Abstract

A system is described which uses a diode array TV camera to view the real-time fringes and digital electronics to measure and store the irradiance levels at a 100 × 100 array of points. A microcomputer calculates the phase at each point from the irradiance values obtained from three successive scans of the array made with the phase of the reference beam shifted in steps of 120° by means of a mirror mounted on a piezoelectric translator. The optical system permits four holograms to be recorded in quick succession, using a photothermoplastic camera, with the object illuminated from four different directions. Phase data from these holograms are processed in a microcomputer to determine the components of the vector displacement at each of these points; these figures can then be transferred to a fast computer for further processing to evaluate the stress distribution.

© 1983 Optical Society of America

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  1. E. B. Aleksandrov, A. M. Bonch-Bruevich, Sov. Phys. Tech. Phys. 12, 258 (1967).
  2. A. E. Ennos, J. Phys. E 1, 731 (1968).
    [CrossRef]
  3. J. E. Sollid, Appl. Opt. 8, 1587 (1969).
    [CrossRef] [PubMed]
  4. K. Shibayama, H. Uchiyama, Appl. Opt. 10, 2150 (1971).
    [CrossRef] [PubMed]
  5. Y. Y. Hung, C. P. Hu, D. R. Henley, C. E. Taylor, Opt. Commun. 8, 48 (1973).
    [CrossRef]
  6. M. Schlüter, Opt. Laser Technol. 12, 93 (1980).
    [CrossRef]
  7. T. M. Kreis, H. Kreitlow, in Digest of Topical Meeting on Holographic Interferometry and Speckle Metrology (Optical Society of America, Washington, D.C., 1980), paper TuB2-1.
  8. S. Nakadate, N. Magome, T. Honda, J. Tsujiuchi, Opt. Eng. 20, 246 (1981).
    [CrossRef]
  9. R. Dändliker, B. Ineichen, F. M. Mottier, Opt. Commun. 9, 412 (1973).
    [CrossRef]
  10. R. Dändliker, Prog. Opt. 17, 1 (1980).
    [CrossRef]
  11. J. L. Goldberg, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 253 (1975).
    [CrossRef]
  12. P. Hariharan, B. F. Oreb, N. Brown, Opt. Commun. 41, 393 (1982).
    [CrossRef]
  13. B. F. Oreb, N. Brown, P. Hariharan, Rev. Sci. Instrum. 53, 697 (1982).
    [CrossRef]
  14. P. Carré, Metrologia 2, 13 (1966).
    [CrossRef]
  15. L. M. Frantz, A. A. Sawchuk, W. von der Ohe, Appl. Opt. 18, 3301 (1979).
    [CrossRef] [PubMed]
  16. R. Dändliker, R. Thalmann, J. F. Willemin, Opt. Commun. 42, 301 (1982).
    [CrossRef]
  17. N. Brown, B. F. Oreb, P. Hariharan, J. Phys. E 15, 703 (1982).
    [CrossRef]

1982 (4)

P. Hariharan, B. F. Oreb, N. Brown, Opt. Commun. 41, 393 (1982).
[CrossRef]

B. F. Oreb, N. Brown, P. Hariharan, Rev. Sci. Instrum. 53, 697 (1982).
[CrossRef]

R. Dändliker, R. Thalmann, J. F. Willemin, Opt. Commun. 42, 301 (1982).
[CrossRef]

N. Brown, B. F. Oreb, P. Hariharan, J. Phys. E 15, 703 (1982).
[CrossRef]

1981 (1)

S. Nakadate, N. Magome, T. Honda, J. Tsujiuchi, Opt. Eng. 20, 246 (1981).
[CrossRef]

1980 (2)

M. Schlüter, Opt. Laser Technol. 12, 93 (1980).
[CrossRef]

R. Dändliker, Prog. Opt. 17, 1 (1980).
[CrossRef]

1979 (1)

1975 (1)

J. L. Goldberg, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 253 (1975).
[CrossRef]

1973 (2)

Y. Y. Hung, C. P. Hu, D. R. Henley, C. E. Taylor, Opt. Commun. 8, 48 (1973).
[CrossRef]

R. Dändliker, B. Ineichen, F. M. Mottier, Opt. Commun. 9, 412 (1973).
[CrossRef]

1971 (1)

1969 (1)

1968 (1)

A. E. Ennos, J. Phys. E 1, 731 (1968).
[CrossRef]

1967 (1)

E. B. Aleksandrov, A. M. Bonch-Bruevich, Sov. Phys. Tech. Phys. 12, 258 (1967).

1966 (1)

P. Carré, Metrologia 2, 13 (1966).
[CrossRef]

Aleksandrov, E. B.

E. B. Aleksandrov, A. M. Bonch-Bruevich, Sov. Phys. Tech. Phys. 12, 258 (1967).

Bonch-Bruevich, A. M.

E. B. Aleksandrov, A. M. Bonch-Bruevich, Sov. Phys. Tech. Phys. 12, 258 (1967).

Brown, N.

