Abstract

A technique for separating the in-plane and out-of-plane motions of a tested object in hologram interferometry is described. In this technique, the object is illuminated with two symmetrically oriented beams, and an image plane hologram is recorded in photoconductor–thermoplastic devices which can be developed in situ and in virtually real time. Then the hologram is read out with the object waves only, thereby reconstructing the reference beam. If the object is moved or deformed during readout, fringes denoting equal in-plane motion appear as long as the motion is less than the speckle size. The exact arrangement is presented along with experimental results, which are compared with conventional holographic interferometry results.

© 1982 Optical Society of America

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References

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  1. J. D. Briers, Opt. Quantum Electron. 8, 469 (1976).
    [CrossRef]
  2. M. Schluter, A. Nowatzyk, Opt. Acta 27, 799 (1980).
    [CrossRef]
  3. K. A. Stetson, Opt. Eng. 14, 482 (1975).
    [CrossRef]
  4. R. K. Erf, Ed., Speckle Metrology (Academic, New York, 1978).
  5. R. Dandliker, Opt. Lasers Eng. 1, 3 (1980).
    [CrossRef]
  6. Ref. 4, Chap. 6.
  7. S. Nakadate, T. Yatagai, H. Saito, Appl. Opt. 19, 1879 (1980).
    [CrossRef] [PubMed]
  8. A. A. Friesem, Y. Katzir, Z. Rav-Noy, B. Sharon, Opt. Eng. 19, 659 (1980).
    [CrossRef]

1980 (4)

M. Schluter, A. Nowatzyk, Opt. Acta 27, 799 (1980).
[CrossRef]

R. Dandliker, Opt. Lasers Eng. 1, 3 (1980).
[CrossRef]

A. A. Friesem, Y. Katzir, Z. Rav-Noy, B. Sharon, Opt. Eng. 19, 659 (1980).
[CrossRef]

S. Nakadate, T. Yatagai, H. Saito, Appl. Opt. 19, 1879 (1980).
[CrossRef] [PubMed]

1976 (1)

J. D. Briers, Opt. Quantum Electron. 8, 469 (1976).
[CrossRef]

1975 (1)

K. A. Stetson, Opt. Eng. 14, 482 (1975).
[CrossRef]

Briers, J. D.

J. D. Briers, Opt. Quantum Electron. 8, 469 (1976).
[CrossRef]

Dandliker, R.

R. Dandliker, Opt. Lasers Eng. 1, 3 (1980).
[CrossRef]

Friesem, A. A.

A. A. Friesem, Y. Katzir, Z. Rav-Noy, B. Sharon, Opt. Eng. 19, 659 (1980).
[CrossRef]

Katzir, Y.

A. A. Friesem, Y. Katzir, Z. Rav-Noy, B. Sharon, Opt. Eng. 19, 659 (1980).
[CrossRef]

Nakadate, S.

Nowatzyk, A.

M. Schluter, A. Nowatzyk, Opt. Acta 27, 799 (1980).
[CrossRef]

Rav-Noy, Z.

A. A. Friesem, Y. Katzir, Z. Rav-Noy, B. Sharon, Opt. Eng. 19, 659 (1980).
[CrossRef]

Saito, H.

Schluter, M.

M. Schluter, A. Nowatzyk, Opt. Acta 27, 799 (1980).
[CrossRef]

Sharon, B.

A. A. Friesem, Y. Katzir, Z. Rav-Noy, B. Sharon, Opt. Eng. 19, 659 (1980).
[CrossRef]

Stetson, K. A.

K. A. Stetson, Opt. Eng. 14, 482 (1975).
[CrossRef]

Yatagai, T.

Appl. Opt. (1)

Opt. Acta (1)

M. Schluter, A. Nowatzyk, Opt. Acta 27, 799 (1980).
[CrossRef]

Opt. Eng. (2)

K. A. Stetson, Opt. Eng. 14, 482 (1975).
[CrossRef]

A. A. Friesem, Y. Katzir, Z. Rav-Noy, B. Sharon, Opt. Eng. 19, 659 (1980).
[CrossRef]

Opt. Lasers Eng. (1)

R. Dandliker, Opt. Lasers Eng. 1, 3 (1980).
[CrossRef]

Opt. Quantum Electron. (1)

J. D. Briers, Opt. Quantum Electron. 8, 469 (1976).
[CrossRef]

Other (2)

Ref. 4, Chap. 6.

R. K. Erf, Ed., Speckle Metrology (Academic, New York, 1978).

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Figures (4)

Fig. 1
Fig. 1

Reconstructed reference wave holographic interferometry: (a) recording, using a photoconductor–thermoplastic device; (b) reconstruction, using a grating to compensate for offset angle.

Fig. 2
Fig. 2

Rotation of the object around an axis normal to the surface at its center (z axis in Fig. 1). Observations of the reconstructed reference wave at four different angles of rotation, all taken through the same hologram. The fringes correspond to equal in-plane displacement in the horizontal x direction.

Fig. 3
Fig. 3

Combination of out-of-plane and in-plane motions. First, a tilt forward around x axis: (a) conventional holographic observation; (b) reconstructed reference. Then, clockwise rotation around z axis: (c) conventional holographic observation; (d) reconstructed reference.

Fig. 4
Fig. 4

Combination of in-plane and out-of-plane motions. First, a clockwise rotation around z axis: (a) reconstructed reference; (b) conventional observation. Then, a tilt forward around x axis; (c) conventional observation with left object beam and (d) right object beam.

Equations (11)

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I = R + O 1 + O 2 2 = R 2 + O 1 + O 2 2 + ( O 1 + O 2 ) R * + ( O 1 * + O 2 * ) R .
C = ( O 1 + O 2 ) I = ( R 2 + O 1 + O 2 2 ) ( O 1 + O 2 ) + ( O 1 + O 2 ) 2 R * + O 1 + O 2 2 R .
R c = O 1 + O 2 2 R = ( O 1 2 + O 2 2 ) R + ( O 1 O 2 * + O 1 * O 2 ) R .
R c = ( O 1 2 + O 2 2 ) R ,
O 1 = O 1 exp [ i ( k 1 · d - k 0 · d ) ] = O 1 exp { i 2 π / λ [ d x sin θ - d z ( 1 + cos θ ) ] } ,
O 2 = O 2 exp [ i ( k 2 · d - k 0 · d ) ] = O 2 exp { i 2 π / λ [ - d x sin θ - d z ( 1 + cos θ ) ] } ,
R c = ( O 1 * O 1 + O 2 * O 2 ) R = F · R ,
F = O 1 * O 1 + O 2 * O 2 = O 1 2 exp { i 2 π / λ [ d x sin θ - d z ( 1 + cos θ ) ] } + O 2 2 exp { i 2 π / λ [ - d x sin θ - d z ( 1 + cos θ ) ] } .
R c 2 = 2 O 4 R 2 { 1 + cos [ ( 4 π d x sin θ ) / λ ] } .
M = λ f # m λ / ( 2 sin θ ) = ( 2 / m ) f # sin θ ,
d x = β y ,

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