Abstract

A five-aperture shearing and two-Fourier filtering technique to measure simultaneously pure curvature and twist distribution fields of a deformed object is proposed. In this method the slope fringes that are contained in the patterns of curvature and twist fringes can be completely eliminated. Thus patterns of pure curvature and twist fringes with a good contrast can be obtained. A theoretical analysis and experimental results are given.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Y. Hung, C. E. Taylor, “Speckle-shearing interferometric camera—a tool for measurement of derivatives of surface displacements,” in Developments in Laser Technology II, R. F. Wuerker, ed., Proc. SPIE41, 169–175 (1973).
    [CrossRef]
  2. Y. Y. Hung, “A speckle-shearing interferometer: A tool for measuring derivatives of surface displacements,” Opt. Commun. 11, 132–135 (1974).
    [CrossRef]
  3. Y. Y. Hung, I. M. Daniel, R. E. Rowlands, “A new speckle-shearing interferometer—a full-field strain gauge,” Appl. Opt. 14, 618–622 (1975).
    [CrossRef] [PubMed]
  4. Y. Y. Hung, C. Y. Liang, “Image-shearing camera for direct measurement of surface strain,” Appl. Opt. 18, 1046–1051 (1979).
    [CrossRef] [PubMed]
  5. D. K. Sharma, R. S. Sirohi, M. P. Kothiyal, “Simultaneous measurement of slope and curvature with a three-aperture speckle shearing interferometer,” Appl. Opt. 23, 1542–1546 (1984).
    [CrossRef] [PubMed]
  6. R. K. Mohanty, C. Jonathan, R. S. Sirohi, “Speckle and speckle-shearing interferometers combined for the simultaneous determination of out-of-plane displacement and slope,” Appl. Opt. 24, 3106–3109 (1985).
    [CrossRef]
  7. D. K. Sharma, R. S. Sirohi, M. P. Kothiyal, “Multiaperture speckle shearing arrangements for stress analysis,” Opt. Commun 49, 313–317 (1984).
    [CrossRef]
  8. Y. Y. Hung, “Displacement and strain measurement,” in Speckle Metrology, R. K. Erf, ed. (Academic, New York, 1978), pp. 51–71.
    [CrossRef]
  9. P. K. Rastogi, “Techniques of displacement and deformation measurements in speckle metrology,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), pp. 41–98.
  10. R. S. Sirohi, “Speckle methods in experimental mechanics,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), pp. 99–155.
  11. C. J. Tay, S. L. Toh, H. M. Shang, Q. Y. Lin, “Direct determination of second-order derivatives in plate bending using multiple-exposure shearography,” Opt. Laser Technol. 26, 91–98 (1994).
    [CrossRef]
  12. H. Reismann, Elastic Plates: Theory and Application (Wiley, New York, 1988), pp. 121–123.

1994 (1)

C. J. Tay, S. L. Toh, H. M. Shang, Q. Y. Lin, “Direct determination of second-order derivatives in plate bending using multiple-exposure shearography,” Opt. Laser Technol. 26, 91–98 (1994).
[CrossRef]

1985 (1)

1984 (2)

D. K. Sharma, R. S. Sirohi, M. P. Kothiyal, “Multiaperture speckle shearing arrangements for stress analysis,” Opt. Commun 49, 313–317 (1984).
[CrossRef]

D. K. Sharma, R. S. Sirohi, M. P. Kothiyal, “Simultaneous measurement of slope and curvature with a three-aperture speckle shearing interferometer,” Appl. Opt. 23, 1542–1546 (1984).
[CrossRef] [PubMed]

1979 (1)

1975 (1)

1974 (1)

Y. Y. Hung, “A speckle-shearing interferometer: A tool for measuring derivatives of surface displacements,” Opt. Commun. 11, 132–135 (1974).
[CrossRef]

Daniel, I. M.

Hung, Y. Y.