P. Hariharan, B. F. Oreb, N. Brown, Opt. Commun. 41, 393 (1982).
[CrossRef]

N. Brown, B. F. Oreb, P. Hariharan, J. Phys. E 15, 703 (1982).
[CrossRef]

B. F. Oreb, N. Brown, P. Hariharan, Rev. Sci. Instrum. 53, 697 (1982).
[CrossRef]

Carré, P.

P. Carré, Metrologia 2, 13 (1966).
[CrossRef]

Dändliker, R.

R. Dändliker, R. Thalmann, J. F. Willemin, Opt. Commun. 42, 301 (1982).
[CrossRef]

R. Dändliker, Prog. Opt. 17, 1 (1980).
[CrossRef]

R. Dändliker, B. Ineichen, F. M. Mottier, Opt. Commun. 9, 412 (1973).
[CrossRef]

Ennos, A. E.

A. E. Ennos, J. Phys. E 1, 731 (1968).
[CrossRef]

Frantz, L. M.

Goldberg, J. L.

J. L. Goldberg, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 253 (1975).
[CrossRef]

Hariharan, P.

B. F. Oreb, N. Brown, P. Hariharan, Rev. Sci. Instrum. 53, 697 (1982).
[CrossRef]

N. Brown, B. F. Oreb, P. Hariharan, J. Phys. E 15, 703 (1982).
[CrossRef]

P. Hariharan, B. F. Oreb, N. Brown, Opt. Commun. 41, 393 (1982).
[CrossRef]

Henley, D. R.

Y. Y. Hung, C. P. Hu, D. R. Henley, C. E. Taylor, Opt. Commun. 8, 48 (1973).
[CrossRef]

Honda, T.

S. Nakadate, N. Magome, T. Honda, J. Tsujiuchi, Opt. Eng. 20, 246 (1981).
[CrossRef]

Hu, C. P.

Y. Y. Hung, C. P. Hu, D. R. Henley, C. E. Taylor, Opt. Commun. 8, 48 (1973).
[CrossRef]

Hung, Y. Y.

Y. Y. Hung, C. P. Hu, D. R. Henley, C. E. Taylor, Opt. Commun. 8, 48 (1973).
[CrossRef]

Ineichen, B.

R. Dändliker, B. Ineichen, F. M. Mottier, Opt. Commun. 9, 412 (1973).
[CrossRef]

Kreis, T. M.

T. M. Kreis, H. Kreitlow, in Digest of Topical Meeting on Holographic Interferometry and Speckle Metrology (Optical Society of America, Washington, D.C., 1980), paper TuB2-1.

Kreitlow, H.

T. M. Kreis, H. Kreitlow, in Digest of Topical Meeting on Holographic Interferometry and Speckle Metrology (Optical Society of America, Washington, D.C., 1980), paper TuB2-1.

Magome, N.

S. Nakadate, N. Magome, T. Honda, J. Tsujiuchi, Opt. Eng. 20, 246 (1981).
[CrossRef]

Mottier, F. M.

R. Dändliker, B. Ineichen, F. M. Mottier, Opt. Commun. 9, 412 (1973).
[CrossRef]

Nakadate, S.

S. Nakadate, N. Magome, T. Honda, J. Tsujiuchi, Opt. Eng. 20, 246 (1981).
[CrossRef]

Oreb, B. F.

P. Hariharan, B. F. Oreb, N. Brown, Opt. Commun. 41, 393 (1982).
[CrossRef]

N. Brown, B. F. Oreb, P. Hariharan, J. Phys. E 15, 703 (1982).
[CrossRef]

B. F. Oreb, N. Brown, P. Hariharan, Rev. Sci. Instrum. 53, 697 (1982).
[CrossRef]

Sawchuk, A. A.

Schlüter, M.

M. Schlüter, Opt. Laser Technol. 12, 93 (1980).
[CrossRef]

Shibayama, K.

Sollid, J. E.

Taylor, C. E.

Y. Y. Hung, C. P. Hu, D. R. Henley, C. E. Taylor, Opt. Commun. 8, 48 (1973).
[CrossRef]

Thalmann, R.

R. Dändliker, R. Thalmann, J. F. Willemin, Opt. Commun. 42, 301 (1982).
[CrossRef]

Tsujiuchi, J.

S. Nakadate, N. Magome, T. Honda, J. Tsujiuchi, Opt. Eng. 20, 246 (1981).
[CrossRef]

Uchiyama, H.

von der Ohe, W.

Willemin, J. F.

