Abstract

An improved speckle-shearing interferometric method is presented that allows simultaneous determination of derivatives of surface displacements of a structure with respect to four different directions. The technique relaxes several limitations associated with conventional interferometry and thus is adaptable to nonlaboratory environments. The relevant theory is presented, and the method demonstrated by determining spatial derivatives of in-plane and out-of-plane displacements of statically loaded and vibrated structures.

© 1975 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. A. Leendertz, J. Phys. E 3, (1970).
    [Crossref]
  2. E. Archbold, J. M. Burch, A. E. Ennos, Optica Acta 17, 883 (1970).
    [Crossref]
  3. Y. Y. Hung, J. D. Hovanesian, Exptl. Mech. 12(10), 454 (1972).
    [Crossref]
  4. E. Archbold, A. E. Ennos, Optica Acta 19, 253 (1972).
    [Crossref]
  5. D. E. Duffy, Appl. Opt. 11(8), 1778 (1972).
    [Crossref] [PubMed]
  6. Y. Y. Hung, C. E. Taylor, Proc. 7th Southeastern Conf. Theoret. Appl. Mech. 8, 497 (1974).
  7. Y. Y. Hung, C. E. Taylor, Proc. Soc. Photo-Opt. Instrum. Eng. 17th Annual Tech. Mtg.August 27–29, 1973, San Diego, Calif., 41, 169 (1973).
  8. J. D. Hovanesian, Y. Y. Hung, Appl. Opt. 10(12), 2734 (1971).
    [Crossref] [PubMed]
  9. F. K. Ligtenberg, Proc. SESA, 12(2), 83 (1954).

1974 (1)

Y. Y. Hung, C. E. Taylor, Proc. 7th Southeastern Conf. Theoret. Appl. Mech. 8, 497 (1974).

1972 (3)

Y. Y. Hung, J. D. Hovanesian, Exptl. Mech. 12(10), 454 (1972).
[Crossref]

E. Archbold, A. E. Ennos, Optica Acta 19, 253 (1972).
[Crossref]

D. E. Duffy, Appl. Opt. 11(8), 1778 (1972).
[Crossref] [PubMed]

1971 (1)

1970 (2)

J. A. Leendertz, J. Phys. E 3, (1970).
[Crossref]

E. Archbold, J. M. Burch, A. E. Ennos, Optica Acta 17, 883 (1970).
[Crossref]

1954 (1)

F. K. Ligtenberg, Proc. SESA, 12(2), 83 (1954).

Archbold, E.

E. Archbold, A. E. Ennos, Optica Acta 19, 253 (1972).
[Crossref]

E. Archbold, J. M. Burch, A. E. Ennos, Optica Acta 17, 883 (1970).
[Crossref]

Burch, J. M.

E. Archbold, J. M. Burch, A. E. Ennos, Optica Acta 17, 883 (1970).
[Crossref]

Duffy, D. E.

Ennos, A. E.

E. Archbold, A. E. Ennos, Optica Acta 19, 253 (1972).
[Crossref]

E. Archbold, J. M. Burch, A. E. Ennos, Optica Acta 17, 883 (1970).
[Crossref]

Hovanesian, J. D.

Y. Y. Hung, J. D. Hovanesian, Exptl. Mech. 12(10), 454 (1972).
[Crossref]

J. D. Hovanesian, Y. Y. Hung, Appl. Opt. 10(12), 2734 (1971).
[Crossref] [PubMed]

Hung, Y. Y.

Y. Y. Hung, C. E. Taylor, Proc. 7th Southeastern Conf. Theoret. Appl. Mech. 8, 497 (1974).

Y. Y. Hung, J. D. Hovanesian, Exptl. Mech. 12(10), 454 (1972).
[Crossref]

J. D. Hovanesian, Y. Y. Hung, Appl. Opt. 10(12), 2734 (1971).
[Crossref] [PubMed]

Y. Y. Hung, C. E. Taylor, Proc. Soc. Photo-Opt. Instrum. Eng. 17th Annual Tech. Mtg.August 27–29, 1973, San Diego, Calif., 41, 169 (1973).

Leendertz, J. A.

J. A. Leendertz, J. Phys. E 3, (1970).
[Crossref]

Ligtenberg, F. K.

F. K. Ligtenberg, Proc. SESA, 12(2), 83 (1954).

Taylor, C. E.

