Abstract

Hitherto no method, to our knowledge, was known to incorporate spatial phase shifting for the measurement of pure in-plane displacements. We demonstrate that the modified Duffy two-aperture configuration [Opt. Lett. 22, 1958 (1996)], which is sensitive to only the in-plane displacement component and offers increased sensitivity, lends itself to measurement with spatial phase shifting. The configuration can also be used for obtaining displacement derivatives by the introduction of shear with the tilt of a mirror.

© 1997 Optical Society of America

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References

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  1. K. Creath, “Phase-shifting holographic interferometry,” in Holographic Interferometry, P. K. Rastogi, ed. (Springer-Verlag, Berlin, Germany, 1994), Chap. 5, pp. 109–150.
    [CrossRef]
  2. M. Kujawinska, “Spatial phase measurement methods,” in Interferogram Analysis–Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, U.K., 1993), Chap. 5, pp. 141–193.
  3. H. Steinbichler, J. Gutjahr, “Verfahren zur direkten Phasenmessung von Strahlung, insbesondere Lichtstrahlung, und Vorrichtung zur Durchf ürung dieses Verfahrens,” Offenlegungsschrift Deutsches Patentamt DE 3930632 A1 (14March1991).
  4. T. Bothe, J. Burke, H. Helmers, “Spatial phase shifting in electronic speckle pattern interferometry: minimization of phase reconstruction errors,” Appl. Opt. 36, 5310–5316 (1997).
    [CrossRef] [PubMed]
  5. M. Servin, F. J. Cuevas, “A novel technique for spatial phase-shifting interferometry,” J. Mod. Opt. 42, 1853–1862 (1995).
    [CrossRef]
  6. J. A. Leendertz, “Interferometric displacement measurement on scattering surfaces utilizing speckle effect,” J. Phys. E Sci. Instrum. 3, 214–218 (1970).
    [CrossRef]
  7. D. E. Duffy, “Moiré gauging of in-plane displacement using double aperture imaging,” Appl. Opt. 11, 1778–1781 (1972).
    [CrossRef] [PubMed]
  8. R. S. Sirohi, N. Krishna Mohan, T. Santhanakrishnan, “Optical configuration for measurement in speckle interferometry,” Opt. Lett. 22, 1958–1959 (1996).
    [CrossRef]
  9. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), Chap. 7, pp 275–276.
  10. P. K. Rastogi, “Techniques of displacement and deformation measurements in speckle metrology,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), Chap. 2, pp. 41–98.
  11. G. Pedrini, Y. L. Zou, H. Tiziani, “Quantitative evaluation of digital shearing interferogram using the spatial carrier method,” Pure Appl. Opt. 5, 313–321 (1996).
    [CrossRef]
  12. S. Leidenbach, “Die direkte Phasenmessung—ein neues Verfahren zur Berechnung von Phasenbildern aus nur einem Intensitäatsbild,” Proc. Laser 1, 68–72 (1991).
  13. G. Pedrini, B. Pfister, H. Tiziani, “Double pulse electronic speckle interferometry,” J. Mod. Opt. 40, 89–96 (1993).
    [CrossRef]

1997 (1)

1996 (2)

R. S. Sirohi, N. Krishna Mohan, T. Santhanakrishnan, “Optical configuration for measurement in speckle interferometry,” Opt. Lett. 22, 1958–1959 (1996).
[CrossRef]

G. Pedrini, Y. L. Zou, H. Tiziani, “Quantitative evaluation of digital shearing interferogram using the spatial carrier method,” Pure Appl. Opt. 5, 313–321 (1996).
[CrossRef]

1995 (1)

M. Servin, F. J. Cuevas, “A novel technique for spatial phase-shifting interferometry,” J. Mod. Opt. 42, 1853–1862 (1995).
[CrossRef]

1993 (1)

G. Pedrini, B. Pfister, H. Tiziani, “Double pulse electronic speckle interferometry,” J. Mod. Opt. 40, 89–96 (1993).
[CrossRef]

1991 (1)

S. Leidenbach, “Die direkte Phasenmessung—ein neues Verfahren zur Berechnung von Phasenbildern aus nur einem Intensitäatsbild,” Proc. Laser 1, 68–72 (1991).

1972 (1)

1970 (1)

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

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), Chap. 7, pp 275–276.

Bothe, T.

Burke, J.

Creath, K.

K. Creath, “Phase-shifting holographic interferometry,” in Holographic Interferometry, P. K. Rastogi, ed. (Springer-Verlag, Berlin, Germany, 1994), Chap. 5, pp. 109–150.
[CrossRef]

Cuevas, F. J.

M. Servin, F. J. Cuevas, “A novel technique for spatial phase-shifting interferometry,” J. Mod. Opt. 42, 1853–1862 (1995).
[CrossRef]

Duffy, D. E.

Gutjahr, J.

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

Helmers, H.

Krishna Mohan, N.

R. S. Sirohi, N. Krishna Mohan, T. Santhanakrishnan, “Optical configuration for measurement in speckle interferometry,” Opt. Lett. 22, 1958–1959 (1996).
[CrossRef]

Kujawinska, M.

M. Kujawinska, “Spatial phase measurement methods,” in Interferogram Analysis–Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, U.K., 1993), Chap. 5, pp. 141–193.

Leendertz, J. A.

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

Leidenbach, S.

S. Leidenbach, “Die direkte Phasenmessung—ein neues Verfahren zur Berechnung von Phasenbildern aus nur einem Intensitäatsbild,” Proc. Laser 1, 68–72 (1991).

Pedrini, G.