R. Dändliker, R. Thalmann, J. F. Willemin, Opt. Commun. 42, 301 (1982).
[CrossRef]

Appl. Opt. (3)

J. Phys. E (2)

N. Brown, B. F. Oreb, P. Hariharan, J. Phys. E 15, 703 (1982).
[CrossRef]

A. E. Ennos, J. Phys. E 1, 731 (1968).
[CrossRef]

Jpn. J. Appl. Phys. (1)

J. L. Goldberg, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 253 (1975).
[CrossRef]

Metrologia (1)

P. Carré, Metrologia 2, 13 (1966).
[CrossRef]

Opt. Commun. (4)

P. Hariharan, B. F. Oreb, N. Brown, Opt. Commun. 41, 393 (1982).
[CrossRef]

R. Dändliker, R. Thalmann, J. F. Willemin, Opt. Commun. 42, 301 (1982).
[CrossRef]

R. Dändliker, B. Ineichen, F. M. Mottier, Opt. Commun. 9, 412 (1973).
[CrossRef]

Y. Y. Hung, C. P. Hu, D. R. Henley, C. E. Taylor, Opt. Commun. 8, 48 (1973).
[CrossRef]

Opt. Eng. (1)

S. Nakadate, N. Magome, T. Honda, J. Tsujiuchi, Opt. Eng. 20, 246 (1981).
[CrossRef]

Opt. Laser Technol. (1)

M. Schlüter, Opt. Laser Technol. 12, 93 (1980).
[CrossRef]

Prog. Opt. (1)

R. Dändliker, Prog. Opt. 17, 1 (1980).
[CrossRef]

Rev. Sci. Instrum. (1)

B. F. Oreb, N. Brown, P. Hariharan, Rev. Sci. Instrum. 53, 697 (1982).
[CrossRef]

Sov. Phys. Tech. Phys. (1)

E. B. Aleksandrov, A. M. Bonch-Bruevich, Sov. Phys. Tech. Phys. 12, 258 (1967).

Other (1)

T. M. Kreis, H. Kreitlow, in Digest of Topical Meeting on Holographic Interferometry and Speckle Metrology (Optical Society of America, Washington, D.C., 1980), paper TuB2-1.

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Figures (11)

Fig. 1
Fig. 1

Holographic setup.

Fig. 2
Fig. 2

Schematic of the optical system.

Fig. 3
Fig. 3

Sliding mask used to record two holograms on the same plate.

Fig. 4
Fig. 4

Schematic of the system used for measurements of the phase.

Fig. 5
Fig. 5

Illumination and viewing geometry in the vertical plane in computing the phase.

Fig. 6
Fig. 6

Real-time fringes obtained with a cantilever.

Fig. 7
Fig. 7

Monitor display of a phase map showing isophase contours as well as a phase profile, on an expanded scale, along the horizontal line AA.

Fig. 8
Fig. 8

Measurements of phase along a vertical line down the center of the cantilever: (a) raw phase data; (b) adjusted and scaled phase profile.

Fig. 9
Fig. 9

Monitor display of the vector components Lx, Ly, and Lz of the displacements at points along a vertical line down the center of the cantilever. For legibility, the two displacement profiles derived from the beams in the horizontal plane have been offset.

Fig. 10
Fig. 10

Test object used to study the effects of phase ambiguities.

Fig. 11
Fig. 11

Three-dimensional display of the out-of-plane displacement (Lz) of the test object shown in Fig. 10.

Equations (15)

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ϕ = ( 2 π / λ ) ( k ˆ 2 k ˆ 1 ) · L = K · L ,
V 1 = S [ I R + I O + 2 ( I R I O ) 1 / 2 cos ϕ ] ,
V 2 = S [ I R + I O ( I R I O ) 1 / 2 ( cos ϕ + 3 1 / 2 sin ϕ ) ] ,
V 3 = S [ I R + I O ( I R I O ) 1 / 2 ( cos ϕ 3 1 / 2 sin ϕ ) ] ,
3 1 / 2 tan ϕ = ( V 3 V 2 ) / ( 2 V 1 V 2 V 3 ) .
ϕ 1 = K 1 · L ,
ϕ 2 = K 2 · L ,
ϕ 3 = K 3 · L ,
ϕ 4 = K 4 · L .
ϕ 1 = ( 2 π / λ ) { L z cos [ ( θ V + Δ θ + Δ ψ ) / 2 ] + L y sin [ ( θ V + Δ θ + Δ ψ ) / 2 ] } ,
ϕ 2 = ( 2 π / λ ) { L z cos [ ( θ V Δ θ Δ ψ ) / 2 ] + L y sin [ ( θ V Δ θ Δ ψ ) / 2 ] } .
L y = ( ϕ 1 ϕ 2 ) / 2 sin ( θ V / 2 ) [ ( ϕ 1 + ϕ 2 ) / 2 cos ( θ V / 2 ) ] ( Δ θ + Δ ψ ) / 2 ,
L z = ( ϕ 1 + ϕ 2 ) / 2 cos ( θ V / 2 ) [ ( ϕ 1 ϕ 2 ) / 2 cos ( θ V / 2 ) ] ( Δ θ + Δ ψ ) / 2 .
L x = ( ϕ 3 ϕ 4 ) / 2 sin ( θ H / 2 ) [ ( ϕ 3 + ϕ 4 ) / 2 cos ( θ H / 2 ) ] ( Δ θ + Δ ψ ) / 2 ,
L z = ( ϕ 3 + ϕ 4 ) / 2 cos ( θ H / 2 ) [ ( ϕ 3 ϕ 4 ) / 2 sin ( θ H / 2 ) ] ( Δ θ + Δ ψ ) / 2 ,

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