Abstract

An electronic speckle pattern interferometer is introduced that can produce time-averaged interferograms of harmonically vibrating objects in instances where it is impractical to isolate the object from ambient vibrations. By subtracting two images of the oscillating object, rather than the more common technique of subtracting an image of the oscillating object from one of the static objects, interferograms are produced with excellent visibility even when the object is moving relative to the interferometer. This interferometer is analyzed theoretically and the theory is validated experimentally.

© 2008 Optical Society of America

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References

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  1. R. Jones and C. Wykes, Holographic and Speckle Interferometry, 2nd Ed. (Cambridge, 1989).
  2. P. K. Rastogi, Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).
  3. D. Findeis, D. R. Rowland, and J. Gryzagoridis, “Vibration isolation techniques suitable for portable electronic speckle pattern interferometry,” Proc. SPIE 4704, 159-167 (2002).
    [CrossRef]
  4. T. R. Moore and S. A. Zietlow, “Interferometric studies of a piano soundboard,” J. Acoust. Soc. Am. 119, 1783-1793(2006).
    [CrossRef] [PubMed]
  5. T. R. Moore, “A simple design for an electronic speckle pattern interferometer,” Am. J. Phys. 72, 1380-1384 (2004).
    [CrossRef]
  6. T. R. Moore, “Erratum: a simple design for an electronic speckle pattern interferometer,” Am. J. Phys. 73, 189(2005).
    [CrossRef]
  7. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, 1972).
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  9. K. A. Stetson and W. R. Brohinsky, “Fringe-shifting technique for numerical analysis of time-averaged holograms of vibrating objects,” J. Opt. Soc. Am. A 5, 1472-1476 (1988).
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  10. C. Joenathan, “Vibration fringes by phase stepping on an electronic speckle pattern interferometer: an analysis,” Appl. Opt. 30, 4658-4665 (1991).
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  11. C. Joenathan and B. M. Khorana, “Contrast of the vibration fringes in time-averaged electronic speckle-pattern interferometry: effect of speckle averaging,” Appl. Opt. 31, 1863-1870(1992).
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  12. P. J. de Groot, “Vibration in phase-shifting interferometry,” J. Opt. Soc. Am. A 12, 354-365 (1995).
    [CrossRef]
  13. A. J. Moore, J. D. C. Jones, and J. D. R. Valera, “Dynamic measurements,” in Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 225-288.

2006

T. R. Moore and S. A. Zietlow, “Interferometric studies of a piano soundboard,” J. Acoust. Soc. Am. 119, 1783-1793(2006).
[CrossRef] [PubMed]

2005

T. R. Moore, “Erratum: a simple design for an electronic speckle pattern interferometer,” Am. J. Phys. 73, 189(2005).
[CrossRef]

2004

T. R. Moore, “A simple design for an electronic speckle pattern interferometer,” Am. J. Phys. 72, 1380-1384 (2004).
[CrossRef]

2002

D. Findeis, D. R. Rowland, and J. Gryzagoridis, “Vibration isolation techniques suitable for portable electronic speckle pattern interferometry,” Proc. SPIE 4704, 159-167 (2002).
[CrossRef]

2001

P. K. Rastogi, Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).

A. J. Moore, J. D. C. Jones, and J. D. R. Valera, “Dynamic measurements,” in Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 225-288.

1995

1992

1991

1989

R. Jones and C. Wykes, Holographic and Speckle Interferometry, 2nd Ed. (Cambridge, 1989).

1988

1986

1972

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, 1972).

Abramowitz, M.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, 1972).

Brohinsky, W. R.

de Groot, P. J.

Findeis, D.

D. Findeis, D. R. Rowland, and J. Gryzagoridis, “Vibration isolation techniques suitable for portable electronic speckle pattern interferometry,” Proc. SPIE 4704, 159-167 (2002).
[CrossRef]

Gryzagoridis, J.

D. Findeis, D. R. Rowland, and J. Gryzagoridis, “Vibration isolation techniques suitable for portable electronic speckle pattern interferometry,” Proc. SPIE 4704, 159-167 (2002).
[CrossRef]

Joenathan, C.

Jones, J. D. C.

A. J. Moore, J. D. C. Jones, and J. D. R. Valera, “Dynamic measurements,” in Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 225-288.

Jones, R.

R. Jones and C. Wykes, Holographic and Speckle Interferometry, 2nd Ed. (Cambridge, 1989).

Khorana, B. M.

Moore, A. J.

A. J. Moore, J. D. C. Jones, and J. D. R. Valera, “Dynamic measurements,” in Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 225-288.

Moore, T. R.

T. R. Moore and S. A. Zietlow, “Interferometric studies of a piano soundboard,” J. Acoust. Soc. Am. 119, 1783-1793(2006).
[CrossRef] [PubMed]

T. R. Moore, “Erratum: a simple design for an electronic speckle pattern interferometer,” Am. J. Phys. 73, 189(2005).
[CrossRef]

T. R. Moore, “A simple design for an electronic speckle pattern interferometer,” Am. J. Phys. 72, 1380-1384 (2004).
[CrossRef]

Nakadate, S.

Rastogi, P. K.

P. K. Rastogi, Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).

Rowland, D. R.

D. Findeis, D. R. Rowland, and J. Gryzagoridis, “Vibration isolation techniques suitable for portable electronic speckle pattern interferometry,” Proc. SPIE 4704, 159-167 (2002).
[CrossRef]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, 1972).

Stetson, K. A.

Valera, J. D. R.

A. J. Moore, J. D. C. Jones, and J. D. R. Valera, “Dynamic measurements,” in Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 225-288.

Wykes, C.

