Abstract

A phase-shifting TV speckle interferometer is developed by using the frequency modulation capability of a laser diode and is applied to automatic deformation measurements. Temperature modulation is used for generating the frequency shift of a laser diode. We store four speckle interferograms with relative phase differences of π/2 in a frame grabber by monitoring a phase-shift signal, which is obtained by integrating the fringe intensity over a local window. The optimum size of the local window is examined experimentally. Then, the optimum processing conditions for reducing the speckle noise in interferograms, including an averaging window size, are found. Experimental results of the automatic deformation analysis indicate a displacement accuracy of better than λ/30.

© 1993 Optical Society of America

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References

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  8. P. Hariharan, “Phase-stepping interferometry with laser diodes: effect of changes in laser power with output wavelength,” Appl. Opt. 28, 27–29 (1989).
    [CrossRef] [PubMed]
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    [CrossRef]
  10. M. Kuwahara, K. Hachimura, M. Kinoshita, “Image enhancement and left ventricular contour extraction techniques applied to radioisotope angiocardiograms,” Automedica 3, 327–333 (1980).
  11. D. Ghiglia, G. Mastin, L. Romero, “Cellular-automata method for phase unwrapping,” J. Opt. Soc. Am. A 4, 267–280 (1987).
    [CrossRef]
  12. A. Spik, D. W. Robinson, “Investigation of the cellular automata method for phase unwrapping and its implementation on an array processor,” Opt. Laser Eng. 14, 25–37 (1991).
    [CrossRef]
  13. G. Gülker, O. Haack, K. Hinsch, C. Hölscher, J. Kuls, “Optimization of the ESPI technique for extended practically oriented deformation measurements,” in Laser Interferometry IV: Computer-Aided Interferometry, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1553, 160–167 (1991).

1991

A. Spik, D. W. Robinson, “Investigation of the cellular automata method for phase unwrapping and its implementation on an array processor,” Opt. Laser Eng. 14, 25–37 (1991).
[CrossRef]

1989

S. Johansson, K. G. Predko, “Performance of a phase-shifting speckle interferometer for measuring deformation and vibration,” J. Phys. E 22, 289–292 (1989).
[CrossRef]

P. Hariharan, “Phase-stepping interferometry with laser diodes: effect of changes in laser power with output wavelength,” Appl. Opt. 28, 27–29 (1989).
[CrossRef] [PubMed]

1987

1985

1980

M. Kuwahara, K. Hachimura, M. Kinoshita, “Image enhancement and left ventricular contour extraction techniques applied to radioisotope angiocardiograms,” Automedica 3, 327–333 (1980).

1974

Asakura, T.

Brangaccio, D. J.

Bruning, J. H.

Chen, J.

Creath, K.

K. Creath, “Phase-measurement interferometry,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 26, p. 349.
[CrossRef]

Gallagher, J. E.

Ghiglia, D.

Gülker, G.

G. Gülker, O. Haack, K. Hinsch, C. Hölscher, J. Kuls, “Optimization of the ESPI technique for extended practically oriented deformation measurements,” in Laser Interferometry IV: Computer-Aided Interferometry, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1553, 160–167 (1991).

Haack, O.

G. Gülker, O. Haack, K. Hinsch, C. Hölscher, J. Kuls, “Optimization of the ESPI technique for extended practically oriented deformation measurements,” in Laser Interferometry IV: Computer-Aided Interferometry, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1553, 160–167 (1991).

Hachimura, K.

M. Kuwahara, K. Hachimura, M. Kinoshita, “Image enhancement and left ventricular contour extraction techniques applied to radioisotope angiocardiograms,” Automedica 3, 327–333 (1980).

Hariharan, P.

Herriott, D. R.

Hinsch, K.

G. Gülker, O. Haack, K. Hinsch, C. Hölscher, J. Kuls, “Optimization of the ESPI technique for extended practically oriented deformation measurements,” in Laser Interferometry IV: Computer-Aided Interferometry, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1553, 160–167 (1991).

Hölscher, C.

G. Gülker, O. Haack, K. Hinsch, C. Hölscher, J. Kuls, “Optimization of the ESPI technique for extended practically oriented deformation measurements,” in Laser Interferometry IV: Computer-Aided Interferometry, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1553, 160–167 (1991).

Ishii, Y.

Johansson, S.

S. Johansson, K. G. Predko, “Performance of a phase-shifting speckle interferometer for measuring deformation and vibration,” J. Phys. E 22, 289–292 (1989).
[CrossRef]

Kadono, H.

Kinoshita, M.

M. Kuwahara, K. Hachimura, M. Kinoshita, “Image enhancement and left ventricular contour extraction techniques applied to radioisotope angiocardiograms,” Automedica 3, 327–333 (1980).

Kuls, J.

G. Gülker, O. Haack, K. Hinsch, C. Hölscher, J. Kuls, “Optimization of the ESPI technique for extended practically oriented deformation measurements,” in Laser Interferometry IV: Computer-Aided Interferometry, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1553, 160–167 (1991).

Kuwahara, M.

