Abstract

A set of innovative phase-shifting algorithms developed to facilitate metrology based on electronic speckle pattern interferometry (ESPI) are presented. The theory of a phase-shifting algorithm, called a (5,1) algorithm, that takes five phase-shifted intensity maps before a specimen is deformed and one intensity map after a specimen is deformed is presented first. Because a high-speed camera can be used to record the dynamic image of the specimen, this newly developed algorithm has the potential to retain the phase-shifting capability for ESPI in dynamic measurements. Also shown is an algorithm called a (1,5) algorithm that takes five phase-shifted intensity maps after the specimen is deformed. In addition, a direct-correlation algorithm was integrated with these newly developed (5,1) or (1,5) algorithms to form DC-(5,1) and DC-(1,5) algorithms, which are shown to improve significantly the quality of the phase maps. The theoretical and experimental aspects of these two newly developed techniques, which can extend ESPI to areas such as high-speed dynamic measurements, are examined in detail.

© 2002 Optical Society of America

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References

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  1. R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge University, Cambridge, UK, 1983).
  2. A. J. Moore, J. R. Tyrer, “Phase-stepped ESPI and moire interferometry for measuring the stress-intensity factor and J integral,” Exp. Mech. 35, 306–314 (1995).
    [CrossRef]
  3. J. N. Butters, J. A. Leendertz, “A double exposure technique for speckle pattern interferometry,” J. Phys. E 4, 277–279 (1971).
    [CrossRef]
  4. K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24, 3053–3058 (1985).
    [CrossRef] [PubMed]
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  12. H. Y. Chang, C. W. Chen, C. K. Lee, C. P. Hu, “The tapestry cellular automata phase unwrapping algorithm for nondestructive testing,” J. Opt. Lasers Eng. 30, 487–502 (1998).
    [CrossRef]
  13. C. W. Chen, H. Y. Chang, C. K. Lee, “An innovative phase shifting system for nondestructive testing,” J. Chin. Soc. Appl. Mech. 14, 31–39 (1998).
  14. Y. C. Chen, S. S. Lee, C. M. Lee, C. K. Lee, G. B. Yeh, “New methodology for measuring highly aberrated wave fronts induced by diffractive optical elements,” in Testing, Packaging, Reliability, and Applications of Semiconductor Lasers IV, M. Fallahi, J. Linden, S. Wang, eds., Proc. SPIE3626, 248–259 (1999).
    [CrossRef]
  15. S. Takahashi, “Multilayer piezoelectric ceramics actuators and their applications,” Jpn. J. Appl Phys. 24, 41–45 (1985).
  16. Tokin America Inc., “Multilayer piezoelectric actuator,” Insp. Rec. 912-46S-02039, displacement: 14.4 µm at 100 V dc for 17.981-mm length (1991).

1998 (2)

H. Y. Chang, C. W. Chen, C. K. Lee, C. P. Hu, “The tapestry cellular automata phase unwrapping algorithm for nondestructive testing,” J. Opt. Lasers Eng. 30, 487–502 (1998).
[CrossRef]

C. W. Chen, H. Y. Chang, C. K. Lee, “An innovative phase shifting system for nondestructive testing,” J. Chin. Soc. Appl. Mech. 14, 31–39 (1998).

1997 (1)

1995 (1)

A. J. Moore, J. R. Tyrer, “Phase-stepped ESPI and moire interferometry for measuring the stress-intensity factor and J integral,” Exp. Mech. 35, 306–314 (1995).
[CrossRef]

1994 (2)

1993 (1)

J. Pomarico, R. Arizaga, R. Towoba, H. Rabal, “Algorithm to compute spacing of digital speckle correlation fringes,” Optik (Stuttgart) 95, 125–127 (1993).

1988 (2)

1987 (1)

1985 (2)

K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24, 3053–3058 (1985).
[CrossRef] [PubMed]

S. Takahashi, “Multilayer piezoelectric ceramics actuators and their applications,” Jpn. J. Appl Phys. 24, 41–45 (1985).

1971 (1)

J. N. Butters, J. A. Leendertz, “A double exposure technique for speckle pattern interferometry,” J. Phys. E 4, 277–279 (1971).
[CrossRef]

Arizaga, R.

J. Pomarico, R. Arizaga, R. Towoba, H. Rabal, “Algorithm to compute spacing of digital speckle correlation fringes,” Optik (Stuttgart) 95, 125–127 (1993).

Butters, J. N.

J. N. Butters, J. A. Leendertz, “A double exposure technique for speckle pattern interferometry,” J. Phys. E 4, 277–279 (1971).
[CrossRef]

Chang, H. Y.