Y. Y. Hung, C. E. Taylor, Proc. 7th Southeastern Conf. Theoret. Appl. Mech. 8, 497 (1974).

Y. Y. Hung, C. E. Taylor, Proc. Soc. Photo-Opt. Instrum. Eng. 17th Annual Tech. Mtg.August 27–29, 1973, San Diego, Calif., 41, 169 (1973).

Appl. Opt. (2)

Exptl. Mech. (1)

Y. Y. Hung, J. D. Hovanesian, Exptl. Mech. 12(10), 454 (1972).
[Crossref]

J. Phys. E (1)

J. A. Leendertz, J. Phys. E 3, (1970).
[Crossref]

Optica Acta (2)

E. Archbold, J. M. Burch, A. E. Ennos, Optica Acta 17, 883 (1970).
[Crossref]

E. Archbold, A. E. Ennos, Optica Acta 19, 253 (1972).
[Crossref]

Proc. 7th Southeastern Conf. Theoret. Appl. Mech. (1)

Y. Y. Hung, C. E. Taylor, Proc. 7th Southeastern Conf. Theoret. Appl. Mech. 8, 497 (1974).

Proc. SESA (1)

F. K. Ligtenberg, Proc. SESA, 12(2), 83 (1954).

Other (1)

Y. Y. Hung, C. E. Taylor, Proc. Soc. Photo-Opt. Instrum. Eng. 17th Annual Tech. Mtg.August 27–29, 1973, San Diego, Calif., 41, 169 (1973).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Schematic of speckle-shearing interferometer.

Fig. 2
Fig. 2

An enlarged view of a speckle-grid pattern.

Fig. 3
Fig. 3

The schematic of a Fourier processor.

Fig. 4
Fig. 4

Fourier spectra of a speckle-grid pattern.

Fig. 5
Fig. 5

A rectangular plate clamped along its boundaries is subjected to transverse central loading. Fringe patterns depict (a) (∂w)/(∂x), (b) (∂w)/(∂y), and (c) (∂w)/(∂x45°).

Fig. 6
Fig. 6

A ring is compressed diametrically. (a) Fringe pattern mainly due to ∂u/∂x, (b) fringe pattern mainly due to ∂u/∂y.

Fig. 7
Fig. 7

Time-integrated fringes depicting slope of amplitude of vibration of a rectangular plate oscillating in its foundamental mode.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

δ x = ( R / D i ) S ,
δ x = δ x / m ,
I 1 ( x , y ) = 2 A 2 { 1 + cos ( 2 π / λ ) × [ 2 β x + f 1 ( x , y ' ) f 3 ( x , y ) ] } ,
Δ x [ ( 1 + cos θ ) ( w / x ) + sin θ ( u / x ) ] δ x .
I 2 ( x , y ) = 2 A 2 { 1 + cos ( 2 π / λ ) × [ 2 β x + f 1 ( x , y ) f 3 ( x , y ) + Δ x ] } .
I ( x , y ) = I 1 ( x , y ) + I 2 ( x , y ) = 4 A 2 ( 1 + cos B · cos C ) ,
B = ( 2 π / λ ) [ 2 β x + f 1 ( x , y ) f 3 ( x , y ) + ( Δ x / 2 ) ] ,
C = ( 2 π / λ ) ( Δ x / 2 ) .
( 2 π / λ ) ( Δ x / 2 ) = ( N + 1 2 ) π ,
Δ y [ ( 1 + cos θ ) ( w / y ) + sin θ ( u / y ) ] δ y ,
Δ ξ = [ ( 1 + cos θ ) ( w / ξ ) + sin θ ( u / ξ ) ] δ ξ ,
Δ η = [ ( 1 + cos θ ) ( w / η ) + sin θ ( u / η ) ] δ η .
W ( x , y , t ) = A ( x , y ) cos ( ω t + φ ) ,
Δ x = { ( 1 + cos θ ) [ W ( x , y , t ) / x ] } δ x .
I i ( x , y ) = T [ 1 + cos ψ J 0 ( γ ) ] ,
ψ = ( 2 π / λ ) [ 2 β x + f 1 ( x , y ) f 3 ( x , y ) ] , γ = ( 2 π / λ ) ( 1 + cos θ ) [ A ( x , y ) / x ] δ x .

Metrics