Abstract

Temporal and spatial phase shifting in electronic speckle-pattern interferometry are compared quantitatively with respect to the quality of the resultant deformation phase maps. On the basis of an analysis of the noise in sawtooth fringes a figure of merit is defined and measured for various in-plane and out-of-plane sensitive electronic speckle-pattern interferometry configurations. Varying quantities like the object-illuminating intensity, the beam ratio, the speckle size and shape, and the fringe density allows characteristic behaviors of both phase-shifting methods to be explored.

© 2000 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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1998

J. Burke, H. Helmers, C. Kunze, V. Wilkens, “Speckle intensity and phase gradients: influence on fringe quality in spatial phase-shifting ESPI systems,” Opt. Commun. 151, 144–152 (1998).
[CrossRef]

1997

1996

M. Lehmann, “Phase-shifting speckle interferometry with unresolved speckles: a theoretical investigation,” Opt. Commun. 128, 325–340 (1996).
[CrossRef]

1995

N. Shvartsman, I. Freund, “Speckle spots ride phase saddles sidesaddle,” Opt. Commun. 117, 228–234 (1995), and references therein.

M. Lehmann, “Optimization of wave intensities in phase-shifting speckle interferometry,” Opt. Commun. 118, 199–206 (1995).
[CrossRef]

1993

J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller, N. Streibl, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. 32, 1883–1885 (1993).
[CrossRef]

1992

1991

D. C. Williams, N. S. Nassar, J. E. Banyard, M. S. Virdee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991).
[CrossRef]

H. A. Vrooman, A. A. de Maas, “Image-processing algorithms for the analysis of phase-shifted speckle interference patterns,” Appl. Opt. 30, 1636–1641 (1991).
[CrossRef] [PubMed]

1990

1988

1986

1985

1982

1979

1970

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

Banyard, J. E.

D. C. Williams, N. S. Nassar, J. E. Banyard, M. S. Virdee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991).
[CrossRef]

Bothe, T.

Burke, J.

Cheng, Y. Y.

Colucci, D.

de Maas, A. A.

Donati, S.

Ennos, A. E.

A. E. Ennos, “Speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), p. 210.

Falkenstörfer, O.

J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller, N. Streibl, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. 32, 1883–1885 (1993).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, UK, 1988), p. 305.

Freischlad, K.

Freund, I.

N. Shvartsman, I. Freund, “Speckle spots ride phase saddles sidesaddle,” Opt. Commun. 117, 228–234 (1995), and references therein.

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. 38–39.

Gutjahr, J.

H. Steinbichler, J. Gutjahr, “Verfahren zur direkten Phasenmessung von Strahlung, insbesondere Lichtstrahlung, und Vorrichtung zur Durchführung dieses Verfahrens,” Offenlegungsschrift Deutsches PatentamtDE 3930632 A1 (14March1991).

Helmers, H.

Hinsch, K.

Huntley, J. M.

J. M. Huntley, “Random phase measurement errors in DSPI,” Opt. Laser Eng. 26, 131–150 (1997).
[CrossRef]

Ina, H.

Kerr, D.

Kobayashi, S.

Koliopoulos, C. L.

Kujawinska, M.

Kunze, C.

J. Burke, H. Helmers, C. Kunze, V. Wilkens, “Speckle intensity and phase gradients: influence on fringe quality in spatial phase-shifting ESPI systems,” Opt. Commun. 151, 144–152 (1998).
[CrossRef]

Larkin, K. G.

K. G. Larkin, B. F. Oreb, “Propagation of errors in different phase-shifting algorithms: a special property of the arctangent function,” in Interferometry: Techniques and Analysis, B. M. Brown, O. Y. Kwon, M. Kujawińska, G. T. Reid, eds., Proc. SPIE1755, 219–227 (1992).

Leendertz, J. A.

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

Lehmann, M.

M. Lehmann, “Phase-shifting speckle interferometry with unresolved speckles: a theoretical investigation,” Opt. Commun. 128, 325–340 (1996).
[CrossRef]

M. Lehmann, “Optimization of wave intensities in phase-shifting speckle interferometry,” Opt. Commun. 118, 199–206 (1995).
[CrossRef]

Martini, G.

Mendoza Santoyo, F.

Nassar, N. S.

D. C. Williams, N. S. Nassar, J. E. Banyard, M. S. Virdee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991).
[CrossRef]

Oreb, B. F.

K. G. Larkin, B. F. Oreb, “Propagation of errors in different phase-shifting algorithms: a special property of the arctangent function,” in Interferometry: Techniques and Analysis, B. M. Brown, O. Y. Kwon, M. Kujawińska, G. T. Reid, eds., Proc. SPIE1755, 219–227 (1992).

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, UK, 1988), p. 305.

Robinson, D. W.

Schreiber, H.

J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller, N. Streibl, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. 32, 1883–1885 (1993).
[CrossRef]

Schwider, J.

J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller, N. Streibl, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. 32, 1883–1885 (1993).
[CrossRef]

Shvartsman, N.

N. Shvartsman, I. Freund, “Speckle spots ride phase saddles sidesaddle,” Opt. Commun. 117, 228–234 (1995), and references therein.

Sirohi, R. S.

Slettemoen, G. Å.

Steinbichler, H.

