Abstract

We describe a new high-resolution three-dimensional measurement method for shadow moiré. The method is based on the principle of using shadow moiré to produce moiré fringes and a fringe-scanning technique. In this method, a general function, instead of an arctangent function, is used for detecting the shape of an object. One can subsequently analyze the general function using numerical analysis with a digital computer. Two systems for static and dynamic measurements are proposed.

Experimental results show that measurement accuracies in static and dynamic measurement systems are obtainable to greater than 1/50 and 1/40 fringes, respectively.

© 1995 Optical Society of America

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References

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

1990 (1)

1984 (1)

1977 (1)

1974 (1)

1970 (2)

Allen, J. B.

Brangaccio, D. J.

Bruning, J. H.

Cline, H. E.

Decraemer, W. F.

Dirckx, J. J. J.

Gallagher, J. E.

Herriott, D. R.

Holik, A. S.

Idesawa, M.

Johnson, W. O.

Lorensen, W. E.

Malacara, D.

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992), pp. 653–685.

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.

Takasaki, H.

White, A. D.

Yatagai, T.

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of a shadow moiré system.

Fig. 2
Fig. 2

Functions f1(h) and g1(h) for numerical analysis.

Fig. 3
Fig. 3

Schematic diagram of a shadow moiré system for measuring a dynamic event.

Fig. 4
Fig. 4

Flow chart for numerical calculation of a dynamic shadow moiré.

Fig. 5
Fig. 5

Moiré fringes of a tilted plane object with different Δl displacements.

Fig. 6
Fig. 6

Measured results of a tilted plane object with the help of functions f1(h) and g1(h).

Fig. 7
Fig. 7

Moiré fringes of a tilted plane object with different Δd displacements.

Fig. 8
Fig. 8

Experimental results obtained by use of the method with three TV cameras.

Fig. 9
Fig. 9

Measurement errors in the proposed systems.

Fig. 10
Fig. 10

Applied impulse signal used for speaker excitation.

Fig. 11
Fig. 11

Measured results of the shape of a speaker’s cone paper with excitation.

Equations (11)

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I ( x , z ) = a ( x , z ) + b ( x , z ) cos 2 π h d s ( h + l ) ,
I ( x , z : Δ l ) = a ( x , z ) + b ( x , z ) cos 2 π ( h + Δ l ) d s ( h + l ) ,
I ( x , z : - Δ l ) = a ( x , z ) + b ( x , z ) cos 2 π ( h - Δ l ) d s ( h + l ) ,
f 1 ( h ) = I ( x , z ) - I ( x , z : Δ l ) I ( x , z : - Δ l ) - I ( x , z ) = cos 2 π h d s ( h + l ) - cos 2 π ( h + Δ l ) d s ( h + l ) cos 2 π ( h - Δ l ) d s ( h + l ) - cos 2 π h d s ( h + l ) .
F 1 ( h ) = f 1 ( h ) - α ,
I ( x , z ) = a ( x , z ) + b ( x , z ) cos 2 π h d s ( h + l ) ,
I ( x , z : Δ d 1 ) = a ( x , z ) + b ( x , z ) cos 2 π h ( d + Δ d 1 ) s ( h + l ) ,
I ( x , z : Δ d 2 ) = a ( x , z ) + b ( x , z ) cos 2 π h ( d + Δ d 2 ) s ( h + l ) .
f 2 ( h ) = I ( x , z ) - I ( x , z : Δ d 1 ) I ( x , z : Δ d 2 ) - I ( x , z ) = cos 2 π h d s ( h + l ) - cos 2 π ( d + Δ d 1 ) h s ( h + l ) cos 2 π ( d + Δ d 2 ) h s ( h + l ) - cos 2 π h d s ( h + l ) ,
W 1 = k Δ d 1 l + h i .
W 2 = k Δ d 2 l + h i ,

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