Y. Y. Hung, C. Y. Liang, “Image-shearing camera for direct measurement of surface strain,” Appl. Opt. 18, 1046–1051 (1979).
[CrossRef] [PubMed]

Y. Y. Hung, I. M. Daniel, R. E. Rowlands, “A new speckle-shearing interferometer—a full-field strain gauge,” Appl. Opt. 14, 618–622 (1975).
[CrossRef] [PubMed]

Y. Y. Hung, “A speckle-shearing interferometer: A tool for measuring derivatives of surface displacements,” Opt. Commun. 11, 132–135 (1974).
[CrossRef]

Y. Y. Hung, C. E. Taylor, “Speckle-shearing interferometric camera—a tool for measurement of derivatives of surface displacements,” in Developments in Laser Technology II, R. F. Wuerker, ed., Proc. SPIE41, 169–175 (1973).
[CrossRef]

Y. Y. Hung, “Displacement and strain measurement,” in Speckle Metrology, R. K. Erf, ed. (Academic, New York, 1978), pp. 51–71.
[CrossRef]

Jonathan, C.

Kothiyal, M. P.

D. K. Sharma, R. S. Sirohi, M. P. Kothiyal, “Simultaneous measurement of slope and curvature with a three-aperture speckle shearing interferometer,” Appl. Opt. 23, 1542–1546 (1984).
[CrossRef] [PubMed]

D. K. Sharma, R. S. Sirohi, M. P. Kothiyal, “Multiaperture speckle shearing arrangements for stress analysis,” Opt. Commun 49, 313–317 (1984).
[CrossRef]

Liang, C. Y.

Lin, Q. Y.

C. J. Tay, S. L. Toh, H. M. Shang, Q. Y. Lin, “Direct determination of second-order derivatives in plate bending using multiple-exposure shearography,” Opt. Laser Technol. 26, 91–98 (1994).
[CrossRef]

Mohanty, R. K.

Rastogi, P. K.

P. K. Rastogi, “Techniques of displacement and deformation measurements in speckle metrology,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), pp. 41–98.

Reismann, H.

H. Reismann, Elastic Plates: Theory and Application (Wiley, New York, 1988), pp. 121–123.

Rowlands, R. E.

Shang, H. M.

C. J. Tay, S. L. Toh, H. M. Shang, Q. Y. Lin, “Direct determination of second-order derivatives in plate bending using multiple-exposure shearography,” Opt. Laser Technol. 26, 91–98 (1994).
[CrossRef]

Sharma, D. K.

D. K. Sharma, R. S. Sirohi, M. P. Kothiyal, “Multiaperture speckle shearing arrangements for stress analysis,” Opt. Commun 49, 313–317 (1984).
[CrossRef]

D. K. Sharma, R. S. Sirohi, M. P. Kothiyal, “Simultaneous measurement of slope and curvature with a three-aperture speckle shearing interferometer,” Appl. Opt. 23, 1542–1546 (1984).
[CrossRef] [PubMed]

Sirohi, R. S.

R. K. Mohanty, C. Jonathan, R. S. Sirohi, “Speckle and speckle-shearing interferometers combined for the simultaneous determination of out-of-plane displacement and slope,” Appl. Opt. 24, 3106–3109 (1985).
[CrossRef]

D. K. Sharma, R. S. Sirohi, M. P. Kothiyal, “Multiaperture speckle shearing arrangements for stress analysis,” Opt. Commun 49, 313–317 (1984).
[CrossRef]

D. K. Sharma, R. S. Sirohi, M. P. Kothiyal, “Simultaneous measurement of slope and curvature with a three-aperture speckle shearing interferometer,” Appl. Opt. 23, 1542–1546 (1984).
[CrossRef] [PubMed]

R. S. Sirohi, “Speckle methods in experimental mechanics,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), pp. 99–155.

Tay, C. J.

C. J. Tay, S. L. Toh, H. M. Shang, Q. Y. Lin, “Direct determination of second-order derivatives in plate bending using multiple-exposure shearography,” Opt. Laser Technol. 26, 91–98 (1994).
[CrossRef]

Taylor, C. E.

Y. Y. Hung, C. E. Taylor, “Speckle-shearing interferometric camera—a tool for measurement of derivatives of surface displacements,” in Developments in Laser Technology II, R. F. Wuerker, ed., Proc. SPIE41, 169–175 (1973).
[CrossRef]

Toh, S. L.