G. Pedrini, Y. L. Zou, H. Tiziani, “Quantitative evaluation of digital shearing interferogram using the spatial carrier method,” Pure Appl. Opt. 5, 313–321 (1996).
[CrossRef]

G. Pedrini, B. Pfister, H. Tiziani, “Double pulse electronic speckle interferometry,” J. Mod. Opt. 40, 89–96 (1993).
[CrossRef]

Pfister, B.

G. Pedrini, B. Pfister, H. Tiziani, “Double pulse electronic speckle interferometry,” J. Mod. Opt. 40, 89–96 (1993).
[CrossRef]

Rastogi, P. K.

P. K. Rastogi, “Techniques of displacement and deformation measurements in speckle metrology,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), Chap. 2, pp. 41–98.

Santhanakrishnan, T.

R. S. Sirohi, N. Krishna Mohan, T. Santhanakrishnan, “Optical configuration for measurement in speckle interferometry,” Opt. Lett. 22, 1958–1959 (1996).
[CrossRef]

Servin, M.

M. Servin, F. J. Cuevas, “A novel technique for spatial phase-shifting interferometry,” J. Mod. Opt. 42, 1853–1862 (1995).
[CrossRef]

Sirohi, R. S.

R. S. Sirohi, N. Krishna Mohan, T. Santhanakrishnan, “Optical configuration for measurement in speckle interferometry,” Opt. Lett. 22, 1958–1959 (1996).
[CrossRef]

Steinbichler, H.

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

Tiziani, H.

G. Pedrini, Y. L. Zou, H. Tiziani, “Quantitative evaluation of digital shearing interferogram using the spatial carrier method,” Pure Appl. Opt. 5, 313–321 (1996).
[CrossRef]

G. Pedrini, B. Pfister, H. Tiziani, “Double pulse electronic speckle interferometry,” J. Mod. Opt. 40, 89–96 (1993).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), Chap. 7, pp 275–276.

Zou, Y. L.

G. Pedrini, Y. L. Zou, H. Tiziani, “Quantitative evaluation of digital shearing interferogram using the spatial carrier method,” Pure Appl. Opt. 5, 313–321 (1996).
[CrossRef]

Appl. Opt. (2)

J. Mod. Opt. (2)

G. Pedrini, B. Pfister, H. Tiziani, “Double pulse electronic speckle interferometry,” J. Mod. Opt. 40, 89–96 (1993).
[CrossRef]

M. Servin, F. J. Cuevas, “A novel technique for spatial phase-shifting interferometry,” J. Mod. Opt. 42, 1853–1862 (1995).
[CrossRef]

J. Phys. E Sci. Instrum. (1)

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

Opt. Lett. (1)

R. S. Sirohi, N. Krishna Mohan, T. Santhanakrishnan, “Optical configuration for measurement in speckle interferometry,” Opt. Lett. 22, 1958–1959 (1996).
[CrossRef]

Proc. Laser (1)

S. Leidenbach, “Die direkte Phasenmessung—ein neues Verfahren zur Berechnung von Phasenbildern aus nur einem Intensitäatsbild,” Proc. Laser 1, 68–72 (1991).

Pure Appl. Opt. (1)

G. Pedrini, Y. L. Zou, H. Tiziani, “Quantitative evaluation of digital shearing interferogram using the spatial carrier method,” Pure Appl. Opt. 5, 313–321 (1996).
[CrossRef]

Other (5)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), Chap. 7, pp 275–276.

P. K. Rastogi, “Techniques of displacement and deformation measurements in speckle metrology,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), Chap. 2, pp. 41–98.

K. Creath, “Phase-shifting holographic interferometry,” in Holographic Interferometry, P. K. Rastogi, ed. (Springer-Verlag, Berlin, Germany, 1994), Chap. 5, pp. 109–150.
[CrossRef]

M. Kujawinska, “Spatial phase measurement methods,” in Interferogram Analysis–Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, U.K., 1993), Chap. 5, pp. 141–193.

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

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Figures (6)

Fig. 1
Fig. 1

Duffy’s in-plane displacement-sensitive configuration.

Fig. 2
Fig. 2

Modified configuration for in-plane displacement measurement with SPS.

Fig. 3
Fig. 3

Modified Duffy two-aperture arrangement for shear ESPI with SPS.

Fig. 4
Fig. 4

Magnified portion of the speckle pattern incident on the CCD array.

Fig. 5
Fig. 5

Phase map (mod 2π) of the in-plane displacement introduced by rotation of a plate in its own plane.

Fig. 6
Fig. 6

Filtered shear interferogram (mod 2π) of a plate clamped at the edges and displaced at the center by a micrometer screw.

Equations (11)

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δ1 = K2- K1 · L,δ2 = K2- K1 · L,
δ = 2πλ2Lx sin α,
δ = K2- K1 · Lx+ Δx, y - K2- K1 ·Lx, y,
δ  K2 -K1 · L +K2 -K1 ·LxΔx- K2 -K1 · L= K2- K2 · L+ K2 -K1 ·LxΔx= 2πλ2Lx sin θ+ Lxx sin θ + Lzx1 + cos θΔx.
Lzx= mλ1 +cos θΔx,
δ1 - δ2 =2πλLxx sin θ Δx1- Δx2,
φ = 2πλv2+ x + d221/2- v2 +x - d221/2 2πλxdv1 - 18d2v2 -12x2v2,
φ  2πλdv x.
Ixn, y =Ioxn, y1+ γxn, ysincΦ2× cosϕxn,y + nβ + C, n = 1, 2, , N.
ϕn = tan-13In-1 - In+12In - In-1 -In+1mod π,
In+m = Io1 +γ sincΦ2cosϕn +n + mβ,n = 2, 3, , N - 1, m = -1, 0, + 1.

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