Abstract

Surface point displacements can be measured by using standard phase-stepping speckle interferometry, but the measured data are vulnerable to disturbances during the interferogram recordings. To overcome this an interferometer with a computational system has been developed to record three phase-stepped interferograms simultaneously and to calculate displacements. This system is evaluated by measurements of the out-of-plane rotation of a flat surface. The surface displacement is calculated at a rate of 25 times/s. If one reduces noise by filtering, hardware limitations decrease the speed to 12.5 displacement calculations/s. With this system displacements can be measured with an accuracy exceeding λ/55 if filtering is applied.

© 1994 Optical Society of America

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References

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  1. J. A. Leendertz, “Interferometric displacement measurement on scattering surfaces utilizing speckle effect,” J. Phys. E 3, 214–218 (1970).
    [CrossRef]
  2. E. Archbold, J. M. Burch, A. E. Ennos, “Recording of in-plane surface displacement by double-exposure speckle photography,” Opt. Acta 17, 883–898 (1970).
    [CrossRef]
  3. J. N. Butters, R. Jones, C. Wykes, “Electronic speckle pattern interferometry,” in Speckle Metrology, R. K. Erf, ed. (Academic, New York, 1978), pp. 111–158.
  4. C. Wykes, “Use of electronic speckle pattern interferometry in measurement of static and dynamic surface displacements,” Opt. Eng. 21, 400–406 (1982).
  5. D. W. Robinson, D. C. Williams, “Digital phase stepping speckle interferometry,” Opt. Commun. 57, 26–30 (1986).
    [CrossRef]
  6. K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24, 3053–3058 (1985).
    [CrossRef] [PubMed]
  7. M.-W. Chang, C.-P. Hu, P. S. Lam, J. C. Wyant, “High precision deformation measurement by digital phase shifting holographic interferometry,” Appl. Opt. 24,3780–3783 (1985).
    [CrossRef] [PubMed]
  8. B. Breuckmann, W. Thieme, “Computer-aided analysis of holographic interferograms using the phase-shift method,” Appl. Opt. 24, 2145–2149 (1985).
    [CrossRef] [PubMed]
  9. W. Jüptner, T. M. Kreis, H. Kreitlow, “Automatic evaluation of holographic interferograms by reference beam phase shifting,” in Industrial Applications of Laser Technology, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng 398, 22–29 (1983).
  10. K. Creath, “Phase-measurement interferometric techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. 26, pp. 349–393.
    [CrossRef]
  11. M. P. Kothiyal, C. Delisle, “Shearing interferometer for phase shifting interferometry with polarization phase shifter,” Appl. Opt. 24, 4439–4442 (1985).
    [CrossRef] [PubMed]
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).
  13. A. E. Ennos, “Speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 203–253.
    [CrossRef]
  14. D. Colucci, P. L. Wizinowich, “Millisecond phase acquisition at video rates,” Appl. Opt. 31, 5919–5925 (1992).
    [CrossRef] [PubMed]
  15. H. A. Vrooman, A. A. M. Maas, “New image processing algorithms for the analysis of speckle pattern interferograms,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1163, 51–61 (1989).
  16. S. Donati, G. Martini, “Speckle-pattern intensity and phase: second-order conditional statistics,” J. Opt. Soc. Am 69, 1690–1694(1979).
    [CrossRef]
  17. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 9–75.
    [CrossRef]
  18. R. Höfling, Frauenhofer Institut für Umvormtechnik, Chemnitz, Germany (personal communication, 1993).

1992 (1)

1986 (1)

D. W. Robinson, D. C. Williams, “Digital phase stepping speckle interferometry,” Opt. Commun. 57, 26–30 (1986).
[CrossRef]

1985 (4)

1982 (1)

C. Wykes, “Use of electronic speckle pattern interferometry in measurement of static and dynamic surface displacements,” Opt. Eng. 21, 400–406 (1982).

1979 (1)

S. Donati, G. Martini, “Speckle-pattern intensity and phase: second-order conditional statistics,” J. Opt. Soc. Am 69, 1690–1694(1979).
[CrossRef]

1970 (2)

J. A. Leendertz, “Interferometric displacement measurement on scattering surfaces utilizing speckle effect,” J. Phys. E 3, 214–218 (1970).
[CrossRef]

E. Archbold, J. M. Burch, A. E. Ennos, “Recording of in-plane surface displacement by double-exposure speckle photography,” Opt. Acta 17, 883–898 (1970).
[CrossRef]

Archbold, E.