H. Steinbichler, J. Gutjahr, “Verfahren zur direkten Phasenmessung von Strahlung, insbesondere Lichtstrahlung, und Vorrichtung zur Durchführung dieses Verfahrens,” Offenlegungsschrift Deutsches PatentamtDE 3930632 A1 (14March1991).

Streibl, N.

J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller, N. Streibl, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. 32, 1883–1885 (1993).
[CrossRef]

Takeda, M.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, UK, 1988), p. 305.

Tyrer, J. D.

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, UK, 1988), p. 305.

Virdee, M. S.

D. C. Williams, N. S. Nassar, J. E. Banyard, M. S. Virdee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991).
[CrossRef]

Vrooman, H. A.

Wilkens, V.

J. Burke, H. Helmers, C. Kunze, V. Wilkens, “Speckle intensity and phase gradients: influence on fringe quality in spatial phase-shifting ESPI systems,” Opt. Commun. 151, 144–152 (1998).
[CrossRef]

Williams, D. C.

D. C. Williams, N. S. Nassar, J. E. Banyard, M. S. Virdee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991).
[CrossRef]

Wizinowich, P.

Wyant, J. C.

Zöller, A.

J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller, N. Streibl, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. 32, 1883–1885 (1993).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. E

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

Opt. Commun.

M. Lehmann, “Optimization of wave intensities in phase-shifting speckle interferometry,” Opt. Commun. 118, 199–206 (1995).
[CrossRef]

M. Lehmann, “Phase-shifting speckle interferometry with unresolved speckles: a theoretical investigation,” Opt. Commun. 128, 325–340 (1996).
[CrossRef]

J. Burke, H. Helmers, C. Kunze, V. Wilkens, “Speckle intensity and phase gradients: influence on fringe quality in spatial phase-shifting ESPI systems,” Opt. Commun. 151, 144–152 (1998).
[CrossRef]

N. Shvartsman, I. Freund, “Speckle spots ride phase saddles sidesaddle,” Opt. Commun. 117, 228–234 (1995), and references therein.

Opt. Eng.

J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller, N. Streibl, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. 32, 1883–1885 (1993).
[CrossRef]

Opt. Laser Eng.

J. M. Huntley, “Random phase measurement errors in DSPI,” Opt. Laser Eng. 26, 131–150 (1997).
[CrossRef]

Opt. Laser Technol.

D. C. Williams, N. S. Nassar, J. E. Banyard, M. S. Virdee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991).
[CrossRef]

Other

H. Steinbichler, J. Gutjahr, “Verfahren zur direkten Phasenmessung von Strahlung, insbesondere Lichtstrahlung, und Vorrichtung zur Durchführung dieses Verfahrens,” Offenlegungsschrift Deutsches PatentamtDE 3930632 A1 (14March1991).

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 38–39.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, UK, 1988), p. 305.

K. G. Larkin, B. F. Oreb, “Propagation of errors in different phase-shifting algorithms: a special property of the arctangent function,” in Interferometry: Techniques and Analysis, B. M. Brown, O. Y. Kwon, M. Kujawińska, G. T. Reid, eds., Proc. SPIE1755, 219–227 (1992).

A. E. Ennos, “Speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), p. 210.

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Figures (8)

Fig. 1
Fig. 1

Optical setup used for TPS and SPS in ESPI. (See text for details.)

Fig. 2
Fig. 2

Figure of merit σ d plotted as a function of the beam ratio B. Measured data for SPS and TPS are represented by the solid curves; theoretical SPS data are represented by the dashed curve.

Fig. 3
Fig. 3

Figure of merit σ d for SPS measurements plotted versus the global phase offset ϕ0 for three different speckle sizes D. The symbols represent measured data; the solid curves are fitted.

Fig. 4
Fig. 4

Figure of merit σ d for (a) SPS and (b) TPS measurements plotted as a function of the speckle size D for various numbers of vertical fringes N x per 1024 pixels.

Fig. 5
Fig. 5

Figure of merit σ d plotted as a function of the speckle size D for different numbers of horizontal fringes N y per 1024 pixels: (a) Pure in-plane setup data obtained by use of TPS (dashed curves with filled symbols), (b) pure in-plane setup data obtained by use of SPS (solid curves with filled symbols), (c) mixed-sensitivity setup data obtained by use of SPS (solid curves with open symbols).

Fig. 6
Fig. 6

Figure of merit σ d plotted as a function of the object-illuminating intensity O I for SPS measurements with a circular aperture (filled symbols) and an elliptical aperture (open symbols): (a) vertical and (b) horizontal fringes.

Fig. 7
Fig. 7

Figure of merit σ d plotted as a function of speckle size D for phase reconstruction by the FTM (dashed curves) and the SPS (solid curves) algorithms for an out-of-plane ESPI configuration.

Fig. 8
Fig. 8

Figure of merit σ d plotted as a function of the object-illuminating intensity O I for TPS (filled symbols) and SPS (open symbols) measurements with an elliptical aperture and phase reconstruction by the FTM.

Equations (6)

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

Iix, y, ti=Ibx, y, ti1+sincΦt2γx, y, ti×cosϕx, y, ti+iαt,
Iix+i, y=Ibx+i, y1+sincΦx2γx+i, y×cosϕx+i, y+iαx,
ϕ mod π=arctan3I-1-I12I0-I-1-I1,
σϕ=σI2γIb83,
σϕσO0,O±12+σe21/22OR1/283,
σO0,O±1=O1-μ22+2O2μ21-μ21/2.

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