Abstract

A method for measurement of continuous displacements that uses phase-shifting speckle interferometry is presented. The initial random phase of the speckle pattern is evaluated by phase shifting before deformation. The changing phase thereafter is evaluated from only one image at a time by a least-squares algorithm. The technique can be used for measuring transients and other dynamic events, heat expansion as well as other phenomena, for which it is difficult to accomplish phase shifting during deformation. Theory along with computer simulations and experimental results are described.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, 1989).
    [CrossRef]
  2. K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24, 3053–3058 (1985).
    [CrossRef] [PubMed]
  3. M. Adachi, Y. Ueyama, K. Inabe, “Automatic deformation analysis in electronic speckle pattern interferometry using one speckle interferogram of deformed object,” Opt. Rev. 4, 429–432 (1997).
    [CrossRef]
  4. G. Pedrini, H. J. Tiziani, “Double-pulse electronic speckle interferometry for vibration analysis,” Appl. Opt. 33, 7857–7863 (1994).
    [CrossRef] [PubMed]
  5. H. O. Saldner, N.-E. Molin, K. A. Stetson, “Fourier-transform evaluation of phase data in spatially phase-biased TV holograms,” Appl. Opt. 35, 332–336 (1996).
    [CrossRef] [PubMed]
  6. S. Schedin, P. Gren, “Phase evaluation and speckle averaging in pulsed television holography,” Appl. Opt. 36, 3941–3947 (1997).
    [CrossRef] [PubMed]
  7. A. Davila, G. H. Kaufmann, C. Pérez-López, “Transient deformation analysis by a carrier method of pulsed electronic speckle-shearing pattern interferometry,” Appl. Opt. 37, 4116–4122 (1992).
    [CrossRef]
  8. G. Gülker, O. Haack, K. D. Hinsch, C. Hölscher, J. Kuls, W. Platen, “Two-wavelength electronic speckle-pattern interferometry for the analysis of discontinuous deformation fields,” Appl. Opt. 31, 4519–4521 (1992).
    [CrossRef] [PubMed]
  9. J. Kato, I. Yamaguchi, Q. Ping, “Automatic deformation analysis by a TV speckle interferometer using a laser diode,” Appl. Opt. 32, 77–83 (1993).
    [CrossRef] [PubMed]
  10. K. A. Stetson, “Theory and applications of electronic holography,” in Proceedings of the International Conference on Hologram Interferometry and Speckle Metrology, K. A. Stetson, R. J. Pryputniewicz, eds. (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 294–300.
  11. R. S. Sirohi, M. A. P. Kothiyal, Optical Components, Systems, and Measurement Techniques (Marcel Dekker, New York, 1991), p. 235.
  12. E. Vikhagen, “Nondestructive testing by use of TV holography and deformation phase gradient calculation,” Appl. Opt. 29, 137–144 (1990).
    [CrossRef] [PubMed]
  13. T. E. Carlsson, A. Wei, “Three-dimensional shape measurement using light-in-flight speckle interferometry,” in Fringe ’97—3rd International Work-Shop on Automatic Processing of Fringe Patterns, Bremen, W. Jüptner, W. Osten, eds. (Akademie Verlag, Berlin, 1997), pp. 164–170.
  14. A. Wei, T. E. Carlsson, “Three-dimensional shape measurement using light-in-flight speckle interferometry,” Opt. Eng. 38, 1366–1370 (1999).
    [CrossRef]
  15. G. A. Korn, T. M. Korn, Mathematical Handbook for Scientists and Engineers, 2nd ed. (McGraw-Hill, New York, 1968), p. 616.
  16. A. Wei, T. E. Carlsson, “Measurement of deformation of solder joint with speckle interferometry,” in Optical Diagnostics for Fluids/Heat/Combustion and Photomechanics for Solids, S. S. Cha, P. J. Bryanston-Cross, C. R. Mercer, eds., Proc. SPIE3783, 382–388 (1999).
    [CrossRef]
  17. C. S. Vikram, M. J. Pechersky, “Effect of low-frequency vibration on speckle interferometry fringes,” Opt. Eng. 37, 1602–1607 (1998).
    [CrossRef]

1999 (1)

A. Wei, T. E. Carlsson, “Three-dimensional shape measurement using light-in-flight speckle interferometry,” Opt. Eng. 38, 1366–1370 (1999).
[CrossRef]

1998 (1)

C. S. Vikram, M. J. Pechersky, “Effect of low-frequency vibration on speckle interferometry fringes,” Opt. Eng. 37, 1602–1607 (1998).
[CrossRef]

1997 (2)

M. Adachi, Y. Ueyama, K. Inabe, “Automatic deformation analysis in electronic speckle pattern interferometry using one speckle interferogram of deformed object,” Opt. Rev. 4, 429–432 (1997).
[CrossRef]

S. Schedin, P. Gren, “Phase evaluation and speckle averaging in pulsed television holography,” Appl. Opt. 36, 3941–3947 (1997).
[CrossRef] [PubMed]

1996 (1)

1994 (1)

1993 (1)

1992 (2)

1990 (1)

1985 (1)

Adachi, M.