H. Y. Chang, C. W. Chen, C. K. Lee, C. P. Hu, “The tapestry cellular automata phase unwrapping algorithm for nondestructive testing,” J. Opt. Lasers Eng. 30, 487–502 (1998).
[CrossRef]

C. W. Chen, H. Y. Chang, C. K. Lee, “An innovative phase shifting system for nondestructive testing,” J. Chin. Soc. Appl. Mech. 14, 31–39 (1998).

Chen, C. W.

H. Y. Chang, C. W. Chen, C. K. Lee, C. P. Hu, “The tapestry cellular automata phase unwrapping algorithm for nondestructive testing,” J. Opt. Lasers Eng. 30, 487–502 (1998).
[CrossRef]

C. W. Chen, H. Y. Chang, C. K. Lee, “An innovative phase shifting system for nondestructive testing,” J. Chin. Soc. Appl. Mech. 14, 31–39 (1998).

Chen, Y. C.

Y. C. Chen, S. S. Lee, C. M. Lee, C. K. Lee, G. B. Yeh, “New methodology for measuring highly aberrated wave fronts induced by diffractive optical elements,” in Testing, Packaging, Reliability, and Applications of Semiconductor Lasers IV, M. Fallahi, J. Linden, S. Wang, eds., Proc. SPIE3626, 248–259 (1999).
[CrossRef]

Creath, K.

Eiju, T.

Ghiglia, D. C.

Gorecki, C.

Hariharan, P.

Hu, C. P.

H. Y. Chang, C. W. Chen, C. K. Lee, C. P. Hu, “The tapestry cellular automata phase unwrapping algorithm for nondestructive testing,” J. Opt. Lasers Eng. 30, 487–502 (1998).
[CrossRef]

Hunt, R. W.

Jones, R.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge University, Cambridge, UK, 1983).

Lee, C. K.

H. Y. Chang, C. W. Chen, C. K. Lee, C. P. Hu, “The tapestry cellular automata phase unwrapping algorithm for nondestructive testing,” J. Opt. Lasers Eng. 30, 487–502 (1998).
[CrossRef]

C. W. Chen, H. Y. Chang, C. K. Lee, “An innovative phase shifting system for nondestructive testing,” J. Chin. Soc. Appl. Mech. 14, 31–39 (1998).

Y. C. Chen, S. S. Lee, C. M. Lee, C. K. Lee, G. B. Yeh, “New methodology for measuring highly aberrated wave fronts induced by diffractive optical elements,” in Testing, Packaging, Reliability, and Applications of Semiconductor Lasers IV, M. Fallahi, J. Linden, S. Wang, eds., Proc. SPIE3626, 248–259 (1999).
[CrossRef]

Lee, C. M.

Y. C. Chen, S. S. Lee, C. M. Lee, C. K. Lee, G. B. Yeh, “New methodology for measuring highly aberrated wave fronts induced by diffractive optical elements,” in Testing, Packaging, Reliability, and Applications of Semiconductor Lasers IV, M. Fallahi, J. Linden, S. Wang, eds., Proc. SPIE3626, 248–259 (1999).
[CrossRef]

Lee, S. S.

Y. C. Chen, S. S. Lee, C. M. Lee, C. K. Lee, G. B. Yeh, “New methodology for measuring highly aberrated wave fronts induced by diffractive optical elements,” in Testing, Packaging, Reliability, and Applications of Semiconductor Lasers IV, M. Fallahi, J. Linden, S. Wang, eds., Proc. SPIE3626, 248–259 (1999).
[CrossRef]

Leendertz, J. A.

J. N. Butters, J. A. Leendertz, “A double exposure technique for speckle pattern interferometry,” J. Phys. E 4, 277–279 (1971).
[CrossRef]

Moore, A. J.

A. J. Moore, J. R. Tyrer, “Phase-stepped ESPI and moire interferometry for measuring the stress-intensity factor and J integral,” Exp. Mech. 35, 306–314 (1995).
[CrossRef]

Orbel, B. F.

Pomarico, J.

J. Pomarico, R. Arizaga, R. Towoba, H. Rabal, “Algorithm to compute spacing of digital speckle correlation fringes,” Optik (Stuttgart) 95, 125–127 (1993).

Rabal, H.

J. Pomarico, R. Arizaga, R. Towoba, H. Rabal, “Algorithm to compute spacing of digital speckle correlation fringes,” Optik (Stuttgart) 95, 125–127 (1993).

Romero, L. A.

Schmitt, D. R.

Takahashi, S.

S. Takahashi, “Multilayer piezoelectric ceramics actuators and their applications,” Jpn. J. Appl Phys. 24, 41–45 (1985).

Takahashi, T.

Takajo, H.

Towoba, R.

J. Pomarico, R. Arizaga, R. Towoba, H. Rabal, “Algorithm to compute spacing of digital speckle correlation fringes,” Optik (Stuttgart) 95, 125–127 (1993).

