Abstract

A method for high-resolution three-dimensional shape measurement for a shadow moiré system is proposed. To increase the resolving power of the method, the problem caused by the harmonics of the moiré profile needs to be solved. It is well known that moiré fringes in a shadow moiré system have a nonsinusoidal profile caused by harmonics. The influence of the harmonics in moiré profile on the measurement accuracy of the method is discussed. The method is improved to eliminate the error caused by the harmonics in the moiré profile. Both simulation and experimental results show that the improved method can effectively reduce the influence of harmonics.

© 1999 Optical Society of America

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References

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1977

1974

1970

Allen, J. B.

Arai, Y.

Brangaccio, D. J.

Bruning, J. H.

Cline, H. E.

Creath, K.

K. Creath, J. C. Wyant, “Moiré and fringe projection techniques,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley Interscience, New York, 1992), Chap. 16, pp. 653–686.

Deraemer, W. F.

Dirckx, J. J. J.

Gallagher, J. E.

Herriott, D. R.

Holik, A. S.

Idesawa, M.

Johnson, W. O.

Lorensen, W. E.

Meadows, D. M.

Rice, J. R.

J. R. Rice, Numerical Methods, Software, and Analysis (McGraw-Hill, New York, 1983), pp. 220–230.

Rosenfeld, D. P.

Soma, T.

Surrel, Y.

Takasaki, H.

White, A. D.

Wyant, J. C.

K. Creath, J. C. Wyant, “Moiré and fringe projection techniques,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley Interscience, New York, 1992), Chap. 16, pp. 653–686.

Yamada, T.

Yatagai, T.

Yokozeki, S.

Appl. Opt.

Other

K. Creath, J. C. Wyant, “Moiré and fringe projection techniques,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley Interscience, New York, 1992), Chap. 16, pp. 653–686.

J. R. Rice, Numerical Methods, Software, and Analysis (McGraw-Hill, New York, 1983), pp. 220–230.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the optical shadow moiré system with three TV cameras.

Fig. 2
Fig. 2

Frequency analysis of the moiré profile: (A) profile position, (B) spectrum of the profile.

Fig. 3
Fig. 3

Simulation results of fringe analysis of moiré profiles with higher harmonics: (A) moiré profiles, (B) ratio function, (C) measured profile of object by the standard method, (D) measured profile of object by the new method.

Fig. 4
Fig. 4

Error comparison of simulation results: (A) result error with the standard method, (B) result error with the new method.

Fig. 5
Fig. 5

Experimental moiré fringes from three TV cameras: (A) Δd 2 = 30 mm, (B) d = 230 mm, (C) Δd 1 = 30 mm.

Fig. 6
Fig. 6

Experimental results of fringe analysis of moiré profiles with higher harmonics: (A) moiré profiles, (B) ratio function, (C) measured profile of object by the standard method, (D) measured profile of object by the new method.

Fig. 7
Fig. 7

Error comparison of experimental results: (A) result error with the standard method, (B) result error with the new method.

Equations (5)

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Ix, z=ax, z+bx, zcos2πdhsh+l,
IΔd1x, z=ax, z+bx, zcos2πhd+Δd1sh+l,
IΔd2x, z=ax, z+bx, zcos2πhd-Δd2sh+l,
Fh=Ix, z-IΔd1x, zIΔd2x, z-Ix, z=cos2πdhsh+l-cos2πhd+Δd1sh+lcos2πhd-Δd2sh+l-cos2πdhsh+l.
Ix, z=ax, z+bx, zA1 cos2πdhsh+l+ A2 cos2 2πdhsh+l+A3 cos3 2πdhsh+l,

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