Abstract

A fringe-formation theory for a dual-beam illumination configuration that leads to a twofold increase in sensitivity for the measurement of in-plane displacement is described. Here we have taken into account all four beams simultaneously that are generated at the image plane owing to two-beam illumination and their cross-interference terms for fringe formation. We show that the sensitivity obtainable is the usual interferometric sensitivity when we take into account all four beams simultaneously and doubles only when the retroreflected beams are observed. A detailed theory and an experimental demonstration of the method are presented.

© 1998 Optical Society of America

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References

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  1. R. S. Sirohi, N. Krishna Mohan, “In-plane displacement measurement configuration with twofold sensitivity,” Appl. Opt. 32, 6387–6390 (1993).
    [CrossRef] [PubMed]
  2. J. A. Leendertz, “Interferometric displacement measurement on scattering surface utilizing speckle effect,” J. Phys. E 3, 214–218 (1970).
    [CrossRef]
  3. D. E. Duffy, “Moiré gauging of in-plane displacement using double aperture imaging,” Appl. Opt. 11, 1778–1781 (1972).
    [CrossRef] [PubMed]
  4. A. Sohmer, C. Joenathan, “Twofold increase in sensitivity with a dual-beam illumination arrangement for electronic speckle pattern interferometry,” Opt. Eng. 35, 1943–1948 (1996).
    [CrossRef]
  5. N. Krishna Mohan, T. Santhanakrishnan, P. Senthilkumaran, R. S. Sirohi, “Simultaneous implementation of Leendertz and Duffy’s methods for in-plane displacement measurement,” Opt. Commun. 124, 235–239 (1996).
    [CrossRef]
  6. R. S. Sirohi, N. Krishna Mohan, “Role of lens aperturing in speckle metrology,” J. Sci. Indust. Res. (India) 54, 67–74 (1995).
  7. P. K. Rastogi, “Techniques of displacement and deformation measurements in speckle metrology,”; R. S. Sirohi, ed. “Speckle methods in experimental mechanics,” in Speckle Metrology, (Marcel Dekker, New York, 1993).

1996 (2)

A. Sohmer, C. Joenathan, “Twofold increase in sensitivity with a dual-beam illumination arrangement for electronic speckle pattern interferometry,” Opt. Eng. 35, 1943–1948 (1996).
[CrossRef]

N. Krishna Mohan, T. Santhanakrishnan, P. Senthilkumaran, R. S. Sirohi, “Simultaneous implementation of Leendertz and Duffy’s methods for in-plane displacement measurement,” Opt. Commun. 124, 235–239 (1996).
[CrossRef]

1995 (1)

R. S. Sirohi, N. Krishna Mohan, “Role of lens aperturing in speckle metrology,” J. Sci. Indust. Res. (India) 54, 67–74 (1995).

1993 (1)

1972 (1)

1970 (1)

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

Duffy, D. E.

Joenathan, C.

A. Sohmer, C. Joenathan, “Twofold increase in sensitivity with a dual-beam illumination arrangement for electronic speckle pattern interferometry,” Opt. Eng. 35, 1943–1948 (1996).
[CrossRef]

Leendertz, J. A.

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

Mohan, N. Krishna

N. Krishna Mohan, T. Santhanakrishnan, P. Senthilkumaran, R. S. Sirohi, “Simultaneous implementation of Leendertz and Duffy’s methods for in-plane displacement measurement,” Opt. Commun. 124, 235–239 (1996).
[CrossRef]

R. S. Sirohi, N. Krishna Mohan, “Role of lens aperturing in speckle metrology,” J. Sci. Indust. Res. (India) 54, 67–74 (1995).

R. S. Sirohi, N. Krishna Mohan, “In-plane displacement measurement configuration with twofold sensitivity,” Appl. Opt. 32, 6387–6390 (1993).
[CrossRef] [PubMed]

Santhanakrishnan, T.

N. Krishna Mohan, T. Santhanakrishnan, P. Senthilkumaran, R. S. Sirohi, “Simultaneous implementation of Leendertz and Duffy’s methods for in-plane displacement measurement,” Opt. Commun. 124, 235–239 (1996).
[CrossRef]

Senthilkumaran, P.