E. Archbold, J. M. Burch, A. E. Ennos, “Recording of in-plane surface displacement by double-exposure speckle photography,” Opt. Acta 17, 883–898 (1970).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Breuckmann, B.

Burch, J. M.

E. Archbold, J. M. Burch, A. E. Ennos, “Recording of in-plane surface displacement by double-exposure speckle photography,” Opt. Acta 17, 883–898 (1970).
[CrossRef]

Butters, J. N.

J. N. Butters, R. Jones, C. Wykes, “Electronic speckle pattern interferometry,” in Speckle Metrology, R. K. Erf, ed. (Academic, New York, 1978), pp. 111–158.

Chang, M.-W.

Colucci, D.

Creath, K.

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

K. Creath, “Phase-measurement interferometric techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. 26, pp. 349–393.
[CrossRef]

Delisle, C.

Donati, S.

S. Donati, G. Martini, “Speckle-pattern intensity and phase: second-order conditional statistics,” J. Opt. Soc. Am 69, 1690–1694(1979).
[CrossRef]

Ennos, A. E.

E. Archbold, J. M. Burch, A. E. Ennos, “Recording of in-plane surface displacement by double-exposure speckle photography,” Opt. Acta 17, 883–898 (1970).
[CrossRef]

A. E. Ennos, “Speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 203–253.
[CrossRef]

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 9–75.
[CrossRef]

Höfling, R.

R. Höfling, Frauenhofer Institut für Umvormtechnik, Chemnitz, Germany (personal communication, 1993).

Hu, C.-P.

Jones, R.

J. N. Butters, R. Jones, C. Wykes, “Electronic speckle pattern interferometry,” in Speckle Metrology, R. K. Erf, ed. (Academic, New York, 1978), pp. 111–158.

Jüptner, W.

W. Jüptner, T. M. Kreis, H. Kreitlow, “Automatic evaluation of holographic interferograms by reference beam phase shifting,” in Industrial Applications of Laser Technology, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng 398, 22–29 (1983).

Kothiyal, M. P.

Kreis, T. M.

W. Jüptner, T. M. Kreis, H. Kreitlow, “Automatic evaluation of holographic interferograms by reference beam phase shifting,” in Industrial Applications of Laser Technology, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng 398, 22–29 (1983).

Kreitlow, H.

W. Jüptner, T. M. Kreis, H. Kreitlow, “Automatic evaluation of holographic interferograms by reference beam phase shifting,” in Industrial Applications of Laser Technology, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng 398, 22–29 (1983).

Lam, P. S.

Leendertz, J. A.

J. A. Leendertz, “Interferometric displacement measurement on scattering surfaces utilizing speckle effect,” J. Phys. E 3, 214–218 (1970).
[CrossRef]

Maas, A. A. M.

H. A. Vrooman, A. A. M. Maas, “New image processing algorithms for the analysis of speckle pattern interferograms,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1163, 51–61 (1989).

Martini, G.

S. Donati, G. Martini, “Speckle-pattern intensity and phase: second-order conditional statistics,” J. Opt. Soc. Am 69, 1690–1694(1979).
[CrossRef]

Robinson, D. W.

D. W. Robinson, D. C. Williams, “Digital phase stepping speckle interferometry,” Opt. Commun. 57, 26–30 (1986).
[CrossRef]

Thieme, W.

Vrooman, H. A.

H. A. Vrooman, A. A. M. Maas, “New image processing algorithms for the analysis of speckle pattern interferograms,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1163, 51–61 (1989).

Williams, D. C.

D. W. Robinson, D. C. Williams, “Digital phase stepping speckle interferometry,” Opt. Commun. 57, 26–30 (1986).
[CrossRef]

Wizinowich, P. L.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Wyant, J. C.

Wykes, C.

C. Wykes, “Use of electronic speckle pattern interferometry in measurement of static and dynamic surface displacements,” Opt. Eng. 21, 400–406 (1982).

