Abstract

The addition correlation of two speckle fields by simultaneous illumination at different wavelengths is used for object contouring in a Twyman–Green-type interferometer. Fringe visibility is enhanced when the stochastic speckle background intensity obtained from a reference plane modulation is subtracted. We calculate the contour phase map by using a phase-shift algorithm in the synthetic wavelength. A comparison with a sequential illumination, phase difference method based on a laser wavelength phase shift is given. The test setup does not need to be stable on an interferometric scale, and therefore a method is provided that lends itself to applications in noisy environments.

© 1998 Optical Society of America

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  1. T. Tsuruta, N. Shiotake, J. Tsujiuchi, K. Matsuda, “Holographic generation of contour map of diffusely reflecting surface by using immersion method,” Jpn. J. Appl. Phys. 6, 661–662 (1967).
    [CrossRef]
  2. B. P. Hildebrand, K. A. Haines, “Multiple-wavelength and multiple-source holography applied to contour generation,” J. Opt. Soc. Am. 57, 155–162 (1967).
    [CrossRef]
  3. H. Atcha, R. P. Tatam, C. H. Buckberry, J. C. Davies, J. D. C. Jones, “Surface contouring using TV holography,” in Fiber-Optic Metrology and Standards, O. D. Soares, ed., Proc. SPIE1504, 221–232 (1991).
    [CrossRef]
  4. X. Peng, Y. L. Zou, H. Y. Diao, H. J. Tiziani, “A simplified multiwavelength ESPI contouring technique based on a diode laser system,” Optik 91(2), 81–85 (1992).
  5. G. Gülker, O. Haack, K. D. Hinsch, C. Hölscher, J. Kuls, W. Platen, “Two-wavelength electronic speckle-pattern interferometry for the analysis of discontinuous deformation fields,” Appl. Opt. 31, 4519–4521 (1992).
    [CrossRef] [PubMed]
  6. Y. Zou, X. Peng, H. Tiziani, “Two-wavelength DSPI surface contouring through the temperature modulation of a laser diode,” Optik 94 (4), 155–158 (1993).
  7. T. Maack, G. Notni, W. Schreiber, “Three-coordinate measurement of an object surface with a combined two-wavelength and two-source phase-shifting speckle interferometer,” Opt. Commun. 115, 576–584 (1995).
    [CrossRef]
  8. R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1989).
  9. C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12, 2071–2074 (1973).
    [CrossRef] [PubMed]
  10. T. C. Chatters, B. F. Pouet, S. Krishnaswamy, “Additive–subtractive phase-modulated shearography with synchronized acoustic stressing,” Exp. Mech. 35, 159–165 (1995).
    [CrossRef]
  11. L. Wang, S. Krishnaswamy, “Additive–subtractive speckle interferometry: extraction of phase data in noisy environments,” Opt. Eng. 35, 794–801 (1996).
    [CrossRef]
  12. U. Vry, “Calculation of complex correlation coefficients of two speckle fields of different wavelengths and their application to two-wavelength-measurement techniques,” J. Opt. Soc. Am. A 5, 114–125 (1988).
    [CrossRef]
  13. A. F. Fercher, H. Z. Hu, U. Vry, “Rough surface interferometry with a two-wavelength heterodyne speckle interferometer,” Appl. Opt. 24, 2181–2188 (1985).
    [CrossRef] [PubMed]
  14. N. A. Ochoa, F. Mendoza Santoyo, A. J. Moore, C. Pérez López, “Contrast enhancement of electronic speckle pattern interferometry addition fringes,” Appl. Opt. 36, 2783–2787 (1997).
    [CrossRef] [PubMed]

1997 (1)

1996 (1)

L. Wang, S. Krishnaswamy, “Additive–subtractive speckle interferometry: extraction of phase data in noisy environments,” Opt. Eng. 35, 794–801 (1996).
[CrossRef]

1995 (2)

T. Maack, G. Notni, W. Schreiber, “Three-coordinate measurement of an object surface with a combined two-wavelength and two-source phase-shifting speckle interferometer,” Opt. Commun. 115, 576–584 (1995).
[CrossRef]

T. C. Chatters, B. F. Pouet, S. Krishnaswamy, “Additive–subtractive phase-modulated shearography with synchronized acoustic stressing,” Exp. Mech. 35, 159–165 (1995).
[CrossRef]

1993 (1)

Y. Zou, X. Peng, H. Tiziani, “Two-wavelength DSPI surface contouring through the temperature modulation of a laser diode,” Optik 94 (4), 155–158 (1993).