N. Krishna Mohan, T. Santhanakrishnan, P. Senthilkumaran, R. S. Sirohi, “Simultaneous implementation of Leendertz and Duffy’s methods for in-plane displacement measurement,” Opt. Commun. 124, 235–239 (1996).
[CrossRef]

Sirohi, R. S.

N. Krishna Mohan, T. Santhanakrishnan, P. Senthilkumaran, R. S. Sirohi, “Simultaneous implementation of Leendertz and Duffy’s methods for in-plane displacement measurement,” Opt. Commun. 124, 235–239 (1996).
[CrossRef]

R. S. Sirohi, N. Krishna Mohan, “Role of lens aperturing in speckle metrology,” J. Sci. Indust. Res. (India) 54, 67–74 (1995).

R. S. Sirohi, N. Krishna Mohan, “In-plane displacement measurement configuration with twofold sensitivity,” Appl. Opt. 32, 6387–6390 (1993).
[CrossRef] [PubMed]

Sohmer, A.

A. Sohmer, C. Joenathan, “Twofold increase in sensitivity with a dual-beam illumination arrangement for electronic speckle pattern interferometry,” Opt. Eng. 35, 1943–1948 (1996).
[CrossRef]

Appl. Opt. (2)

J. Phys. E (1)

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

J. Sci. Indust. Res. (India) (1)

R. S. Sirohi, N. Krishna Mohan, “Role of lens aperturing in speckle metrology,” J. Sci. Indust. Res. (India) 54, 67–74 (1995).

Opt. Commun. (1)

N. Krishna Mohan, T. Santhanakrishnan, P. Senthilkumaran, R. S. Sirohi, “Simultaneous implementation of Leendertz and Duffy’s methods for in-plane displacement measurement,” Opt. Commun. 124, 235–239 (1996).
[CrossRef]

Opt. Eng. (1)

A. Sohmer, C. Joenathan, “Twofold increase in sensitivity with a dual-beam illumination arrangement for electronic speckle pattern interferometry,” Opt. Eng. 35, 1943–1948 (1996).
[CrossRef]

Other (1)

P. K. Rastogi, “Techniques of displacement and deformation measurements in speckle metrology,”; R. S. Sirohi, ed. “Speckle methods in experimental mechanics,” in Speckle Metrology, (Marcel Dekker, New York, 1993).

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Figures (4)

Fig. 1
Fig. 1

Experimental arrangement for in-plane displacement measurement with a twofold increase in sensitivity.

Fig. 2
Fig. 2

Normalized irradiance profile showing the usual sensitivity when the surface is coated with white paint.

Fig. 3
Fig. 3

Normalized irradiance profile showing the twofold increase in sensitivity when the surface is coated with retroreflective paint.

Fig. 4
Fig. 4

u Component of the in-plane displacement fringes for an in-plane rotation of ∼0.17 mrad. The top half of the fringes are with a twofold increase in sensitivity, and the bottom half are with the usual sensitivity.

Equations (7)

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

I first   order = C 8 + 2   n = 1 3 m = n + 1 4 cos Ω m - Ω n + 2   n = 1 3 m = n + 1 4 cos Ω m - Ω n + Θ m - Θ n + 2   n = 1 4 m = 1 4 cos Ω m - Ω n + Θ m ,
I first   order = C C + 2   cos   δ 21 + 2   cos   δ 23 + 2   cos   δ 43 + 2   cos   δ 41 ,
δ 21 = K 1 - K 2 · L , δ 43 = K 1 - K 2 · L , δ 23 = 0 , δ 41 = 2 K 1 - K 2 · L ,
I first   order = C C + 4   cos   δ 21 1 + cos   δ 21 .
δ 21 = 2 π λ   2 u   sin   θ = 2 m π   or   u = m λ 2   sin   θ .
I first   order     2 + 2   cos   δ 21 .
u = m λ 4   sin   θ .

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