Tyrer, J. R.

A. J. Moore, J. R. Tyrer, “Phase-stepped ESPI and moire interferometry for measuring the stress-intensity factor and J integral,” Exp. Mech. 35, 306–314 (1995).
[CrossRef]

Wykes, C.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge University, Cambridge, UK, 1983).

Yeh, G. B.

Y. C. Chen, S. S. Lee, C. M. Lee, C. K. Lee, G. B. Yeh, “New methodology for measuring highly aberrated wave fronts induced by diffractive optical elements,” in Testing, Packaging, Reliability, and Applications of Semiconductor Lasers IV, M. Fallahi, J. Linden, S. Wang, eds., Proc. SPIE3626, 248–259 (1999).
[CrossRef]

Appl. Opt. (4)

Exp. Mech. (1)

A. J. Moore, J. R. Tyrer, “Phase-stepped ESPI and moire interferometry for measuring the stress-intensity factor and J integral,” Exp. Mech. 35, 306–314 (1995).
[CrossRef]

J. Chin. Soc. Appl. Mech. (1)

C. W. Chen, H. Y. Chang, C. K. Lee, “An innovative phase shifting system for nondestructive testing,” J. Chin. Soc. Appl. Mech. 14, 31–39 (1998).

J. Opt. Lasers Eng. (1)

H. Y. Chang, C. W. Chen, C. K. Lee, C. P. Hu, “The tapestry cellular automata phase unwrapping algorithm for nondestructive testing,” J. Opt. Lasers Eng. 30, 487–502 (1998).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Phys. E (1)

J. N. Butters, J. A. Leendertz, “A double exposure technique for speckle pattern interferometry,” J. Phys. E 4, 277–279 (1971).
[CrossRef]

Jpn. J. Appl Phys. (1)

S. Takahashi, “Multilayer piezoelectric ceramics actuators and their applications,” Jpn. J. Appl Phys. 24, 41–45 (1985).

Optik (Stuttgart) (1)

J. Pomarico, R. Arizaga, R. Towoba, H. Rabal, “Algorithm to compute spacing of digital speckle correlation fringes,” Optik (Stuttgart) 95, 125–127 (1993).

Other (3)

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge University, Cambridge, UK, 1983).

Tokin America Inc., “Multilayer piezoelectric actuator,” Insp. Rec. 912-46S-02039, displacement: 14.4 µm at 100 V dc for 17.981-mm length (1991).

Y. C. Chen, S. S. Lee, C. M. Lee, C. K. Lee, G. B. Yeh, “New methodology for measuring highly aberrated wave fronts induced by diffractive optical elements,” in Testing, Packaging, Reliability, and Applications of Semiconductor Lasers IV, M. Fallahi, J. Linden, S. Wang, eds., Proc. SPIE3626, 248–259 (1999).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

ESPI optical arrangement adopted to demonstrate the new algorithms: BS, beam splitters.

Fig. 2
Fig. 2

Measurement results from using traditional phase-shifting technology.

Fig. 3
Fig. 3

Experimental results retrieved from the (5,1) algorithm.

Fig. 4
Fig. 4

Experimental results computed from the DC-(5,1) algorithm.

Equations (33)

