Abstract

When the method of contouring an object surface by electronic speckle pattern interferometry is based on shifting the illumination beams, the shifted phase of the interference speckle pattern has a new relationship with the depth of the test surface. Therefore the contour interval as well as the fringe sensitivity of this method has new forms. The geometry of such a situation, which differs from that of either the method of two-wavelength contouring or the method of contouring by tilting the test object is presented. The requirements on the experimental conditions for this method are also presented. Experimental results are in agreement with these analyses.

© 1992 Optical Society of America

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References

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  1. J. N. Butters, R. Jones, C. Wykes, “Electronic speckle pattern interferometry,” in Speckle Metrology, R. K. Erf, ed. (Academic, New York, 1978), Chap. 6, pp. 111–158.
  2. R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, 1989), Chap. 4, p. 165; Chap. 5, p. 197.
    [CrossRef]
  3. C. Joenathan, B. Pfister, H. Tiziani, “Contouring by electronic speckle pattern interferometry employing dual beam illumination,” Appl. Opt. 29, 1905–1911 (1990).
    [CrossRef] [PubMed]
  4. B. D. Bergquist, P. Montgomery, “Contouring by electronic speckle pattern interferometry,” in Optics in Engineering Measurement, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.599, 189–195 (1985).
  5. S. Winther, G. Slettemoen, “An ESPI contouring technique in strain analysis,” in Symposium Optika ’84, G. Luprovics, A. Podmaniczby, eds., Proc. Soc. Photo-Opt. Instrum. Eng.473, 44–47 (1984).
  6. X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “Contouring by modified dual-beam ESPI based on tilting illumination beams,” Optik (Stuttgart) 90, 61–64 (1992).
  7. D. Kerr, R. R. Vera, F. M. Santoyo, “Surface contouring using electronic speckle pattern interferometry,” in Second International Conference on Photomechanics and Speckle Metrology, F.-P. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 668–679 (1991).
  8. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), Chap. 2, pp. 12–14.
  9. X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “A novel approach to determine decorrelation effect in a dual-beam electronic speckle pattern interferometer,” to be published in Optik (Stuttgart)90, 129–133 (1992).

1992

X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “Contouring by modified dual-beam ESPI based on tilting illumination beams,” Optik (Stuttgart) 90, 61–64 (1992).

1990

Bergquist, B. D.

B. D. Bergquist, P. Montgomery, “Contouring by electronic speckle pattern interferometry,” in Optics in Engineering Measurement, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.599, 189–195 (1985).

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), Chap. 6, pp. 111–158.

Diao, H. Y.

X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “Contouring by modified dual-beam ESPI based on tilting illumination beams,” Optik (Stuttgart) 90, 61–64 (1992).

X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “A novel approach to determine decorrelation effect in a dual-beam electronic speckle pattern interferometer,” to be published in Optik (Stuttgart)90, 129–133 (1992).

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), Chap. 2, pp. 12–14.

Joenathan, C.

Jones, R.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, 1989), Chap. 4, p. 165; Chap. 5, p. 197.
[CrossRef]

J. N. Butters, R. Jones, C. Wykes, “Electronic speckle pattern interferometry,” in Speckle Metrology, R. K. Erf, ed. (Academic, New York, 1978), Chap. 6, pp. 111–158.

Kerr, D.

D. Kerr, R. R. Vera, F. M. Santoyo, “Surface contouring using electronic speckle pattern interferometry,” in Second International Conference on Photomechanics and Speckle Metrology, F.-P. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 668–679 (1991).

Montgomery, P.

B. D. Bergquist, P. Montgomery, “Contouring by electronic speckle pattern interferometry,” in Optics in Engineering Measurement, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.599, 189–195 (1985).

Peng, X.

X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “Contouring by modified dual-beam ESPI based on tilting illumination beams,” Optik (Stuttgart) 90, 61–64 (1992).