J. N. Butters, R. Jones, C. Wykes, “Electronic speckle pattern interferometry,” in Speckle Metrology, R. K. Erf, ed. (Academic, New York, 1978), pp. 111–158.

Appl. Opt. (5)

J. Opt. Soc. Am (1)

S. Donati, G. Martini, “Speckle-pattern intensity and phase: second-order conditional statistics,” J. Opt. Soc. Am 69, 1690–1694(1979).
[CrossRef]

J. Phys. E (1)

J. A. Leendertz, “Interferometric displacement measurement on scattering surfaces utilizing speckle effect,” J. Phys. E 3, 214–218 (1970).
[CrossRef]

Opt. Acta (1)

E. Archbold, J. M. Burch, A. E. Ennos, “Recording of in-plane surface displacement by double-exposure speckle photography,” Opt. Acta 17, 883–898 (1970).
[CrossRef]

Opt. Commun. (1)

D. W. Robinson, D. C. Williams, “Digital phase stepping speckle interferometry,” Opt. Commun. 57, 26–30 (1986).
[CrossRef]

Opt. Eng. (1)

C. Wykes, “Use of electronic speckle pattern interferometry in measurement of static and dynamic surface displacements,” Opt. Eng. 21, 400–406 (1982).

Other (8)

J. N. Butters, R. Jones, C. Wykes, “Electronic speckle pattern interferometry,” in Speckle Metrology, R. K. Erf, ed. (Academic, New York, 1978), pp. 111–158.

W. Jüptner, T. M. Kreis, H. Kreitlow, “Automatic evaluation of holographic interferograms by reference beam phase shifting,” in Industrial Applications of Laser Technology, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng 398, 22–29 (1983).

K. Creath, “Phase-measurement interferometric techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. 26, pp. 349–393.
[CrossRef]

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 9–75.
[CrossRef]

R. Höfling, Frauenhofer Institut für Umvormtechnik, Chemnitz, Germany (personal communication, 1993).

H. A. Vrooman, A. A. M. Maas, “New image processing algorithms for the analysis of speckle pattern interferograms,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1163, 51–61 (1989).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

A. E. Ennos, “Speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 203–253.
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Polarization phase-stepping configuration. E, Electric field strength.

Fig. 2
Fig. 2

Schematic of the complete system. PZT, piezoelectric transducer.

Fig. 3
Fig. 3

Rms phase error σ versus the ratio of in-plane translation t and speckle size S.

Fig. 4
Fig. 4

Rms phase error σ versus defocus z for various ratios of distance r from the axis of the system and image distance d i . The numerical aperture is 0.04.

Fig. 5
Fig. 5

Scheme of the computer configuration: RGB: red, green, blue.

Fig. 6
Fig. 6

IP flow chart.

Fig. 7
Fig. 7

Data flow diagram for the filtering to reduce speckle noise.

Fig. 8
Fig. 8

Rms phase error versus diameter D of the diaphragm.

Fig. 9
Fig. 9

Phase change calculated by pipeline IP devices: (a) displacement coded in gray values, (b) shape of the object displacement.

Equations (9)

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

I ( m , n ) = I b ( m , n ) + M ( m , n ) × sin [ ϕ o ( m , n ) - ϕ r ( m , n ) + 2 α ] ,
I b ( m , n ) = I o ( m , n ) + I r ( m , n )
M ( m , n ) = 2 [ I o ( m , n ) I r ( m , n ) ] 1 / 2
S = 1.2 λ M z D ,
ϕ = arctan [ I 1 - I 3 2 k ( I 2 - I b , 2 ) ] .
σ = ( ( 1 - μ 12 ) { 3 - ln [ 2 ( 1 - μ 12 ) ] } ) 1 / 2 ,
μ 12 2 = I 1 ( m , n ) I 2 ( m , n ) - I 1 ( m , n ) I 2 ( m , n ) { [ I 1 ( m , n ) 2 - I 1 ( m , n ) 2 ] [ I 2 ( m , n ) 2 - I 2 ( m , n ) 2 ] } 1 / 2 ,
M i = ½ { ( I i [ 0 ] - I i [ π ] ) 2 + ( I i [ π / 2 ] - I i [ 3 π / 2 ] ) 2 } 1 / 2             ( i = 1 , 2 , 3 ) .
I i = ½ I i [ 0 ] + I i [ π ] ,

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