M. Adachi, Y. Ueyama, K. Inabe, “Automatic deformation analysis in electronic speckle pattern interferometry using one speckle interferogram of deformed object,” Opt. Rev. 4, 429–432 (1997).
[CrossRef]

Carlsson, T. E.

A. Wei, T. E. Carlsson, “Three-dimensional shape measurement using light-in-flight speckle interferometry,” Opt. Eng. 38, 1366–1370 (1999).
[CrossRef]

T. E. Carlsson, A. Wei, “Three-dimensional shape measurement using light-in-flight speckle interferometry,” in Fringe ’97—3rd International Work-Shop on Automatic Processing of Fringe Patterns, Bremen, W. Jüptner, W. Osten, eds. (Akademie Verlag, Berlin, 1997), pp. 164–170.

A. Wei, T. E. Carlsson, “Measurement of deformation of solder joint with speckle interferometry,” in Optical Diagnostics for Fluids/Heat/Combustion and Photomechanics for Solids, S. S. Cha, P. J. Bryanston-Cross, C. R. Mercer, eds., Proc. SPIE3783, 382–388 (1999).
[CrossRef]

Creath, K.

Davila, A.

Gren, P.

Gülker, G.

Haack, O.

Hinsch, K. D.

Hölscher, C.

Inabe, K.

M. Adachi, Y. Ueyama, K. Inabe, “Automatic deformation analysis in electronic speckle pattern interferometry using one speckle interferogram of deformed object,” Opt. Rev. 4, 429–432 (1997).
[CrossRef]

Jones, R.

R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, 1989).
[CrossRef]

Kato, J.

Kaufmann, G. H.

Korn, G. A.

G. A. Korn, T. M. Korn, Mathematical Handbook for Scientists and Engineers, 2nd ed. (McGraw-Hill, New York, 1968), p. 616.

Korn, T. M.

G. A. Korn, T. M. Korn, Mathematical Handbook for Scientists and Engineers, 2nd ed. (McGraw-Hill, New York, 1968), p. 616.

Kothiyal, M. A. P.

R. S. Sirohi, M. A. P. Kothiyal, Optical Components, Systems, and Measurement Techniques (Marcel Dekker, New York, 1991), p. 235.

Kuls, J.

Molin, N.-E.

Pechersky, M. J.

C. S. Vikram, M. J. Pechersky, “Effect of low-frequency vibration on speckle interferometry fringes,” Opt. Eng. 37, 1602–1607 (1998).
[CrossRef]

Pedrini, G.

Pérez-López, C.

Ping, Q.

Platen, W.

Saldner, H. O.

Schedin, S.

Sirohi, R. S.

R. S. Sirohi, M. A. P. Kothiyal, Optical Components, Systems, and Measurement Techniques (Marcel Dekker, New York, 1991), p. 235.

Stetson, K. A.

H. O. Saldner, N.-E. Molin, K. A. Stetson, “Fourier-transform evaluation of phase data in spatially phase-biased TV holograms,” Appl. Opt. 35, 332–336 (1996).
[CrossRef] [PubMed]

K. A. Stetson, “Theory and applications of electronic holography,” in Proceedings of the International Conference on Hologram Interferometry and Speckle Metrology, K. A. Stetson, R. J. Pryputniewicz, eds. (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 294–300.

Tiziani, H. J.

Ueyama, Y.

M. Adachi, Y. Ueyama, K. Inabe, “Automatic deformation analysis in electronic speckle pattern interferometry using one speckle interferogram of deformed object,” Opt. Rev. 4, 429–432 (1997).
[CrossRef]

Vikhagen, E.

Vikram, C. S.

C. S. Vikram, M. J. Pechersky, “Effect of low-frequency vibration on speckle interferometry fringes,” Opt. Eng. 37, 1602–1607 (1998).
[CrossRef]

Wei, A.

A. Wei, T. E. Carlsson, “Three-dimensional shape measurement using light-in-flight speckle interferometry,” Opt. Eng. 38, 1366–1370 (1999).
[CrossRef]

T. E. Carlsson, A. Wei, “Three-dimensional shape measurement using light-in-flight speckle interferometry,” in Fringe ’97—3rd International Work-Shop on Automatic Processing of Fringe Patterns, Bremen, W. Jüptner, W. Osten, eds. (Akademie Verlag, Berlin, 1997), pp. 164–170.