X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “A novel approach to determine decorrelation effect in a dual-beam electronic speckle pattern interferometer,” to be published in Optik (Stuttgart)90, 129–133 (1992).

Pfister, B.

Santoyo, F. M.

D. Kerr, R. R. Vera, F. M. Santoyo, “Surface contouring using electronic speckle pattern interferometry,” in Second International Conference on Photomechanics and Speckle Metrology, F.-P. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 668–679 (1991).

Slettemoen, G.

S. Winther, G. Slettemoen, “An ESPI contouring technique in strain analysis,” in Symposium Optika ’84, G. Luprovics, A. Podmaniczby, eds., Proc. Soc. Photo-Opt. Instrum. Eng.473, 44–47 (1984).

Tiziani, H.

X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “Contouring by modified dual-beam ESPI based on tilting illumination beams,” Optik (Stuttgart) 90, 61–64 (1992).

C. Joenathan, B. Pfister, H. Tiziani, “Contouring by electronic speckle pattern interferometry employing dual beam illumination,” Appl. Opt. 29, 1905–1911 (1990).
[CrossRef] [PubMed]

X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “A novel approach to determine decorrelation effect in a dual-beam electronic speckle pattern interferometer,” to be published in Optik (Stuttgart)90, 129–133 (1992).

Vera, R. R.

D. Kerr, R. R. Vera, F. M. Santoyo, “Surface contouring using electronic speckle pattern interferometry,” in Second International Conference on Photomechanics and Speckle Metrology, F.-P. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 668–679 (1991).

Winther, S.

S. Winther, G. Slettemoen, “An ESPI contouring technique in strain analysis,” in Symposium Optika ’84, G. Luprovics, A. Podmaniczby, eds., Proc. Soc. Photo-Opt. Instrum. Eng.473, 44–47 (1984).

Wykes, C.

J. N. Butters, R. Jones, C. Wykes, “Electronic speckle pattern interferometry,” in Speckle Metrology, R. K. Erf, ed. (Academic, New York, 1978), Chap. 6, pp. 111–158.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, 1989), Chap. 4, p. 165; Chap. 5, p. 197.
[CrossRef]

Zou, Y. L.

X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “Contouring by modified dual-beam ESPI based on tilting illumination beams,” Optik (Stuttgart) 90, 61–64 (1992).

X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “A novel approach to determine decorrelation effect in a dual-beam electronic speckle pattern interferometer,” to be published in Optik (Stuttgart)90, 129–133 (1992).

Appl. Opt.

Optik (Stuttgart)

X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “Contouring by modified dual-beam ESPI based on tilting illumination beams,” Optik (Stuttgart) 90, 61–64 (1992).

Other

D. Kerr, R. R. Vera, F. M. Santoyo, “Surface contouring using electronic speckle pattern interferometry,” in Second International Conference on Photomechanics and Speckle Metrology, F.-P. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 668–679 (1991).

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), Chap. 2, pp. 12–14.

X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “A novel approach to determine decorrelation effect in a dual-beam electronic speckle pattern interferometer,” to be published in Optik (Stuttgart)90, 129–133 (1992).

J. N. Butters, R. Jones, C. Wykes, “Electronic speckle pattern interferometry,” in Speckle Metrology, R. K. Erf, ed. (Academic, New York, 1978), Chap. 6, pp. 111–158.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, 1989), Chap. 4, p. 165; Chap. 5, p. 197.
[CrossRef]

B. D. Bergquist, P. Montgomery, “Contouring by electronic speckle pattern interferometry,” in Optics in Engineering Measurement, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.599, 189–195 (1985).

S. Winther, G. Slettemoen, “An ESPI contouring technique in strain analysis,” in Symposium Optika ’84, G. Luprovics, A. Podmaniczby, eds., Proc. Soc. Photo-Opt. Instrum. Eng.473, 44–47 (1984).

