Abstract

In order to establish the quantitative method for measuring three-dimensional displacements by holographic interferometry, the authors have already discussed some problems and presented several practical devices. On the basis of these considerations, the usefulness of this measuring method was shown by a practical example: measurement of deformation in a cylindrical shell under concentrated loading. The displacement components could be measured with high accuracy (order of 0.1 μm) when the optical system was arranged and the fringe order number was read within allowable error given beforehand, respectively. The decision of fringe order number was made easily by applying elastic elongation of a rubber strip as an index and by reconstructing the holographic real image on the original object.

© 1974 Optical Society of America

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References

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  1. A. E. Ennos, J. Sci. Instrum. Ser II, 1, 731 (1968).
    [CrossRef]
  2. A. D. Wilson, Appl. Opt. 10, 908 (1971).
    [CrossRef] [PubMed]
  3. P. Boone, Optik 34, 406 (1972).
  4. J. E. Sollid, Appl. Opt. 8, 1587 (1969).
    [CrossRef] [PubMed]
  5. K. Shibayama, H. Uchiyama, Appl. Opt. 10, 2150 (1970).
    [CrossRef]
  6. T. Matsumoto, K. Iwata, R. Nagata, Appl. Opt. 12, 960 (1973).
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    [CrossRef] [PubMed]
  8. N. Abramson, Appl. Opt. 11, 1143 (1972).
    [CrossRef] [PubMed]
  9. K. Mizoguchi, H. Shiota, K. Shirakawa, Bull. Japan Soc. Mech. Eng. 11, 393 (1968).
    [CrossRef]

1973 (2)

T. Matsumoto, K. Iwata, R. Nagata, Appl. Opt. 12, 960 (1973).

T. Matsumoto, K. Iwata, R. Nagata, Appl. Opt. 12, 1660 (1973).
[CrossRef] [PubMed]

1972 (2)

1971 (1)

1970 (1)

1969 (1)

1968 (2)

A. E. Ennos, J. Sci. Instrum. Ser II, 1, 731 (1968).
[CrossRef]

K. Mizoguchi, H. Shiota, K. Shirakawa, Bull. Japan Soc. Mech. Eng. 11, 393 (1968).
[CrossRef]

Abramson, N.

Boone, P.

P. Boone, Optik 34, 406 (1972).

Ennos, A. E.

A. E. Ennos, J. Sci. Instrum. Ser II, 1, 731 (1968).
[CrossRef]

Iwata, K.

T. Matsumoto, K. Iwata, R. Nagata, Appl. Opt. 12, 1660 (1973).
[CrossRef] [PubMed]

T. Matsumoto, K. Iwata, R. Nagata, Appl. Opt. 12, 960 (1973).

Matsumoto, T.

T. Matsumoto, K. Iwata, R. Nagata, Appl. Opt. 12, 960 (1973).

T. Matsumoto, K. Iwata, R. Nagata, Appl. Opt. 12, 1660 (1973).
[CrossRef] [PubMed]

Mizoguchi, K.

K. Mizoguchi, H. Shiota, K. Shirakawa, Bull. Japan Soc. Mech. Eng. 11, 393 (1968).
[CrossRef]

Nagata, R.

T. Matsumoto, K. Iwata, R. Nagata, Appl. Opt. 12, 1660 (1973).
[CrossRef] [PubMed]

T. Matsumoto, K. Iwata, R. Nagata, Appl. Opt. 12, 960 (1973).

Shibayama, K.

Shiota, H.

K. Mizoguchi, H. Shiota, K. Shirakawa, Bull. Japan Soc. Mech. Eng. 11, 393 (1968).
[CrossRef]

Shirakawa, K.

K. Mizoguchi, H. Shiota, K. Shirakawa, Bull. Japan Soc. Mech. Eng. 11, 393 (1968).
[CrossRef]

Sollid, J. E.

Uchiyama, H.

Wilson, A. D.

Appl. Opt. (6)

Bull. Japan Soc. Mech. Eng. (1)

K. Mizoguchi, H. Shiota, K. Shirakawa, Bull. Japan Soc. Mech. Eng. 11, 393 (1968).
[CrossRef]

J. Sci. Instrum. Ser II (1)

A. E. Ennos, J. Sci. Instrum. Ser II, 1, 731 (1968).
[CrossRef]

Optik (1)

P. Boone, Optik 34, 406 (1972).

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Figures (6)

Fig. 1
Fig. 1

Relation between the coordinate system for the object (X, Y, Z) and that for the optical system (x, y, z). (a) Coordinate system (X, Y, Z) and displacement components (U, V, W) in the cylinder. (b) Relation between coordinate systems in the cylinder and the optical system. (c) Coordinate system (x, y, z) and displacement components (ux, uy, uz) in the optical system. The unit vectors Oj (j = 1, 2, 3) denote the observing directions and the unit vector I denotes the illuminating direction.

Fig. 2
Fig. 2

A part of the optical system. C, cylinder; Lj, Fraunhofer lenses; L4, collimating lens; R, rubber strip; S, stationary support.

Fig. 3
Fig. 3

Loading apparatus and cylindrical shell. C, cylinder; M, middle point on the cylinder; F, framework; U, concave thin blocks; T, thread; SS, strain sensor; SI, strain indicator.

Fig. 4
Fig. 4

Reconstructed images (a), (b), and (c) obtained through the observing directions Oj (j ≡ 1, 2, 3) as shown in Fig. 2, respectively.

Fig. 5
Fig. 5

Distortionless images obtained by using real images. Figures (a), (b), and (c) correspond to three observing directions Oj (j = 1, 2, 3), respectively.

Fig. 6
Fig. 6

Measuring results obtained from Fig. 5. Figures (a), (b), and (c) correspond to three displacement components U, V and W, respectively. These were measured in the region (θ = 20–70°) on the circumference through the loading point M.

Equations (5)

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I = ( cos α , 0 , sin α ) , O 1 = ( cos β , ( - 3 / 2 ) sin β , ( - 1 / 2 ) sin β ) , O 2 = ( cos β , ( 3 / 2 ) sin β , ( - 1 / 2 ) sin β ) , O 3 = ( cos β , 0 , sin β ) .
A · d = N λ .
A = [ I + O 1 I + O 2 I + O 3 ] = [ cos α + cos β ( - 3 / 2 ) sin β ( - 1 / 2 ) sin β cos α + cos β ( 3 / 2 ) sin β ( - 1 / 2 ) sin β cos α + cos β 0 sin α + sin β ] , d = [ u x u y u z ] , and N = [ N 1 N 2 N 3 ] ,
U = u y , V = cos [ 90 ° - ( ξ + θ ) + α ] u x + cos [ 180 ° - ( ξ + θ ) + α ] u z , W = cos [ ( ξ + θ ) - α ] u x + cos [ 90 ° - ( ξ + θ ) + α ] u z
U = 0.517 ( - N 1 + N 2 ) , V = [ 0.215 cos ( 86 ° 3 9 - θ ) - 0.298 cos ( 176 ° 3 9 - θ ) ] ( N 1 + N 2 ) + [ - 0.035 cos ( 86 ° 3 9 - θ ) + 0.597 cos ( 176 ° 3 9 - θ ) ] N 3 , W = [ 0.215 cos ( 3 ° 2 1 + θ ) - 0.298 cos ( 86 ° 3 9 - θ ) ] ( N 1 + N 2 ) + [ - 0.035 cos ( 3 ° 2 1 + θ ) + 0.597 cos ( 86 ° 3 9 - θ ) ] N 3 .

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