A. Wei, T. E. Carlsson, “Measurement of deformation of solder joint with speckle interferometry,” in Optical Diagnostics for Fluids/Heat/Combustion and Photomechanics for Solids, S. S. Cha, P. J. Bryanston-Cross, C. R. Mercer, eds., Proc. SPIE3783, 382–388 (1999).
[CrossRef]

Wykes, C.

R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, 1989).
[CrossRef]

Yamaguchi, I.

Appl. Opt. (8)

Opt. Eng. (2)

A. Wei, T. E. Carlsson, “Three-dimensional shape measurement using light-in-flight speckle interferometry,” Opt. Eng. 38, 1366–1370 (1999).
[CrossRef]

C. S. Vikram, M. J. Pechersky, “Effect of low-frequency vibration on speckle interferometry fringes,” Opt. Eng. 37, 1602–1607 (1998).
[CrossRef]

Opt. Rev. (1)

M. Adachi, Y. Ueyama, K. Inabe, “Automatic deformation analysis in electronic speckle pattern interferometry using one speckle interferogram of deformed object,” Opt. Rev. 4, 429–432 (1997).
[CrossRef]

Other (6)

T. E. Carlsson, A. Wei, “Three-dimensional shape measurement using light-in-flight speckle interferometry,” in Fringe ’97—3rd International Work-Shop on Automatic Processing of Fringe Patterns, Bremen, W. Jüptner, W. Osten, eds. (Akademie Verlag, Berlin, 1997), pp. 164–170.

R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, 1989).
[CrossRef]

G. A. Korn, T. M. Korn, Mathematical Handbook for Scientists and Engineers, 2nd ed. (McGraw-Hill, New York, 1968), p. 616.

A. Wei, T. E. Carlsson, “Measurement of deformation of solder joint with speckle interferometry,” in Optical Diagnostics for Fluids/Heat/Combustion and Photomechanics for Solids, S. S. Cha, P. J. Bryanston-Cross, C. R. Mercer, eds., Proc. SPIE3783, 382–388 (1999).
[CrossRef]

K. A. Stetson, “Theory and applications of electronic holography,” in Proceedings of the International Conference on Hologram Interferometry and Speckle Metrology, K. A. Stetson, R. J. Pryputniewicz, eds. (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 294–300.

R. S. Sirohi, M. A. P. Kothiyal, Optical Components, Systems, and Measurement Techniques (Marcel Dekker, New York, 1991), p. 235.

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

Measurement of out-of-plane displacement: PZT, piezoelectric transducer.

Fig. 2
Fig. 2

Test of the spread of mean phase measurement (σ〈Δϕ〉) by Monte Carlo simulation of computer-generated speckle patterns. Dashed curves, the theoretical values n = 5 × 5 (left) and n = 7 × 7 (right), both for a neighborhood spread, σΔϕ = π/5.

Fig. 3
Fig. 3

Computer simulation of the algorithm. Top, true displacement; second row, unwrapped speckle pattern; third row, median filtered phase. Bottom left, resultant continuous displacement for the center pixel; bottom right, progress of the standard deviation of the difference between true and evaluated displacements.

Fig. 4
Fig. 4

Computer-simulated specklegrams evaluated by the method described. The continuous deformation for one pixel is shown. Top left, true displacement; top right, simulated noisy interferogram; bottom left, evaluated phase; bottom right, unwrapped phase.

Fig. 5
Fig. 5

Measured solder joint.

Fig. 6
Fig. 6

Specklegrams owing to temperature deformation evaluated by the method described. Top left, correlated fringes; applied current, 0.3 A. Top right, correlated fringes; applied current, 0.5 A. Bottom left, evaluated phase map; applied current, 0.3 A. Bottom right, evaluated phase map; applied current, 0.5 A.

Fig. 7
Fig. 7

Evaluated phase during continuous deformation for one pixel. Wrapped and unwrapped phases are shown.