C. J. Tay, S. L. Toh, H. M. Shang, Q. Y. Lin, “Direct determination of second-order derivatives in plate bending using multiple-exposure shearography,” Opt. Laser Technol. 26, 91–98 (1994).
[CrossRef]

Appl. Opt. (4)

Opt. Commun (1)

D. K. Sharma, R. S. Sirohi, M. P. Kothiyal, “Multiaperture speckle shearing arrangements for stress analysis,” Opt. Commun 49, 313–317 (1984).
[CrossRef]

Opt. Commun. (1)

Y. Y. Hung, “A speckle-shearing interferometer: A tool for measuring derivatives of surface displacements,” Opt. Commun. 11, 132–135 (1974).
[CrossRef]

Opt. Laser Technol. (1)

C. J. Tay, S. L. Toh, H. M. Shang, Q. Y. Lin, “Direct determination of second-order derivatives in plate bending using multiple-exposure shearography,” Opt. Laser Technol. 26, 91–98 (1994).
[CrossRef]

Other (5)

H. Reismann, Elastic Plates: Theory and Application (Wiley, New York, 1988), pp. 121–123.

Y. Y. Hung, C. E. Taylor, “Speckle-shearing interferometric camera—a tool for measurement of derivatives of surface displacements,” in Developments in Laser Technology II, R. F. Wuerker, ed., Proc. SPIE41, 169–175 (1973).
[CrossRef]

Y. Y. Hung, “Displacement and strain measurement,” in Speckle Metrology, R. K. Erf, ed. (Academic, New York, 1978), pp. 51–71.
[CrossRef]

P. K. Rastogi, “Techniques of displacement and deformation measurements in speckle metrology,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), pp. 41–98.

R. S. Sirohi, “Speckle methods in experimental mechanics,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), pp. 99–155.

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 (6)

Fig. 1
Fig. 1

Schematic of the recording system.

Fig. 2
Fig. 2

Schematic of the analysis system.

Fig. 3
Fig. 3

(a) Three-dimensional curvature distribution and its contour projection, (b) three-dimensional twist distribution and its contour projection.

Fig. 4
Fig. 4

(a) Two-dimensional distribution of curvature contours, (b) two-dimensional distribution of twist contours.

Fig. 5
Fig. 5

Distribution of diffraction halos.

Fig. 6
Fig. 6

Experimental results: (a) pure curvature contours, (b) pure twist contours.

Equations (34)