1992 (2)

X. Peng, Y. L. Zou, H. Y. Diao, H. J. Tiziani, “A simplified multiwavelength ESPI contouring technique based on a diode laser system,” Optik 91(2), 81–85 (1992).

G. Gülker, O. Haack, K. D. Hinsch, C. Hölscher, J. Kuls, W. Platen, “Two-wavelength electronic speckle-pattern interferometry for the analysis of discontinuous deformation fields,” Appl. Opt. 31, 4519–4521 (1992).
[CrossRef] [PubMed]

1988 (1)

1985 (1)

1973 (1)

1967 (2)

B. P. Hildebrand, K. A. Haines, “Multiple-wavelength and multiple-source holography applied to contour generation,” J. Opt. Soc. Am. 57, 155–162 (1967).
[CrossRef]

T. Tsuruta, N. Shiotake, J. Tsujiuchi, K. Matsuda, “Holographic generation of contour map of diffusely reflecting surface by using immersion method,” Jpn. J. Appl. Phys. 6, 661–662 (1967).
[CrossRef]

Atcha, H.

H. Atcha, R. P. Tatam, C. H. Buckberry, J. C. Davies, J. D. C. Jones, “Surface contouring using TV holography,” in Fiber-Optic Metrology and Standards, O. D. Soares, ed., Proc. SPIE1504, 221–232 (1991).
[CrossRef]

Buckberry, C. H.

H. Atcha, R. P. Tatam, C. H. Buckberry, J. C. Davies, J. D. C. Jones, “Surface contouring using TV holography,” in Fiber-Optic Metrology and Standards, O. D. Soares, ed., Proc. SPIE1504, 221–232 (1991).
[CrossRef]

Chatters, T. C.

T. C. Chatters, B. F. Pouet, S. Krishnaswamy, “Additive–subtractive phase-modulated shearography with synchronized acoustic stressing,” Exp. Mech. 35, 159–165 (1995).
[CrossRef]

Davies, J. C.

H. Atcha, R. P. Tatam, C. H. Buckberry, J. C. Davies, J. D. C. Jones, “Surface contouring using TV holography,” in Fiber-Optic Metrology and Standards, O. D. Soares, ed., Proc. SPIE1504, 221–232 (1991).
[CrossRef]

Diao, H. Y.

X. Peng, Y. L. Zou, H. Y. Diao, H. J. Tiziani, “A simplified multiwavelength ESPI contouring technique based on a diode laser system,” Optik 91(2), 81–85 (1992).

Fercher, A. F.

Gülker, G.

Haack, O.

Haines, K. A.

Hildebrand, B. P.

Hinsch, K. D.

Hölscher, C.

Hu, H. Z.

Jones, J. D. C.

H. Atcha, R. P. Tatam, C. H. Buckberry, J. C. Davies, J. D. C. Jones, “Surface contouring using TV holography,” in Fiber-Optic Metrology and Standards, O. D. Soares, ed., Proc. SPIE1504, 221–232 (1991).
[CrossRef]

Jones, R.

R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1989).

Krishnaswamy, S.

L. Wang, S. Krishnaswamy, “Additive–subtractive speckle interferometry: extraction of phase data in noisy environments,” Opt. Eng. 35, 794–801 (1996).
[CrossRef]

T. C. Chatters, B. F. Pouet, S. Krishnaswamy, “Additive–subtractive phase-modulated shearography with synchronized acoustic stressing,” Exp. Mech. 35, 159–165 (1995).
[CrossRef]

Kuls, J.

Maack, T.

T. Maack, G. Notni, W. Schreiber, “Three-coordinate measurement of an object surface with a combined two-wavelength and two-source phase-shifting speckle interferometer,” Opt. Commun. 115, 576–584 (1995).
[CrossRef]

Matsuda, K.

T. Tsuruta, N. Shiotake, J. Tsujiuchi, K. Matsuda, “Holographic generation of contour map of diffusely reflecting surface by using immersion method,” Jpn. J. Appl. Phys. 6, 661–662 (1967).
[CrossRef]

Mendoza Santoyo, F.

Moore, A. J.

Notni, G.

T. Maack, G. Notni, W. Schreiber, “Three-coordinate measurement of an object surface with a combined two-wavelength and two-source phase-shifting speckle interferometer,” Opt. Commun. 115, 576–584 (1995).
[CrossRef]

Ochoa, N. A.

Peng, X.