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Figures (5)

Fig. 1
Fig. 1

Geometry of dual-beam-shifted ESPI contouring.

Fig. 2
Fig. 2

Vector geometry of the contouring.

Fig. 3
Fig. 3

Experimental arrangement for dual-beam-shifted ESPI contouring.

Fig. 4
Fig. 4

Contour fringes of a pyramid with θ = 30°, δθ = 1.3 mrad, and d = 0.49 mm.

Fig. 5
Fig. 5

Geometry for the analysis of the second order of δθ.

Equations (25)

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U ˜ 1 ( P ) = A s 1 exp i ( ϕ s 1 + ϕ m 1 ) , U ˜ 2 ( P ) = A s 2 exp i ( ϕ s 2 + ϕ m 2 ) ,
Γ 1 ( P ) = I 1 2 + I 2 2 + 2 ( I 1 I 2 ) 1 / 2 cos [ ( ϕ s 1 - ϕ s 2 ) + Ψ m ] ,
I 1 = U ˜ 1 U ˜ 1 * , I 2 = U ˜ 2 U ˜ 2 * , Ψ m = ϕ m 1 - ϕ m 2 .
Γ 2 ( P ) = I 1 2 + I 2 2 + 2 ( I 1 I 2 ) 1 / 2 cos [ ( ϕ s 1 - ϕ s 2 ) + Ψ m ] ,
Ψ m = ϕ m 1 - ϕ m 2 .
V s = ( V 1 - V 2 ) ( Γ 1 - Γ 2 ) = 4 ( I 1 I 2 ) 1 / 2 sin [ ( ϕ s 1 - ϕ s 2 ) + ( Ψ m + Ψ m ) / 2 ] × sin ( Δ Ψ m / 2 ) ,
B ( V 1 - V 2 ) 2 1 / 2 .
B ( I 1 I 2 sin 2 Δ Ψ m 2 ) 1 / 2 .
ϕ m 1 = 2 π λ ( r m + l 1 + r m · K 1 ) , ϕ m 2 = 2 π λ ( r m + l 2 + r m · K 2 ) ,
Ψ m = 2 π λ [ ( l 1 - l 2 ) + r m · ( K 1 - K 2 ) ] .
δ Ψ m = 2 π λ r m · ( δ K 1 - δ K 2 ) = 2 π λ r m δ K 1 - δ K 2 cos ( β - α ) = 2 π λ r m 2 sin ( θ 1 + θ 2 2 ) δ θ cos ( β - α ) = 2 π λ 2 sin ( θ 1 + θ 2 2 ) δ θ h ,
h = r m cos ( β - α ) ,
δ K 1 - δ K 2 = 2 sin ( θ 1 + θ 2 2 ) δ θ ,
α = θ 2 - θ 1 2
d = λ 2 sin θ δ θ .
δ Ψ m = 2 π λ r m · δ K 1 = 2 π λ r m δ K 1 cos ( 90 ° - θ 1 - β ) = 2 π λ r m δ θ sin ( θ 1 + β ) = 2 π λ δ θ h ,
h = r m sin ( θ 1 + β ) .
h = r m cos β .
d = λ δ θ .
α = 90 ° + θ 1 - θ 2 2 .
δ Ψ m = 2 π λ [ δ ( l 1 - l 2 ) + 2 h sin ( θ 1 + θ 2 2 ) δ θ ] 2 π λ [ l 2 - l 1 2 ( δ θ ) 2 + 2 h sin ( θ 1 + θ 2 2 ) δ θ ] .
l 1 = l 1 cos δ θ ;
Δ l 1 = l 1 - l 1 = - 2 l 1 sin 2 ( δ θ 2 ) - l 1 2 ( δ θ ) 2             ( δ θ 1 ) .
Δ l 2 = - l 2 2 ( δ θ ) 2 .
Δ ( l 1 - l 2 ) = l 2 - l 1 2 ( δ θ ) 2 .

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