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

Δ=doμ-1α,
U1=a0 expiφ0+a1 expiφ1+βξ+a2 expiφ2+βη+a3 expiφ3-βη+a4 expiφ4-βξ,
I1=i=04 ai2+2a0a1 cosφ10+βξ+2a0a2 cosφ20+βη+2a0a3 cosφ03+βη+2a0a4 cosφ04+βξ+2a1a2 cosφ12+βξ-βη+2a1a3 cosφ13+βξ+βη+2a1a4 cosφ14+2βξ+2a2a3 cosφ23+2βη+2a2a4 cosφ24+βξ+βη+2a3a4 cosφ34+βξ-βη,
U2=a0 expiφ0+δ0+a1 expiφ1+δ1+βξ+a2 expiφ2+δ2+βη+a3 expiφ3+δ3-βη+a4 expiφ4+δ4-βξ,
δ0=K0-K·Lξ, η=K0-K·Lx, y,  δ1=K1-K·Lξ+Δ, η=K1-K·Lx+Δ/2, y+Δ/2,  δ2=K2-K·Lξ, η+Δ=K2-K·Lx-Δ/2, y+Δ/2,  δ3=K3-K·Lξ, η-Δ=K3-K·Lx+Δ/2, y-Δ/2,  δ4=K4-K·Lξ-Δ, η=K4-K·Lx-Δ/2, y-Δ/2,
I2=i=04 ai2+2a0a1 cosφ10+δ10+βξ+2a0a2 cosφ20+δ20+βη+2a0a3 cosφ03+δ03+βη+2a0a4 cosφ04+δ04+βξ+2a1a2 cosφ12+δ12+βξ-βη+2a1a3 cosφ13+δ13+βξ+βη+2a1a4 cosφ14+δ14+2βξ+2a2a3 cosφ23+δ3+2βη+2a2a4 cosφ24+δ24+βξ+βη+2a3a4 cosφ34+δ34+βξ-βη,
δ10=K1-K·Lξ+Δ/2, ηξ Δ+K1-K0·Lξ, η,  δ04=K4-K·Lξ-Δ/2, ηξ Δ+K0-K4·Lξ, η,  δ12=K1+K2-2K·Lx, y+Δ/2xΔ2+K1-K2·Lx, y+Δ/2,  δ34=K3+K4-2K·Lx, y-Δ/2xΔ2+K3-K4·Lx, y-Δ/2.
U1f curvature=a0a1 expiφ10+βξ+a0a4×expiφ04+βξ
I1f curvature=a02a12+a42+2a02a1a4 cosφ10-φ04.
I2f curvature=a02a12+a42+2a02a1a4×cosφ10-φ04+δ10-δ04.
It curvature=I1f curvature+I2f curvature=2a02a12+a42+2a02a1a4cosφ10-φ04+cosφ10-φ04+δ10-δ04.
Uf curvature=a02a1a4expiφ10-φ04+expiφ10-φ04+δ10-δ04,
If curvature=2a04a12a421+cosδ10-δ04.
δ10-δ04=K1+K4-2K2·2Lξ, ηξ2 Δ2+K1-K4·Lξ, ηξ Δ+K1+K4-2K0·Lξ, η.
Lξ, η=wξ, ηk;
δ10-δ04=K1+K4-2K2·k2wξ, ηξ2 Δ2+K1-K4·kwξ, ηξ Δ+K1+K4-2K0·kwξ, η.
Ki, k  1  i=0, 1, 4,
K1-K4·k0,  K1+K4-2K00;
δ10-δ04=K0-K·k2wξ, ηξ2 Δ2=2πλ1+cos θ2wξ, ηξ2 Δ2,
2wξ, ηξ2=nλ1+cos θΔ2  n=0, ±1, ±2, ,
I1f twist=a12a22+a32a42+2a1a2a3a4 cosφ12-φ34.
I2f twist=a12a22+a32a42+2a1a2a3a4 cosφ12-φ34+δ12-δ34.
It twist=I1f twist+I2f twist=2a12a22+a32a42+2a1a2a3a4cosφ12-φ34+cosφ12-φ34+δ12-δ34.
If twist=2a12a22a32a421+cosδ12-δ34.
δ12-δ34=K1+K2+K3+K4-4K·2Lx, yxyΔ22+K1+K2-K3-K4·Lx, yxΔ2+K1-K2+K3-K4·Lx, yyΔ2+K1-K2-K3+K4·Lx, y.
δ12-δ34=K1+K2+K3+K4-4K·k2wx, yxyΔ2+K1+K2-K3-K4·kwx, yxΔ2+K1-K2+K3-K4·kwx, yyΔ2+K1-K2-K3+K4·kwx, y.
Ki, k  1  i=1, 2, 3, 4,
K1-K4·k0,  K2-K3·k0,  K1+K4-K2-K30,  K1+K2+K3+K4-4K00;
δ12-δ34=4K0-4K·k2wx, yxyΔ22=4πλ1+cos θΔ22wx, yxy,
2wx, yxy=nλ21+cos θΔ2  n=0, ±1, ±2, ,
wx, y=wmax1-x2+y2r2+x2+y2r2 ln x2+y2r2,
2wx, yx2=2wmaxr22x2x2+y2+lnx2+y2r2, x2+y2r,  2wx, yxy=4wmaxr2xyx2+y2, x2+y2r.
2wmaxr22x2x2+y2+lnx2+y2r2=nλ1+cos θΔ2,  4wmaxr2xyx2+y2=nλ21+cos θΔ2x2+y2r, n=0, ±1, ±2, .
2x2x2+y2+lnx2+y2r2=1.7n,  xyx2+y2=0.43nx2+y2r, n=0, ±1, ±2, .

Metrics