuring surface profilometer.

Fig. 2
Fig. 2

Projection system with phase shifter: SF, spatial filter; W, Wollaston prism at 45° relative to the laser polarization; Q, quarter-wave plate with fast axis parallel to laser polarization; P, rotatable polarizer for phase shifting; L, collimating lens.

Fig. 3
Fig. 3

Optical geometry for analysis of the image of the deformed grating.

Fig. 4
Fig. 4

Example of a deformed grating interferogram of a 3-D test object as seen by the detector array.

Fig. 5
Fig. 5

Surface profile plot of the 3-D test object of Fig. 4 generated by the phase-measuring profilometer.

Equations (8)

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I C = a ( x , y ) + b ( x , y ) cos ( 2 π O C / p 0 ) ,
I D = r ( x , y ) [ a ( x , y ) + b ( x , y ) cos ( 2 π O A / p 0 ) ] .
A C = ( p 0 / 2 π ) ϕ C D .
B D = A C tan θ 0 / ( 1 + tan θ 0 / tan θ n ) ,
B D = A C tan θ 0 .
ϕ R = 2 π O C / p 0 = 2 π n + ϕ R ,
I C = a ( x , y ) + b ( x , y ) cos ( ϕ M + ϕ R ) .
tan ϕ R = 1 N I n sin ( 2 π n / N ) / 1 N I n cos ( 2 π n / N ) .

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