R. Jones and C. Wykes, Holographic and Speckle Interferometry, 2nd Ed. (Cambridge, 1989).

Zietlow, S. A.

T. R. Moore and S. A. Zietlow, “Interferometric studies of a piano soundboard,” J. Acoust. Soc. Am. 119, 1783-1793(2006).
[CrossRef] [PubMed]

Am. J. Phys.

T. R. Moore, “A simple design for an electronic speckle pattern interferometer,” Am. J. Phys. 72, 1380-1384 (2004).
[CrossRef]

T. R. Moore, “Erratum: a simple design for an electronic speckle pattern interferometer,” Am. J. Phys. 73, 189(2005).
[CrossRef]

Appl. Opt.

J. Acoust. Soc. Am.

T. R. Moore and S. A. Zietlow, “Interferometric studies of a piano soundboard,” J. Acoust. Soc. Am. 119, 1783-1793(2006).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Proc. SPIE

D. Findeis, D. R. Rowland, and J. Gryzagoridis, “Vibration isolation techniques suitable for portable electronic speckle pattern interferometry,” Proc. SPIE 4704, 159-167 (2002).
[CrossRef]

Other

R. Jones and C. Wykes, Holographic and Speckle Interferometry, 2nd Ed. (Cambridge, 1989).

P. K. Rastogi, Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, 1972).

A. J. Moore, J. D. C. Jones, and J. D. R. Valera, “Dynamic measurements,” in Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 225-288.

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Figures (8)

Fig. 1
Fig. 1

Simple schematic of an electronic speckle pattern interferometer. The object beam with intensity I obj originates with light reflected from a harmonically vibrating object. The reference beam with intensity I ref is coherent with the object beam but has only static speckle.

Fig. 2
Fig. 2

Plot of the intensity of an electronic speckle pattern interferogram versus the displacement of the object for the interferometer described in Subsection 2A.

Fig. 3
Fig. 3

Plot of the intensity of an electronic speckle pattern interferogram versus the displacement of the object for the interferometer described in Subsection 2B for three different values of γ T .

Fig. 4
Fig. 4

Comparison of the exact and approximate solution to Eq. (18) for four different values of γ T .

Fig. 5
Fig. 5

Normalized plot of the maximum value of I m n versus γ T . Note that there will almost always be some steady-state interference observable as long as γ T is not an even-integer multiple of π.

Fig. 6
Fig. 6

Diagram of the experimental arrangement.

Fig. 7
Fig. 7

Comparison of the average intensity of a nodal region of an object ( Δ z = 0 ) to the predictions of Eq. (20).

Fig. 8
Fig. 8

Electronic speckle pattern interferograms of a flat circular plate oscillating in one of the normal modes obtained using the interferometers described in (a) Subsection 2A and (b) Subsection 2B. The numbers in the lower right corner of the interferograms indicate the frequency of oscillation ( 1045.69 ± 0.01 Hz ).

Equations (21)

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I = I obj + I ref + 2 I obj I ref cos ϕ ,
ϕ = ϕ 0 + ξ sin ω 0 t ,
ξ = 2 π Δ z λ ( cos θ i + cos θ r ) ,
I 1 = I obj + I ref + 2 I obj I ref cos [ ϕ 0 + ξ sin ω 0 t ] .
I 1 = I obj + I ref + 2 I obj I ref cos ( ϕ 0 + ξ sin ω 0 t ) ,
cos ( ϕ 0 + ξ sin ω 0 t ) = cos ( ϕ 0 ) T 0 T cos ( ξ sin ω 0 t ) d t sin ( ϕ 0 ) T 0 T sin ( ξ sin ω 0 t ) d t ,
I 1 = I obj + I ref + 2 I obj I ref cos ( ϕ 0 ) J 0 ( ξ ) ,
I 2 = I ref + I obj + 2 I ref I obj cos ϕ 0 ,
I 1 , 2 = 2 I obj I ref | cos ( ϕ 0 ) [ 1 J 0 ( ξ ) ] | .
I 1 , 2 = β | 1 J 0 ( ξ ) | .
ϕ = ϕ 0 + γ t + ξ sin ω 0 t ,
γ = 2 ( v · k ) ,
I n = I obj + I ref + 2 I obj I ref cos ( ϕ n + γ t + ξ sin ω 0 t ) .
cos ( ϕ 0 + γ t + ξ sin ω 0 t ) = cos ( ϕ n ) T 0 T cos ( γ t + ξ sin ω 0 t ) d t sin ( ϕ n ) T 0 T sin ( γ t + ξ sin ω 0 t ) d t ,
I m n = | I m I n | = β | cos ( ϕ m + γ t + ξ sin ω 0 t ) cos ( ϕ n + γ t + ξ sin ω 0 t | ,
ϕ n = ϕ m + γ T .
I m n = β | cos [ ϕ m + γ T τ + ξ sin ( ω 0 T τ ) ] cos [ ϕ m + γ T ( 1 + τ ) + ξ sin { ω 0 T ( 1 + τ ) } ] | ,
I m n = β 0 2 π | 1 T 0 1 cos [ ϕ m + γ T τ + ξ sin { ω 0 T ( τ ) } ] d τ 1 T 0 1 cos [ ϕ m + γ T ( 1 + τ ) + ξ sin { ω 0 T ( 1 + τ ) } ] d τ | d ϕ m .
I m n ( Δ z = 0 ) = β | cos [ ϕ m + γ T τ ] cos [ ϕ m + γ T ( 1 + τ ) ] | .
I m n = β γ T 0 2 π | 2 sin ( ϕ m + γ T ) sin ( ϕ m + 2 γ T ) sin ( ϕ m ) | d ϕ m .
ϕ n = ϕ m + γ T ,

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