Equations (25)

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

Ix, y=I0x, y+γx, ycosϕ0x, y,
Idx, y, t=I0x, y, t+γx, y, tcosϕx, y, t=I0x, y, t+γx, y, tcosϕ0x, y+Δϕx, y, t,  Δϕx, y, t=2πλs¯·Δr¯x, y, t,
I1=I0+γ cos ϕ0,  I2=I0-γ sin ϕ0,  I3=I0-γ cos ϕ0,  I4=I0+γ sin ϕ0.
I1d=I0+γ cosϕ0+Δϕ,  I2d=I0-γ sinϕ0+Δϕ,  I3d=I0-γ cosϕ0+Δϕ,  I4d=I0+γ sinϕ0+Δϕ.
tan Δϕ=sinϕ0+Δϕ-ϕ0cosϕ0+Δϕ-ϕ0=cosϕ0sinϕ0+Δϕ-sinϕ0cosϕ0+Δϕcosϕ0cosϕ0+Δϕ+sinϕ0sinϕ0+Δϕ=C1-C2C3+C4,
C1=I1-I3I4d-I2d,  C2=I4-I2I1d-I3d,  C3=I4-I2I4d-I2d,  C4=I1-I3I1d-I3d.
I1=I0+γ cos ϕ0,  I2=I0-γ sin ϕ0,  I3=I0-γ cos ϕ0,  I4=I0+γ sin ϕ0.
Idt=I0t+γtcos ϕt=I0t+γtcos ϕ0 cos Δϕt-γtsin ϕ0 sin Δϕt,
I0=14i=14 Ii, γ=12(D12+D221/2, tan ϕ0=D1D2,
D1=I4-I2=2γ sin ϕ0,  D2=I1-I3=2γ cos ϕ0.
Imaxx, y, tI0x, y, t+γx, y, tcosδϕx, y, t,  Iminx, y, tI0x, y, t-γx, y, tcosδϕx, y, t.
It=Imaxt+Imint2I0t,  IΔt=Imaxt-Imint2γt.
cos ϕ=Idt-I0tγtIdt-ItIΔt.
cosϕx±i, y±j, t=cosϕ0x±i, y±j+Δϕx±i, y±j, tcosϕ0x±i, y±j×cosΔϕx, y, t-sinϕ0x±i, y±j×sinΔϕx, y, t,
u=Acs,
u=u-i,-ju0,0ui,j,  A=cosϕ0x-i, y-jsinϕ0x-i, y-jcosϕ0x, ysinϕ0x, ycosϕ0x+i, y+jsinϕ0x+i, y+j.
cs=AAT-1ATu,
tanΔϕ=- sc=cos ϕ0×sin ϕ0×cos ϕ×cos ϕ0-cos2 ϕ0×cos ϕ×sin ϕ0sin2 ϕ0×cos ϕ×cos ϕ0-cos ϕ0×sin ϕ0×cos ϕ×sin ϕ0.
ϕ0U-π, π  Ecos ϕ0×sin ϕ0=0, Ecos2 ϕ0=Esin2 ϕ0=1/2 Ecos ϕ0×sin ϕ0×cos ϕ×cos ϕ0-cos2 ϕ0×cos ϕ×sin ϕ0sin2 ϕ0×cos ϕ×cos ϕ0-cos ϕ0×sin ϕ0×cos ϕ×sin ϕ0Ecos ϕ0×sin ϕ0×Ecos ϕ×cos ϕ0-Ecos2 ϕ0×Ecos ϕ×sin ϕ0Esin2 ϕ0×Ecos ϕ×cos ϕ0-Ecos ϕ0×sin ϕ0×Ecos ϕ×sin ϕ0=0-Ecos ϕ×sin ϕ0Ecos ϕ×cos ϕ0-0=-EcosΔϕ×cos ϕ0×sin ϕ0-sin Δϕ×sin2ϕ0Ecos Δϕ×cos2 ϕ0-sin Δϕ×cos ϕ0×sin ϕ0=if Δϕconstant=Δϕ=sinΔϕ×Esin2 ϕ0-cosΔϕ×Ecos ϕ0×sin ϕ0cosΔϕ×Ecos2 ϕ0-sinΔϕ×Ecos ϕ0×sin ϕ0=sin Δϕcos Δϕ=tanΔϕ,
tanΔϕ=D1×D2×Idt-It×D2-D22×Idt-It×D1D12×Idt-It×D2-D1×D2×Idt-It×D1,
kv+1=sinΔϕv+1cosΔϕv-cosΔϕv+1sinΔϕv=sinΔϕv+1-Δϕv Δϕn=v=1narcsinkv.
arctan: σΔϕ12 cos2Δϕ3+4σΔϕ2n1+Δϕ21/2,  arctan2: σΔϕ12 cos2Δϕ23+4σΔϕ2n1+Δϕ21/2,
uI0=±It-I0t=±γtcos δϕt-1±γtδϕt22,
ϕx, y, t=t20+10 sin2π10 tcosx+y+ϕ0+nt, x, y,  ϕ0U-π, π,  nx, y, t=noise termN0, π6, x, y-5, 5,
dZ=λ2Δϕ2π.

Metrics