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IB=I1+I2+2I1I21/2 cosΦR-ΦB,
IA=I1+I2+2I1I21/2 cosΦR-ΦB+ΔΦ,
IF=IB-IA.
Ia=I1+I2+2I1I21/2 cosΦR-ΦB-2β,Ib=I1+I2+2I1I21/2 cosΦR-ΦB-β,Ic=I1+I2+2I1I21/2 cosΦR-ΦB,Id=I1+I2+2I1I21/2 cosΦR-ΦB+β,Ie=I1+I2+2I1I21/2 cosΦR-ΦB+2β.
tanΦR-ΦB=1-cos2βsinβIb-Id2Ic-Ia-Ie.
tanΦR-ΦB=2Ib-Id2Ic-Ia-Ie.
Ia*=I1+I2+2I1I21/2 cosΦR-ΦB+ΔΦ-2β,Ib*=I1+I2+2I1I21/2 cosΦR-ΦB+ΔΦ-β,Ic*=I1+I2+2I1I21/2 cosΦR-ΦB+ΔΦ,Id*=I1+I2+2I1I21/2 cosΦR-ΦB+ΔΦ+β,Ie*=I1+I2+2I1I21/2 cosΦR-ΦB+ΔΦ+2β,
tanΦR-ΦB+ΔΦ=2Ib*-Id*2Ic*-Ia*-Ie*.
ΔΦ=tan-12Ib*-Id*2Ic*-Ia*-Ie*- tan-12Ib-Id2Ic-Ia-Ie.
IF2=16I1I2sin2ΔΦ2sin2ΔΦ2+ΦR-ΦB.
sin2ΔΦ2+ΦR-ΦB12nπ02nπsin2ΔΦ2+ΦR-ΦBdΔΦ2+ΦR-ΦB=12.
IF2=8I1I2sin2ΔΦ2=4I1I21-cosΔΦ.
IAa=I1+I2+2I1I21/2 cosΦR-ΦB+ΔΦ-2β,IAb=I1+I2+2I1I21/2 cosΦR-ΦB+ΔΦ-β,IAc=I1+I2+2I1I21/2 cosΦR-ΦB+ΔΦ,IAd=I1+I2+2I1I21/2 cosΦR-ΦB+ΔΦ+β,IAe=I1+I2+2I1I21/2 cosΦR-ΦB+ΔΦ+2β,
Ia=IB-IAa2=2I1I21/2cosΦR-ΦB-cosΦR-ΦB+ΔΦ-2β2=8I1I2sin2ΔΦ2-β=4I1I21-cosΔΦ-2β,Ib=IB-IAb2=4I1I21-cosΔΦ-β,Ic=IB-IAc2=4I1I21-cosΔΦ,Id=IB-IAd2=4I1I21-cosΔΦ+β,Ie=IB-IAe2=4I1I21-cosΔΦ+2β,
tanΔΦ=1-cos2βsinβIb-Id2Ic-Ia-Ie.
IBa=I1+I2+2I1I21/2 cosΦR-ΦB-2β=I1+I2+2I1I21/2 cosΦ-ΔΦ-2β,IBb=I1+I2+2I1I21/2 cosΦ-ΔΦ-β,IBc=I1+I2+2I1I21/2 cosΦ-ΔΦ,IBd=I1+I2+2I1I21/2 cosΦ-ΔΦ+β,IBe=I1+I2+2I1I21/2 cosΦ-ΔΦ+2β,
IA=I1+I2+2I1I21/2 cosΦ.
Ia=IA-IBa2=2I1I21/2cosΦ-cosΦ-ΔΦ-2β2=8I1I2sin2ΔΦ2-β=4I1I21-cosΔΦ-2β,Ib=IA-IBb2=4I1I21-cosΔΦ-β,Ic=IA-IBc2=4I1I21-cosΔΦ,Id=IA-IBd2=4I1I21-cosΔΦ+β,Ie=IA-IBe2=4I1I21-cosΔΦ+2β,
tanΔΦ=1-cos2βsinβIb-Id2Ic-Ia-Ie.
ΓXY=XY-XYσXσY,
XY=XY,
ΓAB=IBIA-IBIAIB2-IB21/2IA2-IA21/2.
ΓAB=121+cosΔΦ.
ΓAB=1+r2+2r cosΔΦ1+r2.
Γab=1mmakbk-1mmak1mmbkσaσb,
σa=1mmak2-1mmak21/2,σb=1mmbk2-1mmbk21/2,
IB=I1+I2+2I1I21/2 cosΦR-ΦB,IAa=I1+I2+2I1I21/2 cosΦR-ΦB+ΔΦ-2β,IAb=I1+I2+2I1I21/2 cosΦR-ΦB+ΔΦ-β,IAc=I1+I2+2I1I21/2 cosΦR-ΦB+ΔΦ,IAd=I1+I2+2I1I21/2 cosΦR-ΦB+ΔΦ+β,IAe=I1+I2+2I1I21/2 cosΦR-ΦB+ΔΦ+2β,
Γa=121+cosΔΦ-2β,Γb=121+cosΔΦ-β,Γc=121+cosΔΦ,Γd=121+cosΔΦ+β,Γe=121+cosΔΦ+2β;
tanΔΦ=1-cos2βsinβΓb-Γd2Γc-Γa-Γe.
IBa=I1+I2+2I1I21/2 cosΦ-ΔΦ-2β,IBb=I1+I2+2I1I21/2 cosΦ-ΔΦ-β,IBc=I1+I2+2I1I21/2 cosΦ-ΔΦ,IBd=I1+I2+2I1I21/2 cosΦ-ΔΦ+β,IBe=I1+I2+2I1I21/2 cosΦ-ΔΦ+2β,IA=I1+I2+2I1I21/2 cosΦ,
Γa=121+cosΔΦ-2β,Γb=121+cosΔΦ-β,Γc=121+cosΔΦ,Γd=121+cosΔΦ+β,Γe=121+cosΔΦ+2β.
tanΔΦ=1-cos2βsinβΓb-Γd2Γc-Γa-Γe.
ΔΦ=K3-K1 · L=V3-V1 · L=2πλZˆ-sin45°Yˆ-cos45°Zˆ · LXXˆ+LYYˆ+LZZˆ=2πλ1+cos45°LZ-sin45°LY,

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