M. Kuwahara, K. Hachimura, M. Kinoshita, “Image enhancement and left ventricular contour extraction techniques applied to radioisotope angiocardiograms,” Automedica 3, 327–333 (1980).

Mastin, G.

Murata, K.

Nakadate, S.

Predko, K. G.

S. Johansson, K. G. Predko, “Performance of a phase-shifting speckle interferometer for measuring deformation and vibration,” J. Phys. E 22, 289–292 (1989).
[CrossRef]

Robinson, D. W.

A. Spik, D. W. Robinson, “Investigation of the cellular automata method for phase unwrapping and its implementation on an array processor,” Opt. Laser Eng. 14, 25–37 (1991).
[CrossRef]

Romero, L.

Rosenfeld, D. P.

Saito, H.

Spik, A.

A. Spik, D. W. Robinson, “Investigation of the cellular automata method for phase unwrapping and its implementation on an array processor,” Opt. Laser Eng. 14, 25–37 (1991).
[CrossRef]

Takai, N.

White, A. D.

Yamaguchi, I.

I. Yamaguchi, “Fringe formation in deformation and vibration measurements using laser light,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1985), Vol. 22, p. 273.
[CrossRef]

Yonemura, M.

Appl. Opt.

Automedica

M. Kuwahara, K. Hachimura, M. Kinoshita, “Image enhancement and left ventricular contour extraction techniques applied to radioisotope angiocardiograms,” Automedica 3, 327–333 (1980).

J. Opt. Soc. Am. A

J. Phys. E

S. Johansson, K. G. Predko, “Performance of a phase-shifting speckle interferometer for measuring deformation and vibration,” J. Phys. E 22, 289–292 (1989).
[CrossRef]

Opt. Laser Eng.

A. Spik, D. W. Robinson, “Investigation of the cellular automata method for phase unwrapping and its implementation on an array processor,” Opt. Laser Eng. 14, 25–37 (1991).
[CrossRef]

Opt. Lett.

Other

G. Gülker, O. Haack, K. Hinsch, C. Hölscher, J. Kuls, “Optimization of the ESPI technique for extended practically oriented deformation measurements,” in Laser Interferometry IV: Computer-Aided Interferometry, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1553, 160–167 (1991).

K. Creath, “Phase-measurement interferometry,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 26, p. 349.
[CrossRef]

I. Yamaguchi, “Fringe formation in deformation and vibration measurements using laser light,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1985), Vol. 22, p. 273.
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Principle of the phase-shift method using the temperature modulation of a LD. The intensity of the interferogram was averaged over a small local window for the detection of shifted phase.

Fig. 2
Fig. 2

Schematic diagram of a phase-shifting TV speckle interferometer and its specifications. The temperature controller of the LD and a local area intensity integrator were newly equipped to introduce the phase-shifting technique.

Fig. 3
Fig. 3

Dependence of the phase-shift signal on window sizes (4, 6, 8, and 10 pixels square).

Fig. 4
Fig. 4

Examples of four phase-shifted interferograms (upper) stored by using a phase-shift signal (lower) displayed on the computer. The storage in a frame grabber was conducted at the times marked by circles.

Fig. 5
Fig. 5

Smoothing method for speckle noise reduction by using intensity variances in the averaging windows (V filter). The value at the central pixel was determined by the equation shown in the figure.

Fig. 6
Fig. 6

Experimental setup for examining the accuracy and the optimum parameters of the method. A small tilt of a rough flat surface was measured.

Fig. 7
Fig. 7

Example of experimental results. Four phase-shifted interferograms were used for phase calculation after the smoothing process: (a) one of the interferograms, (b) its smoothed result, (c) calculated phase distribution before unwrapping, (d) a bird’s-eye view of out-of-plane displacement after unwrapping.

Fig. 8
Fig. 8

Relationship between the averaging window size and the least-squares phase error. The fringe ratio means the ratio of the fringe spacing to the minimum speckle size (4.6 pixels here).

Fig. 9
Fig. 9

Dependence of phase errors obtained from two smoothing techniques on fringe density for different window sizes.

Fig. 10
Fig. 10

Experimental result from disk bending with central loading: (a) one of the phase-shifted interferograms, (b) the smoothed interferogram, (c), (d) calculated phase distributions before and after phase unwrapping, respectively, (e) bird’s-eye view of the out-of-plane displacement.

Equations (4)

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J i ( x , y ) = ( I a - I b ) 2 = I 2 { 1 + γ cos [ 4 π λ a z ( x , y ) + ϕ 0 + Δ ϕ i ] } ,
a z ( x , y ) = λ 4 π [ tan - 1 ( J 4 - J 2 J 1 - J 3 ) - ϕ 0 ] .
Δ ϕ i = - 2 π Δ λ λ 2 D .
ϕ ( m + 1 ) = { ϕ ( m + 1 ) + 2 π ϕ ( m + 1 ) - ϕ ( m ) π ϕ ( m + 1 ) - 2 π ϕ ( m + 1 ) - ϕ ( m ) < - π ,

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