Y. Zou, X. Peng, H. Tiziani, “Two-wavelength DSPI surface contouring through the temperature modulation of a laser diode,” Optik 94 (4), 155–158 (1993).

X. Peng, Y. L. Zou, H. Y. Diao, H. J. Tiziani, “A simplified multiwavelength ESPI contouring technique based on a diode laser system,” Optik 91(2), 81–85 (1992).

Pérez López, C.

Platen, W.

Polhemus, C.

Pouet, B. F.

T. C. Chatters, B. F. Pouet, S. Krishnaswamy, “Additive–subtractive phase-modulated shearography with synchronized acoustic stressing,” Exp. Mech. 35, 159–165 (1995).
[CrossRef]

Schreiber, W.

T. Maack, G. Notni, W. Schreiber, “Three-coordinate measurement of an object surface with a combined two-wavelength and two-source phase-shifting speckle interferometer,” Opt. Commun. 115, 576–584 (1995).
[CrossRef]

Shiotake, N.

T. Tsuruta, N. Shiotake, J. Tsujiuchi, K. Matsuda, “Holographic generation of contour map of diffusely reflecting surface by using immersion method,” Jpn. J. Appl. Phys. 6, 661–662 (1967).
[CrossRef]

Tatam, R. P.

H. Atcha, R. P. Tatam, C. H. Buckberry, J. C. Davies, J. D. C. Jones, “Surface contouring using TV holography,” in Fiber-Optic Metrology and Standards, O. D. Soares, ed., Proc. SPIE1504, 221–232 (1991).
[CrossRef]

Tiziani, H.

Y. Zou, X. Peng, H. Tiziani, “Two-wavelength DSPI surface contouring through the temperature modulation of a laser diode,” Optik 94 (4), 155–158 (1993).

Tiziani, H. J.

X. Peng, Y. L. Zou, H. Y. Diao, H. J. Tiziani, “A simplified multiwavelength ESPI contouring technique based on a diode laser system,” Optik 91(2), 81–85 (1992).

Tsujiuchi, J.

T. Tsuruta, N. Shiotake, J. Tsujiuchi, K. Matsuda, “Holographic generation of contour map of diffusely reflecting surface by using immersion method,” Jpn. J. Appl. Phys. 6, 661–662 (1967).
[CrossRef]

Tsuruta, T.

T. Tsuruta, N. Shiotake, J. Tsujiuchi, K. Matsuda, “Holographic generation of contour map of diffusely reflecting surface by using immersion method,” Jpn. J. Appl. Phys. 6, 661–662 (1967).
[CrossRef]

Vry, U.

Wang, L.

L. Wang, S. Krishnaswamy, “Additive–subtractive speckle interferometry: extraction of phase data in noisy environments,” Opt. Eng. 35, 794–801 (1996).
[CrossRef]

Wykes, C.

R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1989).

Zou, Y.

Y. Zou, X. Peng, H. Tiziani, “Two-wavelength DSPI surface contouring through the temperature modulation of a laser diode,” Optik 94 (4), 155–158 (1993).

Zou, Y. L.

X. Peng, Y. L. Zou, H. Y. Diao, H. J. Tiziani, “A simplified multiwavelength ESPI contouring technique based on a diode laser system,” Optik 91(2), 81–85 (1992).

Appl. Opt. (4)

Exp. Mech. (1)

T. C. Chatters, B. F. Pouet, S. Krishnaswamy, “Additive–subtractive phase-modulated shearography with synchronized acoustic stressing,” Exp. Mech. 35, 159–165 (1995).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Jpn. J. Appl. Phys. (1)

T. Tsuruta, N. Shiotake, J. Tsujiuchi, K. Matsuda, “Holographic generation of contour map of diffusely reflecting surface by using immersion method,” Jpn. J. Appl. Phys. 6, 661–662 (1967).
[CrossRef]

Opt. Commun. (1)

T. Maack, G. Notni, W. Schreiber, “Three-coordinate measurement of an object surface with a combined two-wavelength and two-source phase-shifting speckle interferometer,” Opt. Commun. 115, 576–584 (1995).
[CrossRef]

Opt. Eng. (1)

L. Wang, S. Krishnaswamy, “Additive–subtractive speckle interferometry: extraction of phase data in noisy environments,” Opt. Eng. 35, 794–801 (1996).
[CrossRef]

Optik (2)

X. Peng, Y. L. Zou, H. Y. Diao, H. J. Tiziani, “A simplified multiwavelength ESPI contouring technique based on a diode laser system,” Optik 91(2), 81–85 (1992).

Y. Zou, X. Peng, H. Tiziani, “Two-wavelength DSPI surface contouring through the temperature modulation of a laser diode,” Optik 94 (4), 155–158 (1993).

Other (2)

H. Atcha, R. P. Tatam, C. H. Buckberry, J. C. Davies, J. D. C. Jones, “Surface contouring using TV holography,” in Fiber-Optic Metrology and Standards, O. D. Soares, ed., Proc. SPIE1504, 221–232 (1991).
[CrossRef]

R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1989).

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Figures (7)

Fig. 1
Fig. 1

2λ-ESPI setup based on a Twyman–Green-type interferometer: BS, beam-splitter plate.

Fig. 2
Fig. 2

Experimental setup: SDL, diode lasers; BSO, beam-shaping optics; NPBS, nonpolarizing beam-splitter cube; λ/2, half-wave plate; M, mirror; BS, beam-splitter plate; CCD, CCD camera; LS, loud speaker; TS, translation stage; FC, fiber coupling to the spectrometer.

Fig. 3
Fig. 3

Tuning spectra of two SDL-5422-H1 diode lasers at 115 mW output power, showing mode hops.

Fig. 4
Fig. 4

Shape measurement of a cone with a height of 10 mm and a synthetic wavelength of (a) Λ/2 = 1.35 mm and (b) Λ/2 = 2.00 mm.

Fig. 5
Fig. 5

Comparison of contour phase maps taken (a) by simultaneous illumination and phase shift in Λ and (b) by sequential illumination with a phase shift in λ.

Fig. 6
Fig. 6

Comparison of a cut through the unwrapped phase maps of Fig. 5. Top, unwrapped phase along the cut; bottom, residual deviation after subtraction of the triangular shape.

Fig. 7
Fig. 7

Influence of thermal creep on contour fringes. Additive–subtractive correlation fringes (a) without and (b) with reference plane modulation.

Equations (22)

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A u ,   P ,   λ = a P ,   λ exp ik | u - P | × lens d x d y   f x ,   y ,   u ,   P ,   λ
A obj u = Object   d P   A u ,   P = | A obj u | × exp i φ obj u exp ikD obj u ,
D obj u = | u - P obj u | + d obj - H P obj u .
D ref u = | u - P ref u | + d ref ,
A u = | A obj u | exp i φ obj exp ikD obj + | A ref u | exp i φ ref exp ikD ref ,
D obj - D ref = d obj - d ref - H P obj × 1 + 1 cos   α P obj 2 d obj - d ref - H P obj .
I = I 0 + I Γ × cos k D obj - D ref + ψ sp ,
Δ I = | I λ 1 - I λ 2 | = 2 I Γ sin 2 π λ D obj - D ref + ψ sp × sin 2 π 2 Λ D obj - D ref .
Λ - 1 = k 1 - k 2 2 π = λ 1 λ 2 λ 2 - λ 1 - 1 ,
λ - 1 = k 1 + k 2 2 × 2 π = 1 2 1 λ 1 + 1 λ 2 .
I A = 2 I 0 + 2 I Γ cos 2 π λ D obj - D ref + ψ sp × cos 2 π 2 Λ D obj - D ref .
Δ I = | I A - I B | = 4 I Γ cos 2 π λ D obj - D ref + ψ sp × cos 2 π 2 Λ D obj - D ref .
φ λ 1 = k 1 D obj - D ref + ψ sp , φ λ 2 = k 2 D obj - D ref + ψ sp ,
φ Λ = φ λ 1 - φ λ 2 = 2 π   D obj - D ref Λ .
Δ I = 4 I Γ cos 2 π λ D obj - D ref + ψ sp × cos 2 π 2 Λ D obj - D ref .
Δ I 2 = Ī Γ 2 cos 2 π 2 Λ D obj - D ref 2 = Ī Γ 2 2 1 + cos 2 π Λ D obj - D ref ,
u Λ Λ = 2 u λ λ 2 + u Δ λ Δ λ 2 1 / 2 2 u λ λ 2 + Λ   u Δ λ λ 2 2 1 / 2
S = 1 T 0 T d t   cos Φ + φ t
S = c × cos Φ + ψ ,
c = a 2 + b 2 1 / 2 1 ,       ψ = arctan b / a
a = 1 T 0 T d t   cos φ t ,     b = 1 T 0 T d t   sin φ t .
c = sinc φ 0 π ,     ψ